{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting started with PyMC3\n", "\n", "Authors: John Salvatier, Thomas V. Wiecki, Christopher Fonnesbeck\n", "\n", "Note: This text is taken from the [PeerJ CS publication on PyMC3](https://peerj.com/articles/cs-55/).\n", "\n", "## Abstract\n", "\n", "Probabilistic Programming allows for automatic Bayesian inference on user-defined probabilistic models. Recent advances in Markov chain Monte Carlo (MCMC) sampling allow inference on increasingly complex models. This class of MCMC, known as Hamliltonian Monte Carlo, requires gradient information which is often not readily available. PyMC3 is a new open source Probabilistic Programming framework written in Python that uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on-the-fly to C for increased speed. Contrary to other Probabilistic Programming languages, PyMC3 allows model specification directly in Python code. The lack of a domain specific language allows for great flexibility and direct interaction with the model. This paper is a tutorial-style introduction to this software package.\n", "\n", "## Introduction\n", "\n", "Probabilistic programming (PP) allows flexible specification of Bayesian statistical models in code. PyMC3 is a new, open-source PP framework with an intuitive and readable, yet powerful, syntax that is close to the natural syntax statisticians use to describe models. It features next-generation Markov chain Monte Carlo (MCMC) sampling algorithms such as the No-U-Turn Sampler (NUTS; Hoffman, 2014), a self-tuning variant of Hamiltonian Monte Carlo (HMC; Duane, 1987). This class of samplers works well on high dimensional and complex posterior distributions and allows many complex models to be fit without specialized knowledge about fitting algorithms. HMC and NUTS take advantage of gradient information from the likelihood to achieve much faster convergence than traditional sampling methods, especially for larger models. NUTS also has several self-tuning strategies for adaptively setting the tunable parameters of Hamiltonian Monte Carlo, which means you usually don't need to have specialized knowledge about how the algorithms work. PyMC3, Stan (Stan Development Team, 2014), and the LaplacesDemon package for R are currently the only PP packages to offer HMC.\n", "\n", "Probabilistic programming in Python confers a number of advantages including multi-platform compatibility, an expressive yet clean and readable syntax, easy integration with other scientific libraries, and extensibility via C, C++, Fortran or Cython. These features make it relatively straightforward to write and use custom statistical distributions, samplers and transformation functions, as required by Bayesian analysis.\n", "\n", "While most of PyMC3's user-facing features are written in pure Python, it leverages Theano (Bergstra et al., 2010) to transparently transcode models to C and compile them to machine code, thereby boosting performance. Theano is a library that allows expressions to be defined using generalized vector data structures called *tensors*, which are tightly integrated with the popular NumPy `ndarray` data structure, and similarly allow for broadcasting and advanced indexing, just as NumPy arrays do. Theano also automatically optimizes the likelihood's computational graph for speed and provides simple GPU integration.\n", "\n", "Here, we present a primer on the use of PyMC3 for solving general Bayesian statistical inference and prediction problems. We will first see the basics of how to use PyMC3, motivated by a simple example: installation, data creation, model definition, model fitting and posterior analysis. Then we will cover two case studies and use them to show how to define and fit more sophisticated models. Finally we will show how to extend PyMC3 and discuss other useful features: the Generalized Linear Models subpackage, custom distributions, custom transformations and alternative storage backends." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Installation\n", "\n", "Running PyMC3 requires a working Python interpreter, either version 2.7 (or more recent) or 3.4 (or more recent); we recommend that new users install version 3.4. A complete Python installation for Mac OSX, Linux and Windows can most easily be obtained by downloading and installing the free [`Anaconda Python Distribution`](https://store.continuum.io/cshop/anaconda/) by ContinuumIO. \n", "\n", "`PyMC3` can be installed using `pip` (https://pip.pypa.io/en/latest/installing.html):\n", "\n", "```\n", "pip install git+https://github.com/pymc-devs/pymc3\n", "```\n", "\n", "PyMC3 depends on several third-party Python packages which will be automatically installed when installing via pip. The four required dependencies are: `Theano`, `NumPy`, `SciPy`, and `Matplotlib`. \n", "\n", "To take full advantage of PyMC3, the optional dependencies `Pandas` and `Patsy` should also be installed. These are *not* automatically installed, but can be installed by:\n", "\n", "```\n", "pip install patsy pandas\n", "```\n", "\n", "The source code for PyMC3 is hosted on GitHub at https://github.com/pymc-devs/pymc3 and is distributed under the liberal [Apache License 2.0](https://github.com/pymc-devs/pymc3/blob/master/LICENSE). On the GitHub site, users may also report bugs and other issues, as well as contribute code to the project, which we actively encourage." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Motivating Example: Linear Regression\n", "\n", "To introduce model definition, fitting and posterior analysis, we first consider a simple Bayesian linear regression model with normal priors for the parameters. We are interested in predicting outcomes $Y$ as normally-distributed observations with an expected value $\\mu$ that is a linear function of two predictor variables, $X_1$ and $X_2$.\n", "\n", "$$\\begin{aligned} \n", "Y &\\sim \\mathcal{N}(\\mu, \\sigma^2) \\\\\n", "\\mu &= \\alpha + \\beta_1 X_1 + \\beta_2 X_2\n", "\\end{aligned}$$\n", "\n", "where $\\alpha$ is the intercept, and $\\beta_i$ is the coefficient for covariate $X_i$, while $\\sigma$ represents the observation error. Since we are constructing a Bayesian model, the unknown variables in the model must be assigned a prior distribution. We choose zero-mean normal priors with variance of 100 for both regression coefficients, which corresponds to *weak* information regarding the true parameter values. We choose a half-normal distribution (normal distribution bounded at zero) as the prior for $\\sigma$.\n", "\n", "$$\\begin{aligned} \n", "\\alpha &\\sim \\mathcal{N}(0, 100) \\\\\n", "\\beta_i &\\sim \\mathcal{N}(0, 100) \\\\\n", "\\sigma &\\sim \\lvert\\mathcal{N}(0, 1){\\rvert}\n", "\\end{aligned}$$\n", "\n", "### Generating data\n", "\n", "We can simulate some artificial data from this model using only NumPy's `random` module, and then use PyMC3 to try to recover the corresponding parameters. We are intentionally generating the data to closely correspond the PyMC3 model structure." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Initialize random number generator\n", "np.random.seed(123)\n", "\n", "# True parameter values\n", "alpha, sigma = 1, 1\n", "beta = [1, 2.5]\n", "\n", "# Size of dataset\n", "size = 100\n", "\n", "# Predictor variable\n", "X1 = np.random.randn(size)\n", "X2 = np.random.randn(size) * 0.2\n", "\n", "# Simulate outcome variable\n", "Y = alpha + beta[0]*X1 + beta[1]*X2 + np.random.randn(size)*sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is what the simulated data look like. We use the `pylab` module from the plotting library matplotlib. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline \n", "\n", "fig, axes = plt.subplots(1, 2, sharex=True, figsize=(10,4))\n", "axes[0].scatter(X1, Y)\n", "axes[1].scatter(X2, Y)\n", "axes[0].set_ylabel('Y'); axes[0].set_xlabel('X1'); axes[1].set_xlabel('X2');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Specification\n", "\n", "Specifying this model in PyMC3 is straightforward because the syntax is as close to the statistical notation. For the most part, each line of Python code corresponds to a line in the model notation above. \n", "\n", "First, we import PyMC. We use the convention of importing it as `pm`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import pymc3 as pm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we build our model, which we will present in full first, then explain each part line-by-line." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": true }, "outputs": [], "source": [ "basic_model = pm.Model()\n", "\n", "with basic_model:\n", " \n", " # Priors for unknown model parameters\n", " alpha = pm.Normal('alpha', mu=0, sd=10)\n", " beta = pm.Normal('beta', mu=0, sd=10, shape=2)\n", " sigma = pm.HalfNormal('sigma', sd=1)\n", " \n", " # Expected value of outcome\n", " mu = alpha + beta[0]*X1 + beta[1]*X2\n", " \n", " # Likelihood (sampling distribution) of observations\n", " Y_obs = pm.Normal('Y_obs', mu=mu, sd=sigma, observed=Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first line,\n", "\n", "```python\n", "basic_model = Model()\n", "```\n", "\n", "creates a new `Model` object which is a container for the model random variables.\n", "\n", "Following instantiation of the model, the subsequent specification of the model components is performed inside a `with` statement:\n", "\n", "```python\n", "with basic_model:\n", "```\n", "This creates a *context manager*, with our `basic_model` as the context, that includes all statements until the indented block ends. This means all PyMC3 objects introduced in the indented code block below the `with` statement are added to the model behind the scenes. Absent this context manager idiom, we would be forced to manually associate each of the variables with `basic_model` right after we create them. If you try to create a new random variable without a `with model:` statement, it will raise an error since there is no obvious model for the variable to be added to.\n", "\n", "The first three statements in the context manager:\n", "\n", "```python\n", "alpha = Normal('alpha', mu=0, sd=10)\n", "beta = Normal('beta', mu=0, sd=10, shape=2)\n", "sigma = HalfNormal('sigma', sd=1)\n", "```\n", "create a **stochastic** random variables with a Normal prior distributions for the regression coefficients with a mean of 0 and standard deviation of 10 for the regression coefficients, and a half-normal distribution for the standard deviation of the observations, $\\sigma$. These are stochastic because their values are partly determined by its parents in the dependency graph of random variables, which for priors are simple constants, and partly random (or stochastic). \n", "\n", "We call the `Normal` constructor to create a random variable to use as a normal prior. The first argument is always the *name* of the random variable, which should almost always match the name of the Python variable being assigned to, since it sometimes used to retrieve the variable from the model for summarizing output. The remaining required arguments for a stochastic object are the parameters, in this case `mu`, the mean, and `sd`, the standard deviation, which we assign hyperparameter values for the model. In general, a distribution's parameters are values that determine the location, shape or scale of the random variable, depending on the parameterization of the distribution. Most commonly used distributions, such as `Beta`, `Exponential`, `Categorical`, `Gamma`, `Binomial` and many others, are available in PyMC3.\n", "\n", "The `beta` variable has an additional `shape` argument to denote it as a vector-valued parameter of size 2. The `shape` argument is available for all distributions and specifies the length or shape of the random variable, but is optional for scalar variables, since it defaults to a value of one. It can be an integer, to specify an array, or a tuple, to specify a multidimensional array (*e.g.* `shape=(5,7)` makes random variable that takes on 5 by 7 matrix values). \n", "\n", "Detailed notes about distributions, sampling methods and other PyMC3 functions are available via the `help` function." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on class Normal in module pymc3.distributions.continuous:\n", "\n", "class Normal(pymc3.distributions.distribution.Continuous)\n", " | Univariate normal log-likelihood.\n", " | \n", " | .. math::\n", " | \n", " | f(x \\mid \\mu, \\tau) =\n", " | \\sqrt{\\frac{\\tau}{2\\pi}}\n", " | \\exp\\left\\{ -\\frac{\\tau}{2} (x-\\mu)^2 \\right\\}\n", " | \n", " | ======== ==========================================\n", " | Support :math:`x \\in \\mathbb{R}`\n", " | Mean :math:`\\mu`\n", " | Variance :math:`\\dfrac{1}{\\tau}` or :math:`\\sigma^2`\n", " | ======== ==========================================\n", " | \n", " | Normal distribution can be parameterized either in terms of precision\n", " | or standard deviation. The link between the two parametrizations is\n", " | given by\n", " | \n", " | .. math::\n", " | \n", " | \\tau = \\dfrac{1}{\\sigma^2}\n", " | \n", " | Parameters\n", " | ----------\n", " | mu : float\n", " | Mean.\n", " | sd : float\n", " | Standard deviation (sd > 0).\n", " | tau : float\n", " | Precision (tau > 0).\n", " | \n", " | Method resolution order:\n", " | Normal\n", " | pymc3.distributions.distribution.Continuous\n", " | pymc3.distributions.distribution.Distribution\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, mu=0, sd=None, tau=None, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | logp(self, value)\n", " | \n", " | random(self, point=None, size=None, repeat=None)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from pymc3.distributions.distribution.Distribution:\n", " | \n", " | __getnewargs__(self)\n", " | \n", " | default(self)\n", " | \n", " | get_test_val(self, val, defaults)\n", " | \n", " | getattr_value(self, val)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from pymc3.distributions.distribution.Distribution:\n", " | \n", " | dist(*args, **kwargs) from builtins.type\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from pymc3.distributions.distribution.Distribution:\n", " | \n", " | __new__(cls, name, *args, **kwargs)\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from pymc3.distributions.distribution.Distribution:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", "\n" ] } ], "source": [ "help(pm.Normal) #try help(Model), help(Uniform) or help(basic_model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having defined the priors, the next statement creates the expected value `mu` of the outcomes, specifying the linear relationship:\n", "\n", "```python\n", "mu = alpha + beta[0]*X1 + beta[1]*X2\n", "```\n", "This creates a **deterministic** random variable, which implies that its value is *completely* determined by its parents' values. That is, there is no uncertainty beyond that which is inherent in the parents' values. Here, `mu` is just the sum of the intercept `alpha` and the two products of the coefficients in `beta` and the predictor variables, whatever their values may be. \n", "\n", "PyMC3 random variables and data can be arbitrarily added, subtracted, divided, multiplied together and indexed-into to create new random variables. This allows for great model expressivity. Many common mathematical functions like `sum`, `sin`, `exp` and linear algebra functions like `dot` (for inner product) and `inv` (for inverse) are also provided. \n", "\n", "The final line of the model, defines `Y_obs`, the sampling distribution of the outcomes in the dataset.\n", "\n", "```python\n", "Y_obs = Normal('Y_obs', mu=mu, sd=sigma, observed=Y)\n", "```\n", "\n", "This is a special case of a stochastic variable that we call an **observed stochastic**, and represents the data likelihood of the model. It is identical to a standard stochastic, except that its `observed` argument, which passes the data to the variable, indicates that the values for this variable were observed, and should not be changed by any fitting algorithm applied to the model. The data can be passed in the form of either a `numpy.ndarray` or `pandas.DataFrame` object.\n", "\n", "Notice that, unlike for the priors of the model, the parameters for the normal distribution of `Y_obs` are not fixed values, but rather are the deterministic object `mu` and the stochastic `sigma`. This creates parent-child relationships between the likelihood and these two variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model fitting\n", "\n", "Having completely specified our model, the next step is to obtain posterior estimates for the unknown variables in the model. Ideally, we could calculate the posterior estimates analytically, but for most non-trivial models, this is not feasible. We will consider two approaches, whose appropriateness depends on the structure of the model and the goals of the analysis: finding the *maximum a posteriori* (MAP) point using optimization methods, and computing summaries based on samples drawn from the posterior distribution using Markov Chain Monte Carlo (MCMC) sampling methods.\n", "\n", "#### Maximum a posteriori methods\n", "\n", "The **maximum a posteriori (MAP)** estimate for a model, is the mode of the posterior distribution and is generally found using numerical optimization methods. This is often fast and easy to do, but only gives a point estimate for the parameters and can be biased if the mode isn't representative of the distribution. PyMC3 provides this functionality with the `find_MAP` function.\n", "\n", "Below we find the MAP for our original model. The MAP is returned as a parameter **point**, which is always represented by a Python dictionary of variable names to NumPy arrays of parameter values. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 149.017982\n", " Iterations: 16\n", " Function evaluations: 21\n", " Gradient evaluations: 21\n" ] }, { "data": { "text/plain": [ "{'alpha': array(0.9065985497559482),\n", " 'beta': array([ 0.94848602, 2.60705514]),\n", " 'sigma_log__': array(-0.03278147017403069)}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "map_estimate = pm.find_MAP(model=basic_model)\n", " \n", "map_estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, `find_MAP` uses the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm to find the maximum of the log-posterior but also allows selection of other optimization algorithms from the `scipy.optimize` module. For example, below we use Powell's method to find the MAP." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 149.019762\n", " Iterations: 4\n", " Function evaluations: 176\n" ] }, { "data": { "text/plain": [ "{'alpha': array(0.9090521898977764),\n", " 'beta': array([ 0.95140146, 2.61437458]),\n", " 'sigma_log__': array(-0.030009775203258385)}" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy import optimize\n", "\n", "map_estimate = pm.find_MAP(model=basic_model, fmin=optimize.fmin_powell)\n", " \n", "map_estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is important to note that the MAP estimate is not always reasonable, especially if the mode is at an extreme. This can be a subtle issue; with high dimensional posteriors, one can have areas of extremely high density but low total probability because the volume is very small. This will often occur in hierarchical models with the variance parameter for the random effect. If the individual group means are all the same, the posterior will have near infinite density if the scale parameter for the group means is almost zero, even though the probability of such a small scale parameter will be small since the group means must be extremely close together. \n", "\n", "Most techniques for finding the MAP estimate also only find a *local* optimum (which is often good enough), but can fail badly for multimodal posteriors if the different modes are meaningfully different." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sampling methods\n", "\n", "Though finding the MAP is a fast and easy way of obtaining estimates of the unknown model parameters, it is limited because there is no associated estimate of uncertainty produced with the MAP estimates. Instead, a simulation-based approach such as Markov chain Monte Carlo (MCMC) can be used to obtain a Markov chain of values that, given the satisfaction of certain conditions, are indistinguishable from samples from the posterior distribution. \n", "\n", "To conduct MCMC sampling to generate posterior samples in PyMC3, we specify a **step method** object that corresponds to a particular MCMC algorithm, such as Metropolis, Slice sampling, or the No-U-Turn Sampler (NUTS). PyMC3's `step_methods` submodule contains the following samplers: `NUTS`, `Metropolis`, `Slice`, `HamiltonianMC`, and `BinaryMetropolis`. These step methods can be assigned manually, or assigned automatically by PyMC3. Auto-assignment is based on the attributes of each variable in the model. In general:\n", "\n", "* Binary variables will be assigned to `BinaryMetropolis`\n", "* Discrete variables will be assigned to `Metropolis`\n", "* Continuous variables will be assigned to `NUTS`\n", "\n", "Auto-assignment can be overriden for any subset of variables by specifying them manually prior to sampling." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Gradient-based sampling methods\n", "\n", "PyMC3 has the standard sampling algorithms like adaptive Metropolis-Hastings and adaptive slice sampling, but PyMC3's most capable step method is the No-U-Turn Sampler. NUTS is especially useful on models that have many continuous parameters, a situation where other MCMC algorithms work very slowly. It takes advantage of information about where regions of higher probability are, based on the gradient of the log posterior-density. This helps it achieve dramatically faster convergence on large problems than traditional sampling methods achieve. PyMC3 relies on Theano to analytically compute model gradients via automatic differentiation of the posterior density. NUTS also has several self-tuning strategies for adaptively setting the tunable parameters of Hamiltonian Monte Carlo. For random variables that are undifferentiable (namely, discrete variables) NUTS cannot be used, but it may still be used on the differentiable variables in a model that contains undifferentiable variables. \n", "\n", "NUTS requires a scaling matrix parameter, which is analogous to the variance parameter for the jump proposal distribution in Metropolis-Hastings, although NUTS uses it somewhat differently. The matrix gives the rough shape of the distribution so that NUTS does not make jumps that are too large in some directions and too small in other directions. It is important to set this scaling parameter to a reasonable value to facilitate efficient sampling. This is especially true for models that have many unobserved stochastic random variables or models with highly non-normal posterior distributions. Poor scaling parameters will slow down NUTS significantly, sometimes almost stopping it completely. A reasonable starting point for sampling can also be important for efficient sampling, but not as often.\n", "\n", "Fortunately `PyMC3` automatically initializes NUTS using another inference algorithm called ADVI (auto-diff variational inference). Moreover, `PyMC3` will automatically assign an appropriate sampler if we don't supply it via the `step` keyword argument (see below for an example of how to explicitly assign step methods)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using ADVI...\n", "Average Loss = 156.08: 5%|▌ | 10932/200000 [00:01<00:31, 6082.63it/s]\n", "Convergence archived at 11100\n", "Interrupted at 11,100 [5%]: Average Loss = 237.04\n", "100%|██████████| 1000/1000 [00:01<00:00, 710.94it/s]\n" ] } ], "source": [ "from scipy import optimize\n", "\n", "with basic_model:\n", " # draw 500 posterior samples\n", " trace = pm.sample() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `sample` function runs the step method(s) assigned (or passed) to it for the given number of iterations and returns a `Trace` object containing the samples collected, in the order they were collected. The `trace` object can be queried in a similar way to a `dict` containing a map from variable names to `numpy.array`s. The first dimension of the array is the sampling index and the later dimensions match the shape of the variable. We can see the last 5 values for the `alpha` variable as follows:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.80339734, 0.94747946, 0.93063514, 0.89569059, 0.89569059])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trace['alpha'][-5:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we wanted to use the slice sampling algorithm to `sigma` instead of NUTS (which was assigned automatically), we could have specified this as the `step` argument for `sample`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " 1%| | 38/5500 [00:00<00:14, 376.26it/s]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 149.019762\n", " Iterations: 4\n", " Function evaluations: 176\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 5500/5500 [00:10<00:00, 498.93it/s]\n" ] } ], "source": [ "with basic_model:\n", " \n", " # obtain starting values via MAP\n", " start = pm.find_MAP(fmin=optimize.fmin_powell)\n", " \n", " # instantiate sampler\n", " step = pm.Slice() \n", " \n", " # draw 5000 posterior samples\n", " trace = pm.sample(5000, step=step, start=start) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Posterior analysis\n", "`PyMC3` provides plotting and summarization functions for inspecting the sampling output. A simple posterior plot can be created using `traceplot`." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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ng9v+uI72rm4e/2I5BbpmU8TMKyvg3y+dypvbK/nd8j12h6NUHyKyUUS+KyIT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qmlAC6V3Lutv62efX0thMKaOq87JvCsz+WJw5tZWQsxtxKkrd6Lx61iDZfft7OLzqZaguFIrJff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\nnPf/E/xuG7RMu1IqtsYXZrF2f6PdYfRz0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_ = pm.traceplot(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The left column consists of a smoothed histogram (using kernel density estimation) of the marginal posteriors of each stochastic random variable while the right column contains the samples of the Markov chain plotted in sequential order. The `beta` variable, being vector-valued, produces two histograms and two sample traces, corresponding to both predictor coefficients.\n", "\n", "In addition, the `summary` function provides a text-based output of common posterior statistics:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "alpha:\n", "\n", " Mean SD MC Error 95% HPD interval\n", " -------------------------------------------------------------------\n", " \n", " 0.905 0.099 0.001 [0.715, 1.103]\n", "\n", " Posterior quantiles:\n", " 2.5 25 50 75 97.5\n", " |--------------|==============|==============|--------------|\n", " \n", " 0.711 0.838 0.904 0.971 1.101\n", "\n", "\n", "beta:\n", "\n", " Mean SD MC Error 95% HPD interval\n", " -------------------------------------------------------------------\n", " \n", " 0.949 0.086 0.002 [0.786, 1.118]\n", " 2.599 0.507 0.014 [1.590, 3.591]\n", "\n", " Posterior quantiles:\n", " 2.5 25 50 75 97.5\n", " |--------------|==============|==============|--------------|\n", " \n", " 0.784 0.889 0.948 1.007 1.117\n", " 1.593 2.256 2.605 2.940 3.599\n", "\n", "\n", "sigma:\n", "\n", " Mean SD MC Error 95% HPD interval\n", " -------------------------------------------------------------------\n", " \n", " 0.991 0.073 0.001 [0.852, 1.134]\n", "\n", " Posterior quantiles:\n", " 2.5 25 50 75 97.5\n", " |--------------|==============|==============|--------------|\n", " \n", " 0.859 0.941 0.986 1.037 1.147\n", "\n" ] } ], "source": [ "pm.summary(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Case study 1: Stochastic volatility\n", "\n", "We present a case study of stochastic volatility, time varying stock market volatility, to illustrate PyMC3's use in addressing a more realistic problem. The distribution of market returns is highly non-normal, which makes sampling the volatilities significantly more difficult. This example has 400+ parameters so using common sampling algorithms like Metropolis-Hastings would get bogged down, generating highly autocorrelated samples. Instead, we use NUTS, which is dramatically more efficient.\n", "\n", "### The Model\n", "\n", "Asset prices have time-varying volatility (variance of day over day `returns`). In some periods, returns are highly variable, while in others they are very stable. Stochastic volatility models address this with a latent volatility variable, which changes over time. The following model is similar to the one described in the NUTS paper (Hoffman 2014, p. 21).\n", "\n", "$$\n", "\\begin{aligned} \n", " \\sigma &\\sim exp(50) \\\\\n", " \\nu &\\sim exp(.1) \\\\\n", " s_i &\\sim \\mathcal{N}(s_{i-1}, \\sigma^{-2}) \\\\\n", " log(y_i) &\\sim t(\\nu, 0, exp(-2 s_i))\n", "\\end{aligned}\n", "$$\n", "\n", "Here, $y$ is the daily return series which is modeled with a Student-t distribution with an unknown degrees of freedom parameter, and a scale parameter determined by a latent process $s$. The individual $s_i$ are the individual daily log volatilities in the latent log volatility process. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Data\n", "\n", "Our data consist of daily returns of the S&P 500 during the 2008 financial crisis. Here, we use `pandas-datareader` to obtain the price data from Yahoo!-Finance; it can be installed with `pip install pandas-datareader`." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "from pandas_datareader import data" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "400" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "returns = data.get_data_yahoo('SPY', start='2008-5-1', end='2009-12-1')['Close'].pct_change()\n", "\n", "len(returns)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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kELMzx9RDxQIIKeUPF2JDmMXnzn1DaEsnsHVjV93PRSfevGGp0M9SRBdzUapZ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\nSzvln1k1F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3VMHm3OAmydhf/ZnW73C0ugpq0ldU5KkqxaLQohvgt5Pvo1pBo5qI5t6zSe\nBdp5O8m87B8JIW5b6FqWvTMHWcb/n0KIf4FMqAURuUJ1TldvzvshW3J8AcB1RPRLSGfu5y1a83xh\nW31bb4HMZehTx78eUtL/FKS60daqY4j52vpJdJ6tuwD8uxDiEwDeBJm7+jxSlcbqM3wrgJ9C5gnu\nJaKfAjgOmbPSCSwHGzVs6/K09RbI6vqV6vdXQRYH/AOA04QQ97dk1fXTNnZ2ZEL3QiDZu2cNgB8K\nIX4IGcO+hYgmIa+E7gDwd0T0UXXcJgA3K/nzcSK6CzLF7GhrLIgP21rV1q0A3qFCF4BMkt8rZA+y\ntmaZ23oMwBAR9QkhDhDRIcjw4gVENA35GX6HEGKfuv8LAThCiLYtSloONmrYVrZV2boVwNu1rZC5\ngk9SymTb0s52Ugco8Q2B5MDpt0Emen8SwCsA/BGA/wRwCWQZ+IeEEF8moj+DzFv4uPacVciqI0r7\n2da6bHVEBxQ2AGwrgD+ArBR/BYAByPL+IuQJ9Q4hc2z0/S3R5pMPloONGraVbUW0rR2x13SEnUKI\nZfNPvQkXqf8/G8C3AWxXv38OwDb1/7Mhpzpk1e92q9fOtrKty9zW50AW5+yAPHE+H8Ar1N9eDDlu\nTt/PavXa2Ua2lW1dWra2u51LOmeOiK4noguJSOcKHQLQrxSKz0MmIl5HRKMAfgu5OQKyV9MMZINV\niM64cmBb2dalbOvnIMPDzxdCHBdCfFoI8RF13HbIHE8A7T2LdDnYqGFb2dZOtrXT7FxyzhxJVhLR\ntwG8FMCLIPOHspClwbsB6LFMfws5zaEImWD6RCL6EeTUgz8Sbd4vjm1lW7G8bP0AgGtJNRcloktJ\n5nWeATk/uC1ZDjZq2Fa2FR1sa0fb2WrpssEyqK1+bgPwL+r/DmSzxVshq/m+BtnRP6P+/lkAv6/+\nnwWwu9V2sK1sK9ta0dZPQ/YUA4DNAJ7ZajuWu41sK9u6FGztdDuXRDUryYaL74QcifFVyE7oRUD2\n7yGi10DOLHw/ZOuJ6yBLhT8NOY7qp+rYSciZd20L28q2YnnbWgDwI3XsbyFDy23HcrBRw7ayrehg\nW5eKnR0fZiWiCyE3sn7Ist8/hRxXdDER7QW8mPUtAN4nhPgYZDjqeiL6X0jPu603Pw3byraCbW17\nW5eDjRq2lW1FB9u6pOxstbTZAGn0fMgZdfr3DwL4PQAvA/BTdZsFObz2cwDWqttGIWf7tdwGtpVt\nZVuXjq3LwUa2lW1dCrYuJTs7XpmD9Ko/Q7IPDCAHia8TQvwzpGz6WiE96zUA8kKIRwFACHFQCPFg\n5CO2L2wr28q2tj/LwUYN28q2drKtS8bOjnfmhJxVNyf81guXQ46fAoCXQw4U/zKAfwXws1assVGw\nrWwr2Na2ZznYqGFb2VZ0sK1Lyc4lUQABeB2aBYARAF9SN09AdsjfBeAhIcdUdTxsK9va6SwHW5eD\njRq2lW3tZJaCnR2vzBmUALiQvWBOU9702wGUhBDfa/c3ok7YVra101kOti4HGzVsK9vayXS8nUtq\nNisRnQPgB+rfR4UQt7Z4SYsG27o0YVuXFsvBRg3bujRZLrZ2up1LzZlbA+AlAN4vhJhr9XoWE7Z1\nacK2Li2Wg40atnVpslxs7XQ7l5QzxzAMwzAMs9xYSjlzDMMwDMMwyw525hiGYRiGYToYduYYhmEY\nhmE6GHbmGIZhGIZhOhh25hiGYRiGYToYduYYhmEiIKIiEf2ciO4iol8Q0U1EVPWcSUQbiOiFzVoj\nwzAMwM4cwzBMJWaEEHuEEDshZzY+DcDNNe6zAQA7cwzDNBXuM8cwDBMBEU0KIbLG75sA/ATAIID1\nAD4BoEv9+TVCiB8Q0Y8AnArgIQAfA/ABAO8BcBGAJIC/E0L8Q9OMYBhmWcDOHMMwTARhZ07ddgLA\nKZBDuEtCiFki2grgX4UQZxHRRQD+UAhxtTr+RgDDQoh3EVESwPcBPFcI8VBTjWEYZknjtHoBDMMw\nHQSpny6AvyWiPQCKALZVOP4KyMHdz1G/9wLYCqncMQzDNAR25hiGYWKgwqxFAIchc+cOATgdMvd4\nttLdALxWCPG1piySYZhlCRdAMAzD1ICIhgB8CMDfCpmb0gvggBCiBDmc21aHTgDoNu76NQC/R0Tu\n/2/fjlETCqIoDJ9TivvIemzcVsAmdTbgGtyBmGwjtd0rLN4rU4pw8fvKGRiY7meGu53z0XYfgCfy\nMgfwv13bW9Yv1SXrwMPntveV5Nz2mOSS5L6t/yZZ2v4k+U5yyjrhem3bJH9JDq+6APAeDEAAAAzm\nmxUAYDAxBwAwmJgDABhMzAEADCbmAAAGE3MAAIOJOQCAwcQcAMBgDzJP8EhvUK4IAAAAAElFTkSu\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "returns.plot(figsize=(10, 6))\n", "plt.ylabel('daily returns in %');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Specification\n", "\n", "As with the linear regression example, specifying the model in PyMC3 mirrors its statistical specification. This model employs several new distributions: the `Exponential` distribution for the $\\nu$ and $\\sigma$ priors, the Student-T (`StudentT`) distribution for distribution of returns, and the `GaussianRandomWalk` for the prior for the latent volatilities. \n", "\n", "In PyMC3, variables with purely positive priors like `Exponential` are transformed with a log transform. This makes sampling more robust. Behind the scenes, a variable in the unconstrained space (named \"variableName_log\") is added to the model for sampling. In this model this happens behind the scenes for both the degrees of freedom, `nu`, and the scale parameter for the volatility process, `sigma`, since they both have exponential priors. Variables with priors that constrain them on two sides, like `Beta` or `Uniform`, are also transformed to be unconstrained but with a log odds transform. \n", "\n", "Although, unlike model specification in PyMC2, we do not typically provide starting points for variables at the model specification stage, we can also provide an initial value for any distribution (called a \"test value\") using the `testval` argument. This overrides the default test value for the distribution (usually the mean, median or mode of the distribution), and is most often useful if some values are illegal and we want to ensure we select a legal one. The test values for the distributions are also used as a starting point for sampling and optimization by default, though this is easily overriden. \n", "\n", "The vector of latent volatilities `s` is given a prior distribution by `GaussianRandomWalk`. As its name suggests GaussianRandomWalk is a vector valued distribution where the values of the vector form a random normal walk of length n, as specified by the `shape` argument. The scale of the innovations of the random walk, `sigma`, is specified in terms of the precision of the normally distributed innovations and can be a scalar or vector. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as sp500_model:\n", " nu = pm.Exponential('nu', 1./10, testval=5.)\n", " sigma = pm.Exponential('sigma', 1./.02, testval=.1)\n", "\n", " s = pm.GaussianRandomWalk('s', sigma**-2, shape=len(returns))\n", " volatility_process = pm.Deterministic('volatility_process', pm.math.exp(-2*s))\n", "\n", " r = pm.StudentT('r', nu, lam=1/volatility_process, observed=returns)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that we transform the log volatility process `s` into the volatility process by `exp(-2*s)`. Here, `exp` is a Theano function, rather than the corresponding function in NumPy; Theano provides a large subset of the mathematical functions that NumPy does.\n", "\n", "Also note that we have declared the `Model` name `sp500_model` in the first occurrence of the context manager, rather than splitting it into two lines, as we did for the first example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fitting" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using ADVI...\n", "Average Loss = -868.62: 32%|███▏ | 63550/200000 [00:23<00:50, 2717.77it/s] \n", "Convergence archived at 63600\n", "Interrupted at 63,600 [31%]: Average Loss = 559.54\n", "100%|██████████| 2500/2500 [02:37<00:00, 15.91it/s]\n" ] } ], "source": [ "with sp500_model:\n", " trace = pm.sample(2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check our samples by looking at the traceplot for `nu` and `sigma`." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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DdAQvHhjMqL6Z6bzAEop/HGXHXBzkItnMYDpwnjGmB0BEHgR+YYz5QKYCy3Wb\n7A6Hp3PzwEgfvXYZvkCA//xjLR638Ln1Z2V9xCellErSCmPMOWGPnxeRHY5FkwN8aW6ylCkn2q1O\n9Mfa+unsH+JUgiGagwMPhI/o9uTOkyypKePM2RUEUhilLV5iuelYO4unl7FmXlXc2rBoOsJqBN44\nag1LPd5vI9XkN9gXKNMaxzkSXjZk7chP4xtFDhIRSuoTFLt2N3Rzsiv2d9HaYx2L3uHwqQMsxoye\nviGdvxnB4mLw+J3sg2AkezlnARBeHzgELEp7NJPIEzsbKS5wcXWeTy6cqvuuW86HrljCT/90go//\nYmfaRylSSqk02SYiFwUfiMhbgFcdjMdxEx2fb3DYH7WwPt4hrhNJdnLfaNf5fIFAKNball62nog+\nB9RIoW/sc9ESmaP2sNjhydy4azvGWUuYqIlgIGDGTJycTpGfd7c9BH0qfY62nejIWuKXbunsW7W7\noSt0ASHRQA7RRuyMdggVuKNvp7lnMOFxEbm5bSeSHzkykKBmNvLzbT6WnnnZnJJsgvUI8KaIPCgi\n/wq8gdW84rTk8wd4evcprlk5k9JCbR4YTkS4/4aVfOzaZfxqaz1//eNNKc0NopRSWfIW4DUROSYi\nx4DXgStEZJeI7HQ2tOR1DQw7fiGre3AYf8Cw7URn1JqbRLVD6e7sHylRguMdjr3/Igt94YXDzcdj\nFwBNxFX+5/c3j5rOZHZlSfygSFzZkcogF+GLtpzo4KndJxO+f7oE+8Wl8j0HaymzJV0tXoMj/QVF\ntuKJdRGjz+vjeJRpEaL1KUzkRNvYfRceRWQfLYNh2B/g9cNtbDrWHjXGyNqloFT6Qe1Ichj/4Dsk\newEFYlfaOfnbmOxEw18A3gd0AJ3A+4wxX0z0OhG5QUQOiEitiNwf5fkiEXnUfv4NEVlkL79ORLbY\nJ7otIpJTw+a+UttKa+8Qt5yjzQOjERE+du1yvnL7Gl473MYd//2nnJxlWyl1WrsBWAxcYd8WAzcB\nN2P1M855xhheONDMm0czU0MEVq3UsD9A/5CPnfWdYwpYw34redh2omNciVJtcy9P7GwMzeWTmuTe\nr7Y5fiE1qZECoyyL1eQtch+19w3RPTjMvlOpNRtM1ti+TdFGJhxZ5lRTvXQlManU7AUChr40z8UW\nT3tf/MEfYoX+8qFWtteN/fsajyOt1vE+OOxPapLe8Li6Y0wSHLzQYIjdByyR4DD+sZLM4N+hz29o\n7hmM2UeaWuQFAAAgAElEQVQslX0U6/NkQyo9PkuBbmPMN4F6EVkcb2URcQPfAW4EVgHvFpFVEau9\nH+gwxiwFvg582V7eCtxijDkbuBurBi1n/HJLPdWlBVy98vQePTCRO9bN56H3XsCJtj7e/q2XeTnF\n2duVUipTjDHHgW6gEpgWvBljjtvPTRoTGVq7q3+YFw40x7zS+8yeU/xxfzPbT3RytLWP1l6rABks\n4gSTqra+obiJSrTkDEYmJY2sRapr76czTRPYT6SGLPIzJbMlq1/KyJrRmhkmVUiMssrGXSd57XBr\n3FicHn8kVlO28H3p9flD30sgYFIaACOVr3NnQxfP7WtKqUlkJvv+xDoWg++ZrspcY0xKF7aDSU+s\n94/XVDZZyQ7e0tbn5fXDbaH5v5IS47fHyT+FpBIsu1ngJ4FP2YsKgJ8meNmFQK0x5ogxZgj4ObA+\nYp31wMP2/V8C14iIGGO2GWOCQxntAYpFpCiZWDOtq3+YZ/c2sX7t3KQmWzvdXbG8hl//3SVUlxby\nnofe5CtP73e8OYtSSonI54CdwLewJh/+GvBVR4NKUToK0ntPdtM1MExH31DM7Q0O+8cUVIIJQl3H\nSHOkeBVBR1v72LCjMdSv5vHtDbx5tJ1hv7WdA/byPq+PPq+PrSc6YvaLCvImKDR39g9FrRkbz36b\nyL52hY3ANlHD/kDUCX0TyVRBM9nahLZe76imaU/vPsWfjliDeexu7OL5/c1JNwmLVbMRTbOdZCRK\nslP9bpLtVxe5WqKkIVGcj29viLo88jiP3E54U8Ux72BGju/wfRt9kLLxH0n+BN9bsl+r0xcQkpVs\nB6J3AOcCWwGMMY0iEn9cVJjL6GHc67HavEddxxjjE5EurKuI4RMx3AZsM8aM+UURkQ8CHwRYsGBB\nkh9lYn63s5EhX4Dbz5+XlffLBytmlbPhnkv5zO/28F8vHOb1I218+bY1LJ+Z6BBSSqmMuQM4w74A\nmNe8Pj9FHnfcdQJm9MAMkSILNcEagVHNzZIodB5p6Q399p/sGsDjcoXuAzy3rynxRpL04sEWigvG\nfu7EfZsmXoIL30Rot4QtSzTyobV6Cn2Wwvrd7I3SD244DYNaGGMIGHjpUAt+v+HaVTM5HqW/TzSn\nugdD30V1aSEd/UOhmtc2u1Z0yB+ghPjHKRC1NuqP+5twu1K/6L2zvpNZFcVUlhaEliUaTCJcui8Y\nx0seow1iERQ5f1m8deNtO9b7N/dYx+tE/jQCxq4xt4fbD5ro8P2Q2neWLckejUPG+sUxACKSzKxx\nyaS+cdcRkdVYzQY/FO0NjDHfN8asM8asq6mpSSKkiTHG8OimOlbOKmf1nIqMv18+KSl086Xb1vCt\nd5/L0dY+bvrmy3z56f0pdWJUSqk02g1UOR3ERCRb1vnTkfakkoaddbH7Vgz5E195T6ZmxesLjLq6\nnumZPCZagzWmieA4Spih5lUpvs4fiP9+4c9tq4tf25dScytbXXs/j29vCO3DLcc7eGJnI90Dw/TZ\ngxtEDuoQTzDe8O9/cNifcjIQLQnvGfSNmfw2meTnaGsfrx9pG3fisCnBCJki0Y/BWOIlWPH6PkXu\nw5cPtY5KOoIJUiyJJpiu7xiw44u7GhA/2XkpSleR5/c38/z+5gnX8Pr8gYwPmJOKZBOsx0Tkv4Eq\nEfkb4DngBwleUw/MD3s8D4icwTC0joh4sNrCt9uP5wG/Ad5jjDmcZJwZta2uk10NXfzFRQt1fqdx\nuvWcOfzhvitYv3Yu333hMNd/40We29uUM5NWKqVOG/+GNVT7MyKyIXhL9CIRmS8iz4vIPhHZIyIf\ntZc/KCINIrLdvt2U6Q+Q7O9mZ3/s5n+hbWHiJlGDEX2kIreXypX8bAyyEK+gFV6QCwTMmJHaDFbN\nRlf/MAfsSXgNhhNt/UnP+9M3FD6HkN1EMMXTXP+QjxcORu+7fLytL6WmcuNRZ4/k1zNoFd6jjQYZ\nNYQoxSNBQns9vMbimT2nJvw5gk0Nw53qGmTjrpNjEssDp3oSJjzhx0esv7HW3iECAUNHX+Lal2f2\nnEq4TlC68oPIfXrgVA9P7rRGjow38p+IxD1O+5IYNTBeohTv4w37kvvw0dZyCTy56yTPprCvMy2p\nJoLGmK+KyHVYHYJXAJ82xvw+wcs2AcvswTAagLuAP49YZwPWIBavA7cDfzTGGBGpAp4EPmWMyZl5\nSR5+7RjlRR7eee5cp0OZ1KZNKeJrd5zD7efP44HHd/OBn2zm8uU1fPrmVSydMcXp8JRSp4eHsVpI\n7AJSaefjA/7RGLPVbiq/RUSC58OvG2Oy1o8rlbJYe3/0lpDBa4UtPd5QQTqayAQqUX+KeBL1rUqH\nJ3ZGXs8dEV7p0hlllLHugWG6B4ZDc1oBdPQNc6Cnh1kVxQnf2xhG1aaM1GClvs+Co6B1DQyPmk9s\ne13y8w+FS6XGKZgoHW7pTSn2WJefM5UPRhvMIVoTzPa+Ifaf6qatz8tbz5gec3vN3V7mTy0FrMFb\nojne1ofHlf4L7eEXBgITzLYi6wGC331kTXMq75LMRZ3IizHJvjZRLWw8bvu7iNfMOdsSJlj2aIDP\nGGOuBRIlVSF2n6p7gGcAN/CQMWaPiHwW2GyM2QD8CHhERGqxaq7usl9+D7AUeEBEHrCXXW+MGd1w\nM4uae6yrIX950ULKinTuq3S4+IxpPPXRy/jJ68f5xnMHueEbL/Hety7i3muXUVFckHgDSik1fq3G\nmG+l+iJjzEngpH2/R0T2YfUnzmmJmgCFJxPJyKWmOKkKTxbcSbZGCTaxSqapXWQyEnyL8e6yPq+P\n1w+3JhzUI92CNW9N3YMxR6RLqXA+ziZg40ljfBEFbYMJ1eqEBnSI8YVsPdFBaaGbaVOKxswZFS6Z\nOaqsfZj85zbG0Ng5QJHHlfS8Uek0nn0dOfddfUf65zCrbY4/6XQu/holzBSMMX4R6ReRSmNMSoPf\nG2M2Ahsjln067P4g8K4or/s88PlU3ivTHn7tGL6A4T0XL3I6lLxS4Hbx/ksXs37tHL727AF+9OpR\nfru9gU+8bSW3nz8PVwauECmlFFbN079htaQIXdI1xmxNdgP23I3nAm8AlwD3iMh7gM1YtVxjLsmm\nc3CmdNQIpDpH4aHmnnGNYheLE7/wo/ZbigEks8tjfS+RfYSSlc6BP1KR6PR7uKU36sTSsbpQJHu8\nRvYnGk9iGe0CQPD9g9HFa5oYMFaiEOx7lC1D/kDCfl0TEa2/W/h0CAETf96waLssODJoJu1pHDnO\nrJqw0cdY7DnpMhlVfMlWxQwCu+xmEKHLXMaYezMSVY5p7xvix68e46azZ7N4ejLje6hUTZ9SxL+9\ncw1/fuFCHvzdHj7xq5389I3j/Ostqzl/YbXT4Sml8s+59r8XhS0zQFIT24vIFOBXwMeMMd0i8l3g\nc/Y2Poc17PtfR77OGPN94PsA69atm9DpPx3Dfqeqpceb1gTLaZm4hpfpvlHZkmikw90N0a+5R9ul\nhxLUQACh7PUPEQnl4ZZeZlcmbpqZcPMRGVa8b+l4W1/UPmepSrW7/p+OZC65grH7FmB/xATYwWZ2\n+6Mkz6kOSJIJe092x/0NypWpgJJNsJ60b6elH7x8hP5hPx+7ZpnToeS9s+dV8ssPX8yGHY18ceM+\nbvvua7zr/Hn8y9tXjRpGVSmlJsIYc9V4XysiBVjJ1f8aY35tb68p7PkfAE9MOMjTQHhfrmiFv0wI\nT4COtKTWNDKZnPZQ0+imY/GameWj8X7ceBcMJlqw9w4HQlsPNn0MPw4ic+KuKH3zsiGdA34lldTG\n0TKBCcwzKVFz5o27TmYpkvjiJlgissAYc8IY83C89fJZU/cgD792jJvXzGGZztuUFSLC+rVzufbM\nmXz7+Vq+/9IRXjzYwhffcTbXrprpdHhKqTwhIm8HVgOhy+PGmM8meI1g9R/eZ4z5j7Dls+3+WWDN\nHbk7/RGPVtee3eZLmRDelCtbV8fDy7DH2lJLsJKpNYzcZr7UaCVrvHMSxdtNsWqTkq1l2nqig9Vz\nKoGwQUfC3m/z8dE1R/nwlcUbtCZX9KRhDqxclWiY9t8G74jIrzIcS84xxvDAb3fjDxj+8brlTodz\n2ikr8vDJG1by27+7hKllhXzgJ5v52M+30RFjVB+llEqWiHwPuBP4e6xGQ+8CFibx0kuAvwKujhiS\n/SsisktEdgJXAf+QodBD4s2Lo2KLNaJiMsZTaM2Hwnoqxl+DFVusJmGbY/RXityW1xcIJcfGWLUg\n4Ylve0S5Il1Jca40V8tVf9yf2bHr0jGJ8XglaiIY/meyJJOB5KKndp/i2b1N3H/jShZp3yvHnD2v\nkg33XMp3nq/lO8/X8kptG5//s7O44axZToemlJq83mqMWSMiO40xnxGRrwG/TvQiY8wrRO9msjHK\nMpWDuh1q/nW6GG+DyEzOhznsD4SStOaeQZp7BjmjJva0MJN4kEwVJlY/wWxIVINlYtzPe7sbuvjk\nL3dy1twKPnDpYqfDOe0Velz8w3XL2XDPpcysKOLDP93CvT/T2iyl1LgF2xb1i8gcYBjQH3uVdsEJ\ne08Xg77EQ9lHk86kJlquFtl3J17tRiaTPXV6SJRgnSMi3SLSA6yx73eLSI+IjB1eJE+8ebSd9zz0\nJhUlBXz/r9bhcSfaTSpbVs2p4LcfuYR/uHY5G3ed5Lqvv5TSLOlKKWV7wp7U/t+BrcAx4GeORqTy\nUi5NfpoN4x3U47XDrbRlc2CFODmU1mDln+YUp6SYqLhNBI0x7mwF4rQvP72f4219tPYO8ebRdmZX\nFvPTD7yFOVUlToemIhS4XXz02mVct2omH//FDj70yBbWr53Dg7esprqs0OnwlFKTgDHmc/bdX4nI\nE0BxqnM9qsRmlBeHJulVp4eJjMD36uG2tMTQmkSiFm+UvNNtYJLTwcGmXmZUTHy4/2Rp1YztRHs/\nh5p66R4Y5hM3rOAP/3iFznmV41bNqeDxey7hY9cu48mdJ7nmP17k52+eiDk7u1JKicgFIjIr7PF7\ngMeAz4nIVOciy08rZunouyp56ZqXbKIJkiZYaqKSnQcr733nz89zOgQ1DgVuFx+7djlvWz2LTz++\nm/t/vYufbarjs7eu5pz5VU6Hp5TKPf8NXAsgIpcDX8IaSXAt1gTAtzsXmlKjlRd7JsVw2+ni1wuk\nKk1KCtwMDI+vP2A6aA2Wygtnzq7gsQ9dzNfvPIfGzgHWf+dVPvzIFvZFmYlcKXVacxtjgmM73wl8\n3xjzK2PMA8BSB+NSagy3S4tp+apQ+/dnlIhQWVIQetzWl92Jk/XbVXlDRHjHufP4wz9ewb3XLOPV\n2lZu/ObL/O1Pt7DleIeOCqSUAnCLSLD1xjXAH8OemzStOowxk6KAVl48aXZpTkpXk7l8s27R5G/N\nG174V+lnjEEiBlx5fHvDmDnPMiX3f52VSlFFcQH3XbecVz55NfdevZRXDrVy23df423feImHXjma\ntT8upVRO+hnwoog8jjVU+8sAIrIUmDSDXIgIq+ZUOB1GXIVuFwVhSeC8ah00KlW+JJrMVRRntqA+\nfUrRhF4f70LA6nEew/mQePozcNFXxw4YMTDspzPKpOIlBdkZv08TLJW3KksLuO/6Fbz+T9fwpXee\nTUmBm88+sZd1n/897/rea3zvxcMcbOrRQTGUOo0YY74A/CPwY+BSM1K17cLqizVpuHO8lBk5Wve5\n86udCSSG8Rbuk3XBOGtZLl06PTQJblEStZTprCWsKR+bTBWnUCC9fFnNmGXzp5bGXH9aWWrJ27zq\nUq5aOQMZ93TGuSMd/c3KCkd/9+nM2davnctNZ89OuF687zdSRXHBqIsuyYg3IfR4lBRqgqVUWkwp\n8nDXhQt4/J5L2XjvZdxz1VL6vH6+9NR+rv/6S5z7ud9z90Nv8s3nDvHsnlMcbe3TjrZK5TFjzJ+M\nMb8xxvSFLTtojNnqZFypmlOZnhqhyGY06TN6u5FvMzfKNCiXRSmgp8PUssIxBbtCt5v1a+dS5Jl4\ngeuaM2eOWZbMNC9vPWP6mGXTwmqMKksLoq4TLp3f34zykWGsbzhrFlcun8F8u+axJkFN1lsWT6O6\nrHDM/lw2M3YBeUoKyeHymeWcv7CaiuIChvNgbrHxjFRY6HZx4eKRxH121ehhx5PZYnGBmzXzkhsE\nLJlkKJV5z+ZWl8RtGhltWwVuF2tTGLTsyuUzov62ZJsmWOq0smpOBfddv4KNH72M1+6/mq/ctoab\nzp7Fqa5BvvGHg3zwkS1c9dUXOPPTT3PDN17inv/byjefO8TGXSepbe7Jix91pVR+cLkkYbO7YC3X\nlCIPZ86OXmMzI0qtxXkLxtY2JVPbEK+wFZkIRBYGZ1eWUFaUvqvLRZ6RIs5ly2pYEHalfc28KuZP\ntfZdoprAS5bGT3DA2r/RzIwy7054k7ua8iKuWzVzTC1UcO6wxs5BpiWY3/GMmjKKPC6mFHkSFiyX\nzSinyONiXrW1L+ZPLQ0lTuctqB71+iKPm8rSAmZUFFuJaIKaLI/b2o/XrxqdbMZKYK89c2ZKtRnh\nx6/XN3p0uOrSxHNgpmNe05WzKrjxrMS1OonMKC9mPMWJG8+ezeywCysrZ1Vw1coZLJxmNQ00xjCl\nyDPqWI90xfIaFk8v45Y1c0LLotU8RnPRkmljlkX7/YDoCbkx0WvZgr8NS2qiN3FM5burLC1IqdY1\nU7T3qTptzakq4Y4L5nPHBfMB6PX6qG3u5VBTD7UtvdQ29bKzvosnd50M/SAUuIXF08tYNrOcFTPL\nOXteJefMq2KqTnCslHLE2OTg/IXVbDneAVhXf/0BP+sWTqWytCA0sqpLJHQF3SVWotYz6OOsuZUU\neVxjhjeeWVHMuQuqqGsfYE9j7K5qly6dzpA/wJ+OtI2psYoUWdAqL/ZQ5HFz/apZnOwaYFdD4i5x\nly6dziu1rVGfKy8uwBs2mezqORUcbukFRvdVuWjJVP64vznme0yfUsS1Z87kuX1NgNVk6ay5lext\n7OZQcw9vWTy20Dmy7Wk8u+cUy2eWs6O+Exj7jZUWeli3aCrPh8UwMGSVvos8roT7saq0kBvCCv2L\ne72c7BpkSpEn9J6h56aXsWpOBcfb+qjv6B8VS1FB/PcKHi9Tywqj9mUOvtTlEt62ehbP7Dk1Zp23\nnjGd1w5b31cwGT9rbiW7E3zXkRcSwpPUIo+Ly5fX8Pj2hpivX792LsCYddbOr2J7nbWPqksL6YjS\nZwdg0bQy3C4Jzet25fIZbD7eTq937BD6RR73qARw5awKjrb24vWNZFQXnzGNp3eP3T+xlBS4uXLF\njFHLCt0u3C6horiApTOmcLytj7nVJZxrXxw50d4/Zjtul4SSD1fYhYXqssKkhjWPdjEiPPlZMasc\nn99wuKWXqtJCugd9o/aFsf+L5BLwG+szza0qoaFzYNTzBW4X69fO5URbP9vqOmLGF4wlF5pPa4Kl\nlG1KkYe186vGVEUPDPk53NLLoeYeDjZZCdiu+i42hiVe86eWsGZeFefMq+TcBdWcPbcyJ66gKKXy\n21lzKwDD3KpS3jjaBlj9VIIJlscuaIhdUVAzpYiWXi9vWTKVjr5h9p/qxiVw/sLR/YXKiwu4ZOl0\nyos9DA4FKCty43G7WDpjSswE67wF1VSXFTIwFLuQFixg15QX4YtxCb+k0M2iaWUxE6yb18zhhQPN\n9Hp9FBW4mVFeHKrxmV1Zwskuq3B29rxKCt0jSYOIsHZ+1ZhatvIkBokoC6uhOmtuJWC1iFg5qzxU\nUL1sWQ0vH2oZ89rrV1vzWpcWunn9SBuIVRAN72xfUVzAtWfOxOcfSWKaewa5aMm0MTV/c6pKaIwo\ngIabNqUo1MywvX+IurCCdrD/SbAAWuB2McDI9xWvBjLYX7m6dHSCFdzn4ee8yPNfSYGbQV+AmvIi\nblkzh55BXyiW2ZXFCROsyOOzqrSQa86cyR/2NYXe67wF1RhD3AJ40KrZFcwoL6aytIDqskKe3988\nKsG6ec0cGjsH2HrC2lbkvJqVpdbfR7Qk8ux5lWw+Zs0EcfbcSpbUTGFJTRn+gBm1fjBhXTajnEPN\nPaHlZYUe+oZGErd51aWcNbeCwrAa2betnjXqu5pS5AklkZHesnha6Lchsu/aZctq8AWsv8OCKBdW\nYPTfVLDP18pZFTR09o+5uLByVgUHm0Y+y5Urahgc9vPiwZbQZ2nqti56rFs0NbSflkyfgsctnFEz\nBV/AIGIdm0db+0Yl/QumlXKwqWfU/gm66ezZoRrRWAlWNgcB0QRLqQRKCt2cNbcydFIN6vX62FXf\nxc76TnbWd7GjrpMnd54ErJquVbMrOHdBNectrObc+VXMqy7JYF8HpdTpqMjj5vyFU8dMQ+F2Cf6A\n4Zz5VRxp6QsVjOZPLaWl18uUIg/eYatgFet3KVhLEK2JV/hV+mABbFal1Rwu2FQsWvPFYAFbBPY0\ndtPS60VEMMaMamrkcgkVJQV0DwyP2YbbJVSVFtLr9eFxCRefYRXyGjsHqCkvYk53MVuOd1BW6BlT\n0Ao2pYq0aFoZx9qsLnkrZ1WwcFpp1MJzpPBagKllhXhcLnyBAEtnjO13FPyGBGHlrLHNNcOTuHWL\nqukf8ocK1ecvrGZgyM/ek92jRtBbNqM8bnznLajmvAXVY2pu5laV4PUFWDStjO6BYQZOdFBdWhgq\nfkcb+S846t2MiiKW1JTxam0by2dOYcHUUnq95aPijxRMMsHaZ5WlI0ltaWH8omispG9KkYflM8tZ\nZH+nwcEW+od9HDhlFfIXTC2lpWfs/EcFblcohoriAi5dOp3q0kJ6vMMUedy4XcL8qaWhBCua4gI3\nt54zhw07GkctDwQM6xZNpcAtoT5tBW4XwZwz+PcW7Ou9YlY5c6tLKClw09Q9SE15UejYm1tVwvkL\nxzbXTeYC7ttWz8LtklHNMM+ZP7ocE976pjLG31uwz5fPH8Bj1yQF4w66ZOn00AXn4N9csLasuMDN\ntWfOxGB9Z8HEckqhh6tWzuD5/c3Mm1oSGg2z0CWcv3Aqde39HKVvzHHltn9fppUVhea2ihyx1BP2\nR7JyVgVdA8OsmlMRsylvJmiCpdQ4TSnycPEZ00Ind4CWHi/b6zrZeqKDrcc7eHRTHT9+7RhgFSzO\nW1BlnfAWai2XUip9goW2YKHn8uU1tPZ4mT6laFRzqvlTS0MXezpcVmEqvK9SMq5fZRXcDrf00trr\nHdXpHqzC5E1nzw4Vcs6dX01950gtSjApWTW7gvnVpaMK2/GE9ytZO7+KM2rKRv2GBpsHzasuDfUx\nStY586vG1FJEqi4tDCWPsVyydBp17QOsnlM55rnqUmugjfCCaSwFbheVJeFD3Jfi9fk53NLH0ppy\nAsZqUhktUUuGiIRGZ6suKxw1SMfymeVR+zQFj5NCt4vSQg/XhfW1ilULGDnKXSxXrpjBCwdGmkiu\nmFXOgVM9VJUWcsXy2P2DovUrXDmrIpRgnRulLyFYtTXhgjV+0QYUqYrTv0tEuHnNHPqHfLxyqJUh\nf4BZlcUx+5atml3BDLtf3gWLpnKkpRe3a2RC3GCSePOaOeyo72RVjH6TyQj/27hoyTSKC9xxB5g4\nZ14VsyuLefNoe9TnPXH6y4X/xiyeVsaQb/RFhvAkaWnNFLae6KC0yB1q+hfN/KmllBd7xuz/ixZP\no6Gzn3nV1kWQZTPKx/xNBROp2ZUlSf29ZYLky+Sr69atM5s3b3Y6DKVG8fkD7D/VE0q4ttV1crzN\nKmh47PbcK2ZZ/bmC92dVFGtNlzotiMgWY8w6p+NwitPnLWMMR1r7Qv1Lcs2bR9s52TXA5ctqcLsl\n4/M9RQrW+sQqAE4mz+9vZmpZYcIkMp5hf4CTnYMsmJZc8jow5MfjlqQHsnj5UAvtfUOsnV8Vs6Yx\nWW29Xnq9vjHbCX6nV66YkdREv71eH0UeV1KfwRiDMaNrNSejIV8Ag0nL6JqZNjjst/spjt7ngYBh\nT2M3S2rK4tasjkey5y1NsJTKstZeL9tOWLVcuxu6ONjUE2qTDFBR7GHFrHIWTy9j4bQyFkwtZeG0\nUhZOLUv6Sq9Sk4EmWHreimfYH6CtdyjU9DDbjrf14bE73avMGxz2U9/Rz9IEzR4n4oUDzXQNDHPd\nqpkJmyYqFU2y5y09upTKsulTrGF5w5tXdPYPcbCplwOnujnQ1MPBU708f6CFlp76Ua8tKXBTU15k\n3aZY/1aUeCgt9FBS4KasyE1Jocdujyx47H8L3C48dltsj1vwuMKeD1te4HZFvRqklEpMRG4Avgm4\ngR8aY77kcEiTWoHb5VhyBbH7a6nMKC5wZzS5AqtZ3smuAU2uVMZl9AhLdLIRkSLgJ8D5QBtwpzHm\nmP3cp4D3A37gXmPMM5mMVSknVZUWcuHiqWP6MvQP+TjR3s/xtn5OtPVzqnuQ1l4vLT1eDrf08qej\nbfQM+tI6MbJLoKKkgIriAipKPFQG7xcXUFlaQEWxJ/R8ZYm1TvB+UYEbl1idW10SvI10ejVmpKN3\nsPZ85DGh4VsjK9YL3a5J3+xC5TcRcQPfAa4D6oFNIrLBGLPX2ciUUkFlRZ6MJ3FKQQYTrCRPNu8H\nOowxS0XkLuDLwJ0isgq4C1gNzAGeE5Hlxpj4A/QrlWdKC61OzPE6MhtjGPIHGBjy0zfkZ2DIh9cX\nwOc3DPsDDPsNvsDIY1/A/jf4fMDgCz4OBOj3+ukeHKZ7YJiugWG6B300d/fa94cZHM7+ZMsiUFrg\npqzIw5QiD2VFHkoL3ZQXeygvLrD/te5XhD22EkEPU4oKKPRYtXaFHhcFLk3YVNpdCNQaY44AiMjP\ngfWAJlhKKXWayWQNVjInm/XAg/b9XwLfFqtt0nrg58YYL3BURGrt7b2ewXiVmpREhCKPmyKPm6rU\nBs4aF6/PT8+gz0q47AQsmIx5fQECAUPAGPx2h19/wOC357UAa4jikfvBzzB2qOjwh4PDAfq8Pvq8\nPnvushsAACAASURBVHq9PvqH/PR6fTR2DtLj7aFn0JdyTZ7HZSVbbhGw/kfEii10f1Qc4c+NfI7g\nutGMzL8TtixsHpLRy4PLRha6XYLHJXjcgttlNed02489LqvZZ3AY3uC6CKH9HjD2LcDI/Yjn/AHr\neV8ggN+A307GA8bgCxgCgYh/7eX+gOH+G1fyF29ZmPQ+z3Nzgbqwx/XAWyJXEpEPAh8EWLBgQXYi\nU0oplVWZTLCSOdmE1jHG+ESkC5hmL/9TxGvHDOMTfqICekXkQMQq04HoU7yrZOj+mxjdf+On+25i\nsrL//vIz8JcT20Q+ZWfRsuwxGb8x5vvA9wFEpEVEjk/wfSfD38pkiBE0znSaDDHC5IhzMsQIp0+c\nSZ23MplgJXOyibVOyieqqAGIbD6dR6iaKN1/E6P7b/x0302M7j9H1APzwx7PAxpjrAuAMSb2BD9J\nmgzf9WSIETTOdJoMMcLkiHMyxAgaZ6TUZhdMTTInm9A6IuIBKoH2JF+rlFJK5YpNwDIRWSwihVj9\niDc4HJNSSikHZDLBSuZkswG4275/O/BHYw0ttgG4S0SKRGQxsAx4M4OxKqWUUuNmjPEB9wDPAPuA\nx4wxe5yNSimllBMy1kTQ7lMVPNm4gYeMMXtE5LPAZmPMBuBHwCP2IBbtWEkY9nqPYQ2I4QM+Ms4R\nBGM2H1RJ0f03Mbr/xk/33cTo/nOAMWYjsDHLbzsZvuvJECNonOk0GWKEyRHnZIgRNM5RxEROOKOU\nUkoppZRSalwy2URQKaWUUkoppU4rmmAppZRSSimlVJrkbYIlIjeIyAERqRWR+52OJ5eJyHwReV5E\n9onIHhH5qL18qoj8XkQO2f9WOx1rLhMRt4hsE5En7MeLReQNe/89ag/2oqIQkSoR+aWI7LePw4v1\n+EuOiPyD/Xe7W0R+JiLFeuzlv1w6x8U5hzwoIg0ist2+3RT2mk/ZsR8QkbdlKc5jIrLLjmWzvSzq\n74xYvmXHuFNEzstSjCvC9td2EekWkY/lwr4UkYdEpFlEdoctS3n/icjd9vqHROTuaO+V5hj/3T63\n7BSR34hIlb18kYgMhO3T74W95nz7WKm1P0f02eTTG2fK33EmfwdixPhoWHzHRGS7vdzJfZlSGTZr\nx6YxJu9uWINqHAaWAIXADmCV03Hl6g2YDZxn3y8HDgKrgK8A99vL7we+7HSsuXwD7gP+D3jCfvwY\ncJd9/3vA3zodY67egIeBD9j3C4EqPf6S2m9zgaNAif34MeC9euzl9y3XznFxziEPAh+Psv4qO+Yi\nYLH9WdxZiPMYMD1iWdTfGeAm4CmseTkvAt5w6Hs+hTWxqeP7ErgcOA/YPd79B0wFjtj/Vtv3qzMc\n4/WAx77/5bAYF4WvF7GdN4GL7fifAm7Mwr5M6TvO9O9AtBgjnv8a8Okc2JcplWGzdWzmaw3WhUCt\nMeaIMWYI+Dmw3uGYcpYx5qQxZqt9vwdriOG5WPvsYXu1h4E/cybC3Cci84C3Az+0HwtwNfBLexXd\nfzGISAXWD/mPAIwxQ8aYTvT4S5YHKBFrLsFS4CR67OW7nDrHxTmHxLIe+LkxxmuMOQrUYn0mJ8T6\nnVkP/MRY/gRUicjsLMd2DXDYGHM8zjpZ25fGmJewRnyOfP9U9t/bgN8bY9qNMR3A74EbMhmjMeZZ\nY02jAPAnrLlVY7LjrDDGvG6skvdPSPNvaIx9GUus7zijvwPxYrTLOHcAP4u3jSzty1TLsFk5NvM1\nwZoL1IU9rif+j72yicgi4FzgDWCmMeYkWAcwMMO5yHLeN4BPAAH78TSgM+xHXY/B2JYALcD/iNXE\n8ociUoYefwkZYxqArwInsBKrLmALeuzlu5w9x0WcQwDusZvhPCQjzXydit8Az4rIFhH5oL0s1u9M\nLuzjuxhdgM2lfRmU6v5zOt6/xqq9CFpsn3deFJHL7GVz7biCshljKt+xk/vyMqDJGHMobJnj+zLJ\nMmxW9me+JljR2nfqePQJiMgU4FfAx4wx3U7HM1mIyM1AszFmS/jiKKvqMRidB6sZwneNMecCfVjV\n+SoB+wS8HqvZyBygDLgxyqp67OWXnPx9iXIO+S5wBrAW6wLA14KrRnl5NuK/xBhzHtbfyEdE5PI4\n6zq6j8XqN3kr8At7Ua7ty0RixeVYvCLyz1hzq/6vvegksMA+79wH/J/dosKpGFP9jp387t/N6OTf\n8X2ZQhk2K/szXxOsemB+2ON5QKNDsUwKIlKAdWD+rzHm1/bipmCTCPvfZqfiy3GXALeKyDGsKvqr\nsWq0quxmW6DHYDz1QL0xJnjF+5dYCZcef4ldCxw1xrQYY4aBXwNvRY+9fJdz57ho5xBjTJMxxm+M\nCQA/YKTpmiPxG2Ma7X+bgd/Y8cT6nXF6H98IbDXGNEHu7cswqe4/R+K1Byy4GfgLu6kadpO7Nvv+\nFqz+TMvtGMObEWbr+Ez1O3ZqX3qAdwKPBpc5vS9TLMNmZX/ma4K1CVgm1khahVjV7Bscjiln2W1p\nfwTsM8b8R9hTG4DgKCp3A49nO7bJwBjzKWPMPGPMIqxj7Y/GmL8Angdut1fT/ReDMeYUUCciK+xF\n1wB70eMvGSeAi0Sk1P47Du47PfbyW06d42KdQyL6LL0DCI5GtgG4S0SKRGQxsAyrI3wmYywTkfLg\nfayBD3YT+3dmA/Aee8Sxi4CuYHOjLBlVQ5BL+zJCqvvvGeB6Eam2a+Cvt5dljIjcAHwSuNUY0x+2\nvEZE3Pb9JVj77ogdZ4+IXGQf2+8hC7+h4/iOnfoduBbYb4wJNf1zcl+OowybnWMzmZEwJuMNa5SQ\ng1hZ9D87HU8u34BLsapBdwLb7dtNWP2I/gAcsv+d6nSsuX4DrmRkFMElWD+CtVjNPIqcji9Xb1hN\nIjbbx+BvsUbw0eMvuX33GWA/1sn4EayRpvTYy/NbLp3j4pxDHgF22cs3ALPDXvPPduwHSPOoYjFi\nXII1ytoOYE9wn8X6ncFqLvQdO8ZdwLos7s9SoA2oDFvm+L7ESvhOAsNYV/vfP579h9UPqta+vS8L\nMdZi9a0JHpvfs9e9zT4WdgBbgVvCtrPO/k09DHwbkCzEmfJ3nMnfgWgx2st/DHw4Yl0n92VKZdhs\nHZtib1AppZRSSiml1ATlaxNBpZRSSimllMo6TbCUUkoppZRSKk00wVJKKaWUUkqpNNEESymllFJK\nKaXSRBMspZRSSimllEoTTbCUUkoppZRSKk00wVJKKaWUUkqpNNEESymllFJKKaXSRBMspZRSSiml\nlEoTTbCUUkoppZRSKk00wVJKKaWUUkqpNNEESyml/j975x3nRnnt7+dI2l69zWXd7bWNbWxjbIyp\nARJCd0ISSgqEFFLJzS83NyGNkNzkppcb0iAXEkpoARJK6L0ZcG+497W93t6rpPf3x2i0o9GorFa7\n0u6+z+cjWytNeWc00pzznnO+R6PRaDQajSZJaAdLo0kBIvJtEfm/VI9Do9FoNJpY6HuWRjMwRCmV\n6jFoNBqNRqPRaDQazahAR7A0Go1Go9FoNBqNJkloB0ujGWJE5JsickRE2kRkp4icJyI3i8g9lmWu\nEZGDItIgIt8TkQMi8t7AezeLyD9E5J7ANraIyBwR+ZaI1IrIYRE537Kt60Rke2DZfSLyuVQct0aj\n0WhGHvqepdEMHu1gaTRDiIjMBb4MLFdKFQDvBw7YlpkP/BH4GDARKAIqbZu6FLgbGAdsAJ7B+P5W\nAj8EbrUsWwtcAhQC1wG/EZGlyTwujUaj0Yw+9D1Lo0kO2sHSaIYWH5AFzBeRDKXUAaXUXtsyHwYe\nV0q9rpTqBW4C7MWRrymlnlFKeYF/AOXAT5VSfcD9wHQRKQZQSv1bKbVXGbwCPAucOXSHqNFoNJpR\ngr5naTRJQDtYGs0QopTaA3wVuBmoFZH7RWSSbbFJwGHLOp1Ag22Z45bnXUC9Uspn+RsgH0BELhSR\nt0SkUUSagYuAsmQcj0aj0WhGL/qepdEkB+1gaTRDjFLqXqXUGcA0jFm+n9kWOQZMNv8QkRygNJF9\niUgW8DDwS2C8UqoYeBKQRLan0Wg0mrGFvmdpNINHO1gazRAiInNF5NzATaQbY+bOZ1vsIeBSETlN\nRDKBH5D4zSUTI72jDvCKyIXA+dFX0Wg0Go1G37M0mmShHSyNZmjJAn4K1AM1QAXwbesCSqltwA0Y\neenHgDaMot+ege5MKdUGfAV4EGgCPgo8lvjwNRqNRjOG0PcsjSYJ6EbDGk2aISL5QDNQpZTan+rx\naDQajUYTCX3P0mjC0REsjSYNEJFLRSRXRPIwctG3YJPG1Wg0Go0mHdD3LI0mOtrB0mjSg1XA0cCj\nCrhK6fCyRqPRaNITfc/SaKKQ8hRBEckGXsXI+/UADymlvi8iMzDye0uA9cAnAv0WNBqNRqPRaDQa\njSYtSYcIVg9wrlJqMbAEuEBETsWQBf2NUqoKo/Dx0ykco0aj0Wg0Go1Go9HExJPqAQRCyu2BPzMC\nDwWci6EmA3AnRtO7P0XaTllZmZo+ffqQjVOj0Wg0yWXdunX1SqnyVI8jVej7lkaj0Yws4r1vpdzB\nAhARN7AOmA38AdgLNCulvIFFqoFKh/WuB64HmDp1KmvXrh2eAWs0Go1m0IjIwVSPIZVMnz5d37c0\nGo1mBBHvfSsdUgRRSvmUUkswOoOfApzgtJjDercppZYppZaVl4/ZSVCNRqPRaDQajUaTJqRFBMtE\nKdUsIi8DpwLFIuIJRLEmYyjVaNIQpRRHW7o5UN9Ba1cfIlCQncGs8nzGF2YhkmiDd41Go9FoNBpN\nPLT3ePH5FUU5Gakeypgn5Q6WiJQDfQHnKgd4L4bAxUvAhzGUBK8FHk3dKDVOrDvYxMPrq3l223Hq\n250buBfnZjBvQgGLJxdz6sxSlk0fR0G2/uJrNBqNRqPRJJMXth8HYNWSsKoazTCTcgcLmAjcGajD\ncgEPKqWeEJF3gftF5EfABuD2VA5S08+2oy385MkdvL6nnpwMN+edUMGKGSXMriigKCcDhaKlq489\nte3sqGlj+7FW7nhjP7e+ug+XwImVRayYWcqpM0tYNr2EwkE4XH6/orPPh8+v8PsVCsjNdJOd4U7e\nAWs0Go1mxNDj9dHr9ZOf5UFEeHTjEWaV57OwsijVQ9NoNGOElDtYSqnNwEkOr+/DqMfSpAk9Xh+/\nfX43t726j6KcDL5z0Ql87NSp5GY6X0anzSoLPu/q9bHhUBNv7W/krX0N/O2NA9z26j5EoLI4hxll\necwoy6OiIIucTA+5mW48LqGz10d7j5eOHi9NnX00dfTS2NlLU0cvTZ29NHX24fOH93LL9Lgoysmg\noiCLaaW5TCvNY3ppLlNL8qgan09ZftaQnSeNRqPRpIbuPh/PbKsBYGZZPgsrCwHYW9euHSyNRjNs\npNzB0owMjrd284V71rH+UDNXLJvMdy6aT1Fu/JGnnEw3p80u47TZhtPV3edj/aEm1h5oYm9dO/vr\nO3hk/RHae7yO63tcQnFuJiV5GYzLzWR2RT7j8jIpyc2kINuD2yW4XYIAHb0+Wrv7aO3qo6almx3H\n2nh223G8FkessjiHEyuLWDylmBUzS1hUWYTHnRaaLxqNRqNJkA7LPeRoSxdV4/NTOBqNJjXUtHQz\noSg71cMY02gHSxOT3cfb+Pjtb9PW7eUPH13KxYsmDnqb2RluTptVFhLlUkrR6/PT1eujs9eH16fI\ny3KTl+Uhy+MalFiG1+fnWEs3++s72FnTxuYjLWypbubpwExnfpaHU2aUsHJmKafNLmX+xEItzqHR\naDQjDJ/qn0jr7vNh/unSv+eaMcTb+xt0HVaK0Q6WJipbqlu45o638bhdPPyF0zhhYuGQ7UtEyPK4\nyfK4Kc5N7rY9bhdTSnKZUpLLWXP6Jf0b2nt4a18jb+6tZ/XeBl7cUQvAlJIcLlo4kQtPnMjiyUXa\n2dJoNJoRgD1l3B/wsPRPuEYTndq2btYfbOK8E8aToTN6Bo12sDQR2X6slY/f/jYF2R7+/pkVTCvN\nS/WQkk5pfhYXL5oYjMrVtHTzyq5antpaExTmmFmex0dPmcqHlk5mXF5mikes0Wg0mkjYHSzzLyOB\nXKPRRGLrkRZ6vH46e30U5WgHa7BoB0vjyMGGDj5x+9vkZrq577OnMqUkySGlNGVCUTZXLp/Klcun\n0tLZxzPv1nD/O4f40b+38/Ond3Lp4kl88ZxZzCrXef0ajUaTbvj9tr91BEujiYter/Fd8bj0lyUZ\naAdLE0ZLVx+f+tsavH7FA59bMWacKztFuRlcsWwKVyybwo6aVu59+xAPrj3MIxuqufjEidxwbhVz\nJxSkepgajUajCeC1eVhmDZY2GTVjicTKGpTlX81g0TFATQhen58v37ueQ42d/PnjJ+tITYB5Ewr5\n4aqFvP7Nc/ncWbN4aUctF/zvq3zjoU3UtnanengajUajoT9iFcR0sLSHpRlDlA2inEHZv0OahNAO\nliaEHz7xLq/trufHHziRU2eWpno4aUdZfhY3XjiP1795Lp85Ywb/3HCEc375Mn94aQ/dfb5UD0+j\n0WjGNHbbMMzh0mhGMUU5RvscLcyVerSDpQlyz1sHuWv1Qa4/ayZXLJ+S6uGkNePyMvnOxfN57v+d\nzemzy/jFMzu56H9f4619DakemkYzphCRHBGZm+pxaNKT/v6H2uDUjB3UIBL99JREctAOlgYw1GN+\n+Pi7vGduOd+8YF6qhzNimF6Wx23XLOOuT52C16+46ra3uPHhzbR09qV6aBrNqEdELgU2Ak8H/l4i\nIo+ldlSadOLNvfWAThHUjA1U2BNNqtAOloa27j6+fO96SvIy+fUVS3BrBZkBc9accp756ll87uyZ\n/GNdNe/7zSu8FOippdFohoybgVOAZgCl1EZgeqyVROQCEdkpIntE5EaH988SkfUi4hWRD9veu1ZE\ndgce11peP1lEtgS2+TvROTopwWpXluZlBZ/rFG7NmGAQjpWZTauzapODdrDGOEopvv3PrRxu6uKW\nj55Eie7zlDA5mW6+deEJPPql0xmXm8l1f1vDtx7ZTHuPN9VD02hGK16lVMtAVhARN/AH4EJgPnC1\niMy3LXYI+CRwr23dEuD7wAoMx+77IjIu8PafgOuBqsDjggEdiSbp5GS6g88LszNSOBKNZnhQyVAC\n1A5WUtAO1hjnvncO8/imo3ztfXNYPr0k1cMZFSysLOKxG07n82fP4oE1h7ngt6/q2iyNZmjYKiIf\nBdwiUiUitwBvxljnFGCPUmqfUqoXuB9YZV1AKXVAKbUZsHVV4v3Ac0qpRqVUE/AccIGITAQKlVKr\nlSHBdRfwgcEfnmaghM6+9/+Rn6270mgGTnefj7bukZPyr6NQ6YN2sMYwe2rb+MHj2zizqowvnD0r\n1cMZVWR53Nx44Twe/NxK3C7h6r+8xX8/8a5OU9FokssNwAKgB7gPaAW+GmOdSuCw5e/qwGvxEGnd\nysDzmNsUketFZK2IrK2rq4tzt5p4sRb3+y1Gps7X1CTC89uP8+IISvc3HauGjp4Br9vrM+aTBiOQ\noelHO1hjlF6vn68+sJG8LA+/umIxLl13NSQsm17Ck185k4+tmMrtr+/nklteZ3N1c6qHpdGMCpRS\nnUqp7yilliullgWex2pM5/RjF69FEWnduLeplLotMNZl5eXlce5WEy/WmfujzV39r6dgLJqRj88/\nsq4cn+UL0NzZG/d6VmEuHf1KDtrBGqP87oXdbD3Syk8uP5GKguxUD2dUk5fl4UcfOJG7PnUK7d1e\nPvjHN/n1szvp9dqzjzQazUAQkZdE5EX7I8Zq1YC1D8Vk4Gicu4y0bnXgeSLb1CQRbRxqxjJ+i0O4\nr74j7vX6/P32iP4KJQftYI1B1h1s5I8v7+GKZZN5/4IJqR7OmMFUGly1eBK/e3EPH/jDG+yoaU31\nsDSakczXgf8KPL6HIdm+NsY6a4AqEZkhIpnAVUC80u7PAOeLyLiAuMX5wDNKqWNAm4icGlAPvAZ4\ndOCHoxkskdKbtOMVmZbOPvbWtad6GJok4E0w4qZzmJJPUh0sEVmYzO1pkk97j5f/98AmKsflcNOl\nC1I9nDFHUW4Gv75yCbd+4mRq27q59JbX+ePLe/D6dDRLoxkoSql1lscbSqmvYSj8RVvHC3wZw1na\nDjyolNomIj8UkcsARGS5iFQDHwFuFZFtgXUbgf/GcNLWAD8MvAbwBeD/gD3AXuCpZB/vWOaxTUfj\nSq+O5Egp7WFF5OVdtWw9MiAxzjHHSLh+6tt78FvGmZPhpqs3vrpv69GNhGMdCSRbVufPgRnBvwH3\nKqV0sUma8dOntnO4qZMHP7eS/CytqpQq3r9gAsumjeO7/9rKz5/eydNba/jJ5SeyYFJRqoem0YwY\nArLpJi7gZCBmWF4p9STwpO21myzP1xCa8mdd7g7gDofX1wJ6knGIUEqxv76DRZOLUz2UlLKzpo3c\nTDdTSnKTsr2RVmOUKnx+hced3nGeN/YYTbULszNo7e5j1/E2dh1vY9WSeDV8NMkkqREspdQZwMcw\nctTXisi9IvK+ZO5Dkzhv7qnnnrcO8ZkzZmhJ9jSgND+LP35sKbdcfRJHm7u47Pdv8JOntsc946TR\naFiHkRK4DlgN/Cfw6ZSOSJNSlIJMd6hpk+F2jZq6kh01raw/1DQgAYNopNLBUkpxtLlrRERMfGk+\nRqtIRaZn4Ka99fDS+0hHDkmvwVJK7Qa+C3wTOBv4nYjsEJHLk70vTfy093j5r4c2M7Msj/88f26q\nh6MJICJcungSz3/tbD60tJJbX9nH+3/7Kq/vrk/10DSatEcpNUMpNTPwf5VS6nyl1OupHleqaGjv\nobqpM9XDSCq9Xj9rDjTGXK6z10tnrxe/Uogt0OASCRqQ3X0+WrpGTl+jSByxKCQmi+F2dA41drLm\nQCMHGtL/mvWneRZ/j7d/YtZ+/Td1xHbGrbWLae5LjhiSmiMmIouA64CLMRowXqqUWi8ikzBmFx9J\n5v408fOzp3ZwtKWLf3xuJdkZ7tgraIaV4txMfv7hxXzgpEq+88+tfPz2t7n8pEq+c/EJlOZnpXp4\nGk1aEWvCTik1Ju81q/c14PMrJo9LTvpYOrC/viNEbj0Sz717POJ7IkZfIJ9f8ebeetq6vVy2eBJi\nt0RHED1JUqE93trf1UCpcON8KOnuM47B6hykK+8ea+Hkaemb+eO2tNpx2T7EAw0djMvLjL4Bi1N1\nsKGD8gJtdwyWZEewfg+sBxYrpb6klFoPoJQ6ihHVCkFEpgRkdreLyDYR+Y/A6yUi8pyI7A78Py7J\n4xxTvLm3nrvfOsinTp/BMp0amNacNquMp/7jTL58zmwe33yU8379Cg+sORQivarRaLg0yuOSFI4r\npeh6GoPSvFDjsLvPh8+veGOP4VxB8hyUVHG4MTlRn/WHmoLP9dUTmeqm5EcMk4n1q1+WnxnxvUhY\nFxmK6OhYJNkqBxcBXUopH4CIuIDsQDPIux2W9wL/GYhyFQDrROQ54JPAC0qpn4rIjcCNGCmHmgHS\n0ePlmw9vZkZZHl/XqYEjguwMN19//1xWLZnEt/+5hW8+vIWH1x3hxx9cSNX4glQPT6NJOUqp61I9\nhnRGKTWiozODZUpJDg0dPcG/PS4XXr+fJkvdUo/Xr7M5bBgpgsN33USS1I+Xlq4+sjNcZHn052ie\ny6VTxzGhKJttR/tbwMST+qnTApNPsiNYzwM5lr9zA685opQ6ZolytWFI5lYCq4A7A4vdCXwgyeMc\nM/zs6R1UN3Xx8w8vIidT/wiNJKrGF/DA9Sv52YdOZFdtGxf97jV+8cwOuvvSP51CoxkuRORiEfmG\niNxkPlI9plQz1o2lHJvjlJcVfu8bCa0xalu7ORSlPqmurSfie4kw0i6bl3fW8vTWmlFRUzdYzBqx\ngmxPWIpgV5+P2rZuh7X6Gaizq5TicGPniBAoSRXJdrCylVLBbnWB53Elg4vIdOAk4G1gfKBxI4H/\nKyKsc72IrBWRtXV1dYMc+ujj7X0N3LX6INedplUDRyoul3Dl8qm88LWzuXTxJP7w0l7O/82rvLpL\nX+8ajYj8GbgSuAFj6v0jwLSUDioNGE0mT3uPd8DruF3C+fP71foz3OGmTrqrwoFRU7fhcFPE99/c\nm1wxpKE4JbuOtw15j62Nh3VHINNBEiSkHgugsaOX1Xsboq9v++wf3Xgk6mTu4cYu1h9qYm9dR2ID\nHgMk28HqEJGl5h8icjIQM5lTRPKBh4GvKqVaYy1vopS6TSm1TCm1rLy8PKEBj1a6+3x865EtTC3J\n5b/er1MDRzql+Vn8+ool3PuZFXhcwjV3vMNX7tsQc1ZKoxnlnKaUugZoUkr9AFiJ0SZkTFDX1sOj\nG4+EtXYYLbPKXp8/IVVEESHLIlXtcYWnvY3EU7T7eFtSt9dni+INNmXPie3HWtlb1x57Qc2gMOus\nJEGr3umTN+sVnej1Gb85yY6ijiaS7WB9FfiHiLwmIq8BDwBfjraCiGRgOFd/tyg/HReRiYH3JwK1\nSR7nqOf3L+5hX30HP/7gQp0aOIo4bXYZT/7HmXz1vVU8vbWG8371Cg+uOTxqDCqNZoCYE3idAbXa\nPmBGCsczrJjOh32iZUdNcg3xeOnz+cOM9sHgTVC0wyWhangepwjWCBQEefdY3PPPjnT1+mjr7k+n\nq7UZx6m6jUgCdV/DIfwUj3plumCeDzM9cHZF/oDWd7Ihojnc5uJDMcmrlGLT4eaQa3UkkuxGw2uA\necAXgC8CJyil1kVaXowq3NuB7UqpX1veegy4NvD8WuDRZI5ztLP9WCt/fmUvH1o6mTOrdGRvtJGd\n4ear753DU189k/kTC/nGw5v5/D3r4up1odGMMp4QkWLgFxgKtgeA+1I6omHETH3r8/lDDKRURQye\n2lrDk1uOpWTfVgQJEfmw12QB+MfgpNSz79bw4o7++WqfL/QcjKRTYk3xHCpZjnj6r6UL5ukwQDuc\nuAAAIABJREFUg7WzysMdLOtvxLGWLh7deCQoke/02afqemjt9nKgoYO1ByKnx44Ekt5oGFgOLMKo\np7paRK6JsuzpwCeAc0VkY+BxEfBT4H0isht4X+BvTRz4/IobH9lCUU4G3734hFQPRzOEzCrP577P\nnsq3L5rHiztqef9vX+W13bo2SzN2UEr9t1KqWSn1MEbt1Tyl1JgRubBGadIhIJPsSHqszT268Qjr\nDjoYYTaLe874cGMz3RvHDgf2CMVAUwS7+3w0RpnYs/a3coyQDOJy2W6J5iVbMFMp5RjhTOeopzlh\nYEawYqXF7qk1JmHabWmA1hYHqZqEGC0CqEl1sETkbuCXwBkYjtZyYFmk5ZVSryulRCm1SCm1JPB4\nUinVoJQ6TylVFfh/5EwjpJi7Vh9g0+Fmbrp0fuzGcpoRj8slXH/WLP71pdMpzMngmjve4Q8v7dEp\ng5oxgYhsEpFvi8gspVSPUmpoq+nTDOvXPJ2+87WtyUkbcjL439nfGHKsTjVadgPNKUVwb307j248\nktZGczwM5nO3rzrQTb2yqy7qpJ7Vie3oTZ76bWt3H/vr+8UVojl5ibD9WBtPbD4a9no6fcfsmM6Q\nee07XfPW0ZtNnj0uY7lgBMyyWqq/GkNREzicJDuCtQw4XSn1RaXUDYHHV5K8D00Eqps6+cUzO3nP\n3HIuWzwp1cPRDCMLJhXx+JfP4LLFk/jFMzv54t/X05GA+pZGM8K4DKOf4oMiskZEvi4iU1M9qOFA\nKWVJBZSUG0NWVu+LrlgWL0727LGWLnq8/qjGbjwT4K0Bae/eEd5wOF6RAaeaJdMoL883ohYDvYRi\ntQzxWjysfQNMW61t7Y7oqA9l/dWu423srk1NDeNgMM9ItHq2xo5evD4/++s76Ow17ANTFMN0ZtyW\n2Yl4Hcpkfx6jJICVdAdrKzAh5lKapKOU4nv/2grAjz6wcEw3mRyr5GS6+e2VS/jORSfwzLYaPvjH\nNzjcOHAFLo1mpKCUOqiU+rlS6mTgoxjp6ftTPKxhwf4bP9Jne52IdERKhQpgtNqK4ZN5/+vz+dO6\nvjXeY3WSpTdfmVhstC9NdoSmz1LjlZ/libic0yGs3tfA6n0NvLmnPuz8D2UgaXsUIZF0/oapYIpg\n/2t2ufY399az5kBTiONqnkszkutxS9h7Thxv7Xfse4ZoksLrS+czHptkO1hlwLsi8oyIPGY+krwP\njQOPbTrKSzvr+Pr5c5k8Lq7WY5pRiIjw2bNmctenVlDT0s3lf3qTd48OTnlKo0lnRGS6iHwDuB9D\nZOkbKR5SSkjj7KWEiSQy4FMqxPg6WB86kWQ1K6eV5g1qDOsONvHq7rqkqSPGq4xmrV8yKc4NT/uP\nt07GaTkzemdGLRK9hCI5Ztb0wU6HFMF4zmldew+v2tIQnfY2HKme6fwdMw/f2mT4kkWTOGVGaA/U\n+vaekPRB87MzHSbr+pGurcONnTR09DtYyZ7cMbfWFSNCmu5EnlJIjJuTvD1NHDR19PLDx99l8ZRi\nrj1teqqHo0kDzqgq46EvnMa1d7zDlbeu5rZrlrFyVmmqh6XRJBUReRvIAB4EPqKU2pfiIaWMdDb+\nEsVM47PjVyrEqO+zKVaYNuKqJZWDHoMZPUm04F8pFYwy7a1rZ+uRFs6eU+7oLFlxagzr5MjEK2Xv\nNPxdgb5a5vlK9BryK3DHCKQ5OYwdPcZr9khLLJzOQ5/Pj9s1NlvS+P0qGHlz2c5llif0nPiVCqlb\nPNTYSXefPyi3br3Otx9rY2pJbliUdJetH1uyfdvR8luWbJn2VzBkcjMCz9dgSOdqhpAfP7mdlq4+\nfnr5iQP+odKMXuaML+DhL5zGhKJsrr3jHZ7emnr5ZI0myVyrlFqqlPrpWHauRNJfdry+vWdAPXO8\nUaIbyh8asbCnQg+kr1K02feWzj56A+NI9PQ+tukomw43A1AbiBI4pVT1BWpjjrV00drdR4uDc+k0\nBmv9S3NnLzsj9ECzXh92B8U0ynsSjBjEuvYy3a6QiKPfr0KOzx1HmqOTg2Yl0Z5pAyFd03DbotRb\nZ2dEN/P313eERIrK8vtVBHu8Ph7bdJQjln5gfr+i3bY/8/pOGul5mgdMslUEPws8BNwaeKkS+Fcy\n96EJ5fXd9Ty0rprPnT2TEyYWpno4mjRjUnEO//j8ShZWFvKlezfw783aydKMHpRSO1I9hnSgp88f\nZpPUt8cnfjBcvLGn3jEqE4lo6UF+pULqe+w42etOvbDAcFrq23s4YFGlM3l5V3/PqME4sAcajG2b\nzpqThPY7+xvZXN3MO/sb2W5L6zadSXutmX1cr+yqY0eNc0q41SG1H4rp4Kze1+CoyuiEP8r27ORk\nukMcoG1HW3l5Zy1dfYahvqk6toH+9NaaoJPl5EtFc8hHO9Fq57I9A4vqOU3Sb6nuF2e1R4sh+b81\n6erIDpRk12B9CaO3VSuAUmo3UJHkfWgCdPX6+PY/tzCzLI8bzq1K9XA0aUpxbiZ3fXoFS6cW85X7\nN/D4pnD5WY1GM3LZXdsWFvF4Y099ikaTHEwZaSf8SnGspSvi+wPB61e8saeeTdXN+P2KI81dYTP0\nxj4Hvm274dsXiFytcWigajVS7fVEW4+0RDxep3E5GdzRxm+1qRva4xP0sDpFsZzPopwMWrv6guOq\nD9TvtHUPTOnWvCYGkyoZC2sfKDvpGiSONi57ymAsnEVTYjvTyRRISdfzPFCS7WD1KKWC304R8TBq\ngn3px2+f38Whxk7+5/ITyY4wO6fRgKHg9LfrTuHkqeP4j/s38OjGI6kekkajSSJO4gk+v2L38bak\nCTQMlGe21bDZFp2IV4zAarAtmlwcYvhtO9oa0gfJTrSMswWTCkPuly/v7I9S9fn9rD3QyEs7asPW\nS0REwW4omrLlPV4fb0ZxgOtsEYGDjZ3UtDinVzqNK5bTFfa25XzFe5RWR8zJILburyQvk16fv1/o\nIkGr0NymoyJikixNl4NVPKs8vFF1OnEwhlpwNKfRjtNXx3o9RTrPyRSkGC1OQ7IdrFdE5NtAjoi8\nD/gH8HiS96EBNlc385fX9nH1KVM4daYWL9DEJi/Lw1+vW87y6SX8vwc2aidLM+IRkVwR+Z6I/CXw\nd5WIXBLHeheIyE4R2SMiNzq8nyUiDwTef1tEpgde/5iIbLQ8/CKyJPDey4Ftmu8Na/aGQ+YOL++s\n5d1jrVGlp4eS7j4f++s7QqJr247G1wvaakTnZbo5YUJB8O+mTucoS2F2BmfPKQ8r7Id+Bb4pJblk\neZxNH/McOkVkEpFqt2/FGmWxO1FRt6MUhyIY0c7RqoFFsKw1a/FGIqyfj9P+1h40onSVxTnBz8OM\nWNmXL8mLLvgR3KffEGg40hQezUtWWpnL5p0vmVIcVWI+HTjYEHmyAWDOhH4H0X588eCP8VkDbD3S\nGrMvWrxYr0H7BM1IItkO1o1AHbAF+BzwJPDdJO9jzNPn8/ONhzZTlp/FjReekOrhaEYQppN1ygzD\nyfrXBu1kaUY0fwV6gJWBv6uBH0VbQUTcwB+AC4H5wNUiMt+22KeBJqXUbOA3wM8AlFJ/V0otUUot\nAT4BHFBKbbSs9zHzfaVUeBhkCLHKJpuYqW7R6pWGg6OWIvlokScrdocgngDS8hklEdX5lk4t5swq\nw/mKJAYVrelwtDqhjh4vGw83h9UB2Y1Re7Qp0QatK2eVsmpJJZluF9VNXcH0QTPK5yiGEUXkIpG2\nYUU5Gf3bc3jf/MxFjBos6K8hs39G8Z4GvzJk862iC6fNKos8iAQwT01mQMpcqcGrLKYaa8Q2M8Lk\ngomTA+XzK7YeaYn4PhgNwN/e79xWYaBY9xDv70U6kmwVQb9S6i9KqY8opT4ceD5CL8n05bZX97Gj\npo0ffWBhyI+cRhMPuZke7vjkclbMKOVrD27UNVmakcwspdTPgT4ApVQXzlkuVk4B9iil9gVS2u8H\nVtmWWQXcGXj+EHCehBcnXA3cN5jBJ5PGNGuGa731O4k6xMLqfPgVcd3rokUaPG5XMFISSbWu1+Ig\nDSQlcOPhZg42dNBqqymyWj9OGQOJGkcVBdkAZGW4aO3u4x2bYetkBFtfMp8WZmcwqTgn5AsT72GP\nszhJ0WuwhNyAg2VGT+zXg88p/OqAk0KiuanV+xrCzkMiKBTjcjODzZdHEisjZDNZhS5iRZnMjzIv\nM/S7tLeunfr2nqjXbKIqlJHG0P936At769p5e1/8gjmpItkqgvtFZJ/9kcx9jHX21Lbzvy/s5uIT\nJ3L+ggmpHo5mhJKb6eH2Ty5j2bQSvvrARp7aotUFNSOSXhHJIWAzisgsjIhWNCqBw5a/qwOvOS6j\nlPICLYDdermScAfrr4H0wO85OGQExni9iKwVkbV1dXVOi4wKrCIVEU5FVOxG+4Si7DAD0prqNy5G\nXykrESNYFgfric3xTzyZ6nZhEaoY88uDldbv9fav7/OroKMUqyYq+BrGOhJHc1k70VQJ7fs1Havj\nrd2B/YYSb4TVKUpr/SyTIXxS19ZDn8/ffy7pT6EcDnW77j6fo8hKPES6rjNiNClTDimApfmZYemE\nb+ypj9ibLpnYz7OZWtvc2UtLZx9bj7RQ0xp/y4dUkewUwWXA8sDjTOB3wD1J3seYxe9XfOuRzeRk\nuLn5sgWpHo5mhJOb6eGO65azZEoxN9y3gWe31aR6SBrNQPk+8DQwRUT+DrwAfCPGOtFlsuJYRkRW\nAJ1Kqa2W9z+mlDoR4953JkYKYfhGlLpNKbVMKbWsvLw8xlDjx6nuaDixqxiuPdgfTfDGGaGwYvVV\ninON6FWeLUJVXtBfvH/aABqpN0SI9vVFSRGEyPVJpqNjd06OxzACB+tgWZ0cr98fTGWLVYNlvu33\nG85VSAQrzhBWtJRDK4aDYhBJzjtaamYsBtLzLBZmnV17j5eZ5XlkZ7iZWJQdM0VwT2076w6GK0Mm\nwjPbanhh+/GE1o00kRFrgsMa/TaPUUQcI8/Wzyo7w82qJZUDEtGIB/t53na0FaUUr+yqC2mdkO4k\nO0WwwfI4opT6LXBuMvcxlvn72wdZc6CJ710yP+TGotEkiqEuuJwFlUV86d71vLgjsR92jSYVKKWe\nAy4HPokRTVqmlHo5xmrVwBTL35MBe7giuExADbcIsOYfXYUteqWUOhL4vw24FyMVcUi56MSJweex\nGrEebOiIW2AiXurbe4LGtVWND6Ddki7X5w21mOIx4k0D/v0LJgRrSMK84IDhOLUkF487fnPGVFWc\naxHOgNAIlhOPRUinNh1IewTLWivkxLHmwc3CW2f6a1t7ghEHp7Mb4hAFllAY9UXjLCIT8aZGhgof\nRFnOr8JqvOwOmV+pkB5fLZ3xR0kkiVasNWJTkJ0Rcu050dHjZV9dO9uOtsTdPywatYOMyiSQiQuE\nXqfm8RZkexy/U9bP2oyMmZGzZMX37A7WwYYORwc2Veqo8ZLsFMGllscyEfk8UBBzRU1MjjR38dOn\ndnBmVRkfWmrPZtFoEqcgO4O7PnUK8yYU8vm71/PKrtGbtqQZHVjvNcA04BiGkzQ18Fo01gBVIjJD\nRDIxnKXHbMs8BlwbeP5h4EWznlhEXMBHMGq3zPF4RKQs8DwDuATYyhCTMQCnYuPhZvbUtickN+7E\nsZYu3thTH7EI3eqs7KtvD3nPHu1ywnTCrMeYaTte0yA2RRTiZVKgvsaeAtXj0HsrKKIQBfOc7q5t\nj7FkKPbzMlCshqhVWdGxBsthfb8lfa//tfj2bV0uViTOHkFxWvpVy32n3iEVEMLFMSA81BxroiEa\nsZw1+7jf2FPPliPJm7RYPci6omRE8yYUZXParDJmluU51saZ53dScQ4rZhhRY0+MFMSB4pSK6TRZ\nsft4O2sONKato5Vs7clfWZ57gQPAFUnex5hDKcV3/7kFBfzPB09MKJ9do4lGUU4Gd3/6FD76l7e5\n/q613PHJ5Zw+O7ZhodGkiF9FeU8RJXNCKeUVkS8DzwBu4A6l1DYR+SGwVin1GHA7cLeI7MGIXF1l\n2cRZQLVSylpfnAU8E3Cu3MDzwF8SOK4hwTq73tnrpSB7YOJIPr9ic3Uz8ycVBlMRzZ5GBxs6HcUH\novHq7jpOnjaOyeNyIy5jGvDWWXm7ApopVjFQw9IUXbCv5eTwmOmJ0RARlFI02+TjC7IyqGsLdRam\nl+ZxICCr7U1A3XHZ9JLgc+vaeVmeqDVYfoeaKaX667bmTShkR00r+dnxmYVWR72920tZfvxZNU7j\ns27P7kibOKVw2u2hp7fWcNniSQnZSZH8xEibSlZz48EQEg2Mcsjvmz+eurYeNh421DAnFuVErFkz\nM6R6HM733jrj2l0wqZDcgBCG6aQPRqbd51c89+5xTppaHLda4966dvzKECWZXZF+vcqS6mAppc5J\n5vY0Bo9tOspLO+u46ZL5TCmJfEPSaAZDcW4m93xmBR/9y1t8+s41/PWTp7ByAHUNGs1wMdh7jVLq\nSYw2ItbXbrI878aIUjmt+zJwqu21DuDkwYwpUc6ZV8He2vZgnyTT2I9EAuVQHGzo4FBjJx6XixMn\nF4W81+rQ4DgeWru8MC7y+36ljPqgKIZyojPnnkA32XjSCjPcLkrzshwFFuzk2NLJ7A7h+MJsFk0u\noqPXS11bTzDyM5Co4sTCbMfX+3x+S61QdBVB62umcTx3QgF769rjVny07mNTdTNTS3JxxZ2jFv14\n7dupqijgYEMHHb3h4g9Oe+zx+qOm9kUcVQzLfiCi2N19PnbUtHFiZVFE8QkricqRWyPF0XzK3EwP\nGe7+72o8giDvmz+e594NLRvIyXDT2esNOleQmEqona4+Hz1eH2/tawiZRIiG+f3p9fo51NDJ1NL0\nso+T6mCJyNeiva+U+nUy9zcWaGjv4ebHtrFkSjHXnjY91cPRjHJK8gwn6+rbDCfrzk+dwvI4f+w0\nmuFGRLKBLwJnYFhtrwF/DjhIY4LC7AwKLFGHM2aX8druyGm+iQlOGIaMVd1sqBuw+Pwqopw6EBL9\nGmiwwpztnlaSG1cj02jqcS/trA0a3nZncEdNaIPnGWV5iAileVnUtfUE0x+jSU4vmVIcjDoY+7CM\ny/IhGHVuxptO/po1ja+jx0t9ew9+Fbo9l8QvvOFXhqNqXk+Pbz7Kihml5Ga5KYwRIVXKkAHPzzai\nbnZFOF8gsveeuRXkZ3lwu4Renz+soe775o933H6fLzEHK1JEyvxcB9JPbtvRVqqbOinNy4w5Ma6U\nSrih7ubq/hTFWF+DgYqq5GZ6KMrJCEnp7e7zhbVDiMeBjIX1u25e1+fOq+DFHbFFLXbXGhH0isKs\nhD73oWIoVAS/gCFxWwl8HqORYwG6FmvAKKX4zj+30tHj4+cfXpSUi1ijiUVZfhZ//+wKJhRmc+0d\n7/DGnvpUD0mjicRdwALgFuD3GPebu1M6ohTQ1dvvNI2LkdLmS8AzMqNjtW3dPLrxyIBqHiI1/o3l\nFBnRlcjvL5lSTOU4o5ZqYpFzVCcSbpcwd0JB3BGXaAEmq2x1rEiUubc54w0Hz+zLVRdBXQ8IiRSA\nsyJcpttFryWCZX5eVqwje31PPesONjk428L++o6gml40fH4VTLU0eXt/Ay/tqI0pM64AlwtOnVka\nIrBhYqZqZnlcQbunw2GbuZkex/TQRFIvgeC97oSJhSGvdwXSYTcdDnWCkmWRJTJZcbChg5bOvpAm\n3rHSIhPZj32bfqXCPt9k1GBZJzHMy3KgaZ5WB7K6qTPltVnJdrDKgKVKqf9USv0nRsrEZKXUD5RS\nP0jyvkY9/9p4hKe31fC18+cwZ7z2TzXDR0VBNvddfypTxuVy3V/X6D5ZmnRlrlLq00qplwKP64E5\nqR7UcGM1eJyMEuvkXCIpgm22BrotXX0R664uWzwp5O88ixEeK7JhpdfnC0uxA8P4Lcg2ohqF2Rms\nWlI54JoyK9Ei9PZmqxBdATHeCIGIUJDtieiQzRlfwNlzyiM2jrWT4XaF1FPZIz3RxnbAsqy5zKtR\nIqBg1PHVtnVHNKyj1eKYxxzsLeUwLDNiEk80wqnH02Bro+yOo+mIxkqHHUgKoRWnSY9o19nx1m42\nHm4OkyyPFvG1U+jQuPuceRVhr8UzB1E+gPq7SFhPQa/PuH4G6raZEcaWrj7WHWwKc4iHm2Q7WFMB\n69RHLzA9yfsYExxt7uKmR7exbNo4PnvmzFQPRzMGGV+YzYOfW8nCykK+dO967nvnUKqHpNHY2SAi\nwXqoQH+qN1I4npRg1kWZql7RGGzvJZNIqYZ2B8/q3E0ORJyM5aJvv73H52hgzxlfwLnznFPDEmFS\ncQ4XW+TurVQUGoaj9Zwdae4K9gKyG9RODlNIOpXlmEXEMTJ2yaJJnDCxkOLcTCoKsykvyApGuuyY\nMvNul7Gtrjgcm2ivx+uYbDhkGK5t3V6mleaFvR/tEnti81GjP1jgXMwoM9a39lIqzMlggq3WLNL1\n4lRHl6ij079+6N/xTkq09Xipbe3mzb31DES03Gm4r0XJHHkrQkqpawAW/cnTwgsgnSZA4hGQKc3P\noqIgOyRVeaBYnUwz8OQSCWulEI26tu7A+sa2on0fhoNkO1h3A++IyM0i8n3gbYwUDs0A8PsV//XQ\nJnx+xa+uWKxTAzUpoyg3g3s+s4Izq8r51iNb+NWzO+NuRKnRDAMrgDdF5ICIHABWA2eLyBYR2Zza\noQ0f+VkeVi2pZEKEVDmrET3c314zvQqcmyF39Hh5YvPRsKhHV693UAbbQPC4XY51MmaNVGdP/9jW\nH2pi/SGjJ4/9p9DuvGZ5XCE9K63GqhDuCEwozHa83093cGLAUP5btaQSJLZTsf1Ya9T3cRiPE129\nvmDDYJc4m9/W7dhTHMG4Hs31Mj0uinMzbVFWFXYeohn6RbZoTCIRLGsU2O6MRpqUsDt9fV4/7xxo\npK6th4Fkpzltv7mz1/HzqG2LXF4aK4Jl3ZxdkCUS8QbFMj0S5ii2dffF7exusdSSmZM3IgNLawz2\ngRvqAtE4SXaj4R8D1wFNQDNwnVLqf6KtIyJ3iEitiGy1vFYiIs+JyO7A/1G0hkYfd60+wBt7Gvju\nxfMdZ4c0muEkN9PDX65ZxhXLJnPLi3v4/D3rHPPhNZoUcAEwAzg78JgBXITRh+rSFI4rbUmG8SGE\nG7VgSD/bmT+pv57F7bY6GMbzV3fV4fMrXthei9fnDzZbVSo5fX3iZenUcWHRt9J8I3Jkj9YdD4zR\nyTC2Ooo9Xn9InymJEcHKy3J2KCM5ziYukYQd54HIqwMhfRJd4uywe/2KnAw3EiUCYT3XxnasEYxw\nByvaPPPy6SWcMLGQ98ypCK4/UF7Z2X9c9rqweKO+PqUsqY+Di2BFen313siCKAOZjM9wu3jvCeOp\nLA7/zlqJf4tCe4+XrUdaUIHG0S/uqOXdY61xTcrWW+oQrV+3WeVGvWI8aYjpNveb7AgWQC7QqpT6\nX6BaRGbEWP5vGDdJKzcCLyilqoAXAn+PCbYdbeF/ntrBOXPLufqUKakejkYDGLOMP/vQIm66ZD7P\nbz/Oh/70JocdCqk1muFEKXUQaAWKgFLzoZQ6GHhPY6O9xxuzX43dOHQy3JxqvZZOLQ57rTg3k5wM\nN7PK80O2a65uykx7/X42Hm5m9b4GHt90FEX8s+fJ4vz544MS7jPL8qkoiO7YWA1vs16roaOXw42d\nliiXs9VndyogXNbdJMPt4rLFk7h00STH96Hf6bOOJR7mRXCAlFLsrQtvTG1t5Gs4ieHH5/Upuvp8\nTBmXEzwme1Ns67XgktDoh1+FO1izovQ5ysvyMGd8QXBfOyLUB/Z6/RGFD0wnelZ5ftjkgalY6VS3\nZMXnV8FrdiDG/gGHmjmAbq+PhigCKHZiilwErjfTqc7L8sSURHc6jBMri8JeMz+uvXXttHb3/8bs\nqW1n69GBNWO2RrAyPS6KcjLiEqSxX4vDOUHjRFIdrEBa4DeBbwVeygDuibaOUupVjEaOVlYBdwae\n3wl8IInDTFs6erzccO8GxuVm8MuPLNYNhTVphYjwqTNm8LfrTuFocxcX/e41/r1Zi19oUoeI/Dew\nGfgdRvPhXwG/TOmg0ohLFk0KM7Z31rTxzLYann/3uKOx+fruep7cUhPympOPYE1HmlScwwULJ0Ts\nK3X+ggksrCyKOVt+JKCI5lcqabViAyE7w01ulpE6NTWOnpPWIZrrdff5WH+oKTgBZTXWrXd0wQj/\nWFMoo/UTEpGIRmbPIGpNItkZj206ytYjLUEJbCeUUo7RIrP2xVoDY3eYrNLf2Rlu6tt7gufM5yck\n8gdQGqEOzUpOQJwiUmrpU1uP8eSWYyHOqB2nOqSSvMzgREEooWO0qhcOJIIVSbXxtd31vL6nPq5t\nnXdC/HWJ9kjpGbPLYva8NCNJgGODcHtE0npdROvxpZQK1jSadPSYIhcS3HY8p9PcZ7oEspIdwfog\ncBnQAaCUOkpi8uzjlVLHAts4BoRLm4xCvvevrRxo6OB/rzqJ0iSosmg0Q8FZc8p54oYzmVWez5fu\nXc+3HtkcYiRoNMPIFcAspdR7lFLnBB7npnpQqeaM2WWsmFGK2yWcUVXmuExHr5dGB8OuoaMnLCXO\nydmxvlZRkBVSXxXJaLe+Hmv60NoEdzgxjWSrQt458yrC6qCUUkGjL8vjCqYY2o3FDHe/1LjY0gUV\nocp0OZmJ9fCxF/M7fV5FDsIR5nFEw+ivFRmnVFHzHFhTRjOjNHU2HRcz6udziGDFO+Gc5XGHiaMo\npYLOOxgiEdZInHWskZrVuqRf2W/38TYONXSGOcTW2rJo0vt2JlomHlYtqWTxZCMSbEaB4omG2XtT\nORHJATVFKpwwLw+r0IpTRLuuzZLip8LTNCNFDnfXtvPU1tCJWrOpt/mRN3f2OtaeWSdB3C7B51e0\ndfeFjGX38TbH37nhINkOVq8yvq0KQESGtIBIRK4XkbUisrauLrqsaLrz0LpqHtlwhK+OKxb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dpgTRG86MSJLJ0a+X5vNTqXJjEVMpKzOiGBrJlIEYFoV3a/8zlwLykZ0beBfO3MuikzdS3WZWht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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, [nu, sigma]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we plot the distribution of volatility paths by plotting many of our sampled volatility paths on the same graph. Each is rendered partially transparent (via the `alpha` argument in Matplotlib's `plot` function) so the regions where many paths overlap are shaded more darkly." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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FREREFhwFRRFpSfEBqigm411PlRRFREREpqOgKCItKYwTSr7r6SxukJGtUZy1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dPcnchVE8NpB0FQ+0/+5qZhNgFJnxUmeipZvhrrxAp/PpbsVCYg7pfkv7UVKTIQj+5Ju+eyqe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(15, 8))\n", "returns.plot(ax=ax)\n", "ax.plot(returns.index, 1/np.exp(trace['s',::5].T), 'r', alpha=.03);\n", "ax.set(title='volatility_process', xlabel='time', ylabel='volatility');\n", "ax.legend(['S&P500', 'stochastic volatility process'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the model correctly infers the increase in volatility during the 2008 financial crash. Moreover, note that this model is quite complex because of its high dimensionality and dependency-structure in the random walk distribution. NUTS as implemented in PyMC3, however, correctly infers the posterior distribution with ease." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Case study 2: Coal mining disasters\n", "\n", "Consider the following time series of recorded coal mining disasters in the UK from 1851 to 1962 (Jarrett, 1979). The number of disasters is thought to have been affected by changes in safety regulations during this period. Unfortunately, we also have pair of years with missing data, identified as missing by a NumPy MaskedArray using -999 as the marker value. \n", "\n", "Next we will build a model for this series and attempt to estimate when the change occurred. At the same time, we will see how to handle missing data, use multiple samplers and sample from discrete random variables. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "disaster_data = np.ma.masked_values([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n", " 3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n", " 2, 2, 3, 4, 2, 1, 3, -999, 2, 1, 1, 1, 1, 3, 0, 0,\n", " 1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n", " 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n", " 3, 3, 1, -999, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n", " 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1], value=-999)\n", "year = np.arange(1851, 1962)\n", "\n", "plt.plot(year, disaster_data, 'o', markersize=8);\n", "plt.ylabel(\"Disaster count\")\n", "plt.xlabel(\"Year\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Occurrences of disasters in the time series is thought to follow a Poisson process with a large rate parameter in the early part of the time series, and from one with a smaller rate in the later part. We are interested in locating the change point in the series, which perhaps is related to changes in mining safety regulations.\n", "\n", "In our model, \n", "\n", "$$ \n", "\\begin{aligned} \n", " D_t &\\sim \\text{Pois}(r_t), r_t= \\begin{cases} \n", " l, & \\text{if } t \\lt s \\\\\n", " e, & \\text{if } t \\ge s \n", " \\end{cases} \\\\\n", " s &\\sim \\text{Unif}(t_l, t_h)\\\\ \n", " e &\\sim \\text{exp}(1)\\\\\n", " l &\\sim \\text{exp}(1) \n", "\\end{aligned}\n", "$$\n", "\n", "the parameters are defined as follows: \n", " * $D_t$: The number of disasters in year $t$\n", " * $r_t$: The rate parameter of the Poisson distribution of disasters in year $t$.\n", " * $s$: The year in which the rate parameter changes (the switchpoint).\n", " * $e$: The rate parameter before the switchpoint $s$.\n", " * $l$: The rate parameter after the switchpoint $s$.\n", " * $t_l$, $t_h$: The lower and upper boundaries of year $t$.\n", " \n", "This model is built much like our previous models. The major differences are the introduction of discrete variables with the Poisson and discrete-uniform priors and the novel form of the deterministic random variable `rate`." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as disaster_model:\n", "\n", " switchpoint = pm.DiscreteUniform('switchpoint', lower=year.min(), upper=year.max(), testval=1900)\n", "\n", " # Priors for pre- and post-switch rates number of disasters\n", " early_rate = pm.Exponential('early_rate', 1)\n", " late_rate = pm.Exponential('late_rate', 1)\n", "\n", " # Allocate appropriate Poisson rates to years before and after current\n", " rate = pm.math.switch(switchpoint >= year, early_rate, late_rate)\n", "\n", " disasters = pm.Poisson('disasters', rate, observed=disaster_data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The logic for the rate random variable,\n", "```python\n", "rate = switch(switchpoint >= year, early_rate, late_rate)\n", "```\n", "is implemented using `switch`, a Theano function that works like an if statement. It uses the first argument to switch between the next two arguments.\n", "\n", "Missing values are handled transparently by passing a `MaskedArray` or a `pandas.DataFrame` with NaN values to the `observed` argument when creating an observed stochastic random variable. Behind the scenes, another random variable, `disasters.missing_values` is created to model the missing values. All we need to do to handle the missing values is ensure we sample this random variable as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unfortunately because they are discrete variables and thus have no meaningful gradient, we cannot use NUTS for sampling `switchpoint` or the missing disaster observations. Instead, we will sample using a `Metroplis` step method, which implements adaptive Metropolis-Hastings, because it is designed to handle discrete values. `PyMC3` automatically assigns the correct sampling algorithms." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Assigned Metropolis to switchpoint\n", "Assigned NUTS to early_rate_log__\n", "Assigned NUTS to late_rate_log__\n", "Assigned Metropolis to disasters_missing\n", "100%|██████████| 10500/10500 [01:11<00:00, 146.76it/s]\n" ] } ], "source": [ "with disaster_model:\n", " trace = pm.sample(10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the trace plot below we can see that there's about a 10 year span that's plausible for a significant change in safety, but a 5 year span that contains most of the probability mass. The distribution is jagged because of the jumpy relationship between the year switchpoint and the likelihood and not due to sampling error." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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5wTsS3dv2dPbn1AXxucO9bDvUw0vXtbOns5+FTXX0Do1MmZ/KP0YsoatvmNqq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j/wDkCK1tdyG1bVMeAh4EeAn8bbMItS2/QSR/Ex/WnRMXWr6sc87t8YY0zrsuuWMU1kDSxjqvco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\nAXwW+GBcS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tU7EjG4gtHbivPKjmq7+m7MKNTW5Y55HJ5f0xAlunAswBKRDwF/Bu72PVQO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Arbitrary deterministics\n", "\n", "Due to its reliance on Theano, PyMC3 provides many mathematical functions and operators for transforming random variables into new random variables. However, the library of functions in Theano is not exhaustive, therefore Theano and PyMC3 provide functionality for creating arbitrary Theano functions in pure Python, and including these functions in PyMC models. This is supported with the `as_op` function decorator.\n", "\n", "Theano needs to know the types of the inputs and outputs of a function, which are specified for `as_op` by `itypes` for inputs and `otypes` for outputs. The Theano documentation includes [an overview of the available types](http://deeplearning.net/software/theano/library/tensor/basic.html#all-fully-typed-constructors)." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "import theano.tensor as tt\n", "from theano.compile.ops import as_op\n", "\n", "@as_op(itypes=[tt.lscalar], otypes=[tt.lscalar])\n", "def crazy_modulo3(value):\n", " if value > 0: \n", " return value % 3\n", " else :\n", " return (-value + 1) % 3\n", " \n", "with pm.Model() as model_deterministic:\n", " a = pm.Poisson('a', 1)\n", " b = crazy_modulo3(a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important drawback of this approach is that it is not possible for `theano` to inspect these functions in order to compute the gradient required for the Hamiltonian-based samplers. Therefore, it is not possible to use the HMC or NUTS samplers for a model that uses such an operator. However, it is possible to add a gradient if we inherit from `theano.Op` instead of using `as_op`. The PyMC example set includes [a more elaborate example of the usage of as_op](https://github.com/pymc-devs/pymc3/blob/master/pymc3/examples/disaster_model_theano_op.py)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Arbitrary distributions\n", "\n", "Similarly, the library of statistical distributions in PyMC3 is not exhaustive, but PyMC3 allows for the creation of user-defined functions for an arbitrary probability distribution. For simple statistical distributions, the `DensityDist` function takes as an argument any function that calculates a log-probability $log(p(x))$. This function may employ other random variables in its calculation. Here is an example inspired by a blog post by Jake Vanderplas on which priors to use for a linear regression (Vanderplas, 2014). \n", "\n", "```python\n", "import theano.tensor as tt\n", "\n", "with pm.Model() as model:\n", " alpha = pm.Uniform('intercept', -100, 100)\n", " \n", " # Create custom densities\n", " beta = pm.DensityDist('beta', lambda value: -1.5 * tt.log(1 + value**2), testval=0)\n", " eps = pm.DensityDist('eps', lambda value: -tt.log(tt.abs_(value)), testval=1)\n", " \n", " # Create likelihood\n", " like = pm.Normal('y_est', mu=alpha + beta * X, sd=eps, observed=Y)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For more complex distributions, one can create a subclass of `Continuous` or `Discrete` and provide the custom `logp` function, as required. This is how the built-in distributions in PyMC are specified. As an example, fields like psychology and astrophysics have complex likelihood functions for a particular process that may require numerical approximation. In these cases, it is impossible to write the function in terms of predefined theano operators and we must use a custom theano operator using `as_op` or inheriting from `theano.Op`. \n", "\n", "Implementing the `beta` variable above as a `Continuous` subclass is shown below, along with a sub-function." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "class Beta(pm.Continuous):\n", " def __init__(self, mu, *args, **kwargs):\n", " super(Beta, self).__init__(*args, **kwargs)\n", " self.mu = mu\n", " self.mode = mu\n", "\n", " def logp(self, value):\n", " mu = self.mu\n", " return beta_logp(value - mu)\n", " \n", "\n", "def beta_logp(value):\n", " return -1.5 * np.log(1 + (value)**2)\n", "\n", "\n", "with pm.Model() as model:\n", " beta = Beta('slope', mu=0, testval=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If your logp can not be expressed in Theano, you can decorate the function with `as_op` as follows: `@as_op(itypes=[tt.dscalar], otypes=[tt.dscalar])`. Note, that this will create a blackbox Python function that will be much slower and not provide the gradients necessary for e.g. NUTS." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generalized Linear Models\n", "\n", "Generalized Linear Models (GLMs) are a class of flexible models that are widely used to estimate regression relationships between a single outcome variable and one or multiple predictors. Because these models are so common, `PyMC3` offers a `glm` submodule that allows flexible creation of various GLMs with an intuitive `R`-like syntax that is implemented via the `patsy` module.\n", "\n", "The `glm` submodule requires data to be included as a `pandas` `DataFrame`. Hence, for our linear regression example:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "# Convert X and Y to a pandas DataFrame\n", "import pandas \n", "\n", "df = pandas.DataFrame({'x1': X1, 'x2': X2, 'y': Y})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model can then be very concisely specified in one line of code." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using ADVI...\n", "Average Loss = 164.12: 5%|▌ | 10845/200000 [00:01<00:21, 8809.19it/s]\n", "Convergence archived at 11100\n", "Interrupted at 11,100 [5%]: Average Loss = 220.44\n", "100%|██████████| 1000/1000 [00:01<00:00, 831.50it/s]\n" ] } ], "source": [ "from pymc3.glm import GLM\n", "\n", "with pm.Model() as model_glm:\n", " GLM.from_formula('y ~ x1 + x2', df)\n", " trace = pm.sample()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The error distribution, if not specified via the `family` argument, is assumed to be normal. In the case of logistic regression, this can be modified by passing in a `Binomial` family object." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "from pymc3.glm.families import Binomial\n", "\n", "df_logistic = pandas.DataFrame({'x1': X1, 'y': Y > np.median(Y)})\n", "\n", "with pm.Model() as model_glm_logistic:\n", " GLM.from_formula('y ~ x1', df_logistic, family=Binomial())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a more complete and flexible formula interface, including hierarchical GLMs, see [Bambi](https://github.com/bambinos/bambi)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion\n", "\n", "Probabilistic programming is an emerging paradigm in statistical learning, of which Bayesian modeling is an important sub-discipline. The signature characteristics of probabilistic programming--specifying variables as probability distributions and conditioning variables on other variables and on observations--makes it a powerful tool for building models in a variety of settings, and over a range of model complexity. Accompanying the rise of probabilistic programming has been a burst of innovation in fitting methods for Bayesian models that represent notable improvement over existing MCMC methods. Yet, despite this expansion, there are few software packages available that have kept pace with the methodological innovation, and still fewer that allow non-expert users to implement models.\n", "\n", "PyMC3 provides a probabilistic programming platform for quantitative researchers to implement statistical models flexibly and succinctly. A large library of statistical distributions and several pre-defined fitting algorithms allows users to focus on the scientific problem at hand, rather than the implementation details of Bayesian modeling. The choice of Python as a development language, rather than a domain-specific language, means that PyMC3 users are able to work interactively to build models, introspect model objects, and debug or profile their work, using a dynamic, high-level programming language that is easy to learn. The modular, object-oriented design of PyMC3 means that adding new fitting algorithms or other features is straightforward. In addition, PyMC3 comes with several features not found in most other packages, most notably Hamiltonian-based samplers as well as automatical transforms of constrained random variables which is only offered by STAN. Unlike STAN, however, PyMC3 supports discrete variables as well as non-gradient based sampling algorithms like Metropolis-Hastings and Slice sampling.\n", "\n", "Development of PyMC3 is an ongoing effort and several features are planned for future versions. Most notably, variational inference techniques are often more efficient than MCMC sampling, at the cost of generalizability. More recently, however, black-box variational inference algorithms have been developed, such as automatic differentiation variational inference (ADVI; Kucukelbir et al., in prep). This algorithm is slated for addition to PyMC3. As an open-source scientific computing toolkit, we encourage researchers developing new fitting algorithms for Bayesian models to provide reference implementations in PyMC3. Since samplers can be written in pure Python code, they can be implemented generally to make them work on arbitrary PyMC3 models, giving authors a larger audience to put their methods into use." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "Patil, A., D. Huard and C.J. Fonnesbeck. (2010) PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical Software, 35(4), pp. 1-81\n", "\n", "Bastien, F., Lamblin, P., Pascanu, R., Bergstra, J., Goodfellow, I., Bergeron, A., Bouchard, N., Warde-Farley, D., and Bengio, Y. (2012) “Theano: new features and speed improvements”. NIPS 2012 deep learning workshop.\n", "\n", "Bergstra, J., Breuleux, O., Bastien, F., Lamblin, P., Pascanu, R., Desjardins, G., Turian, J., Warde-Farley, D., and Bengio, Y. (2010) “Theano: A CPU and GPU Math Expression Compiler”. Proceedings of the Python for Scientific Computing Conference (SciPy) 2010. June 30 - July 3, Austin, TX\n", "\n", "Lunn, D.J., Thomas, A., Best, N., and Spiegelhalter, D. (2000) WinBUGS -- a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10:325--337.\n", "\n", "Neal, R.M. Slice sampling. Annals of Statistics. (2003). doi:10.2307/3448413.\n", "\n", "van Rossum, G. The Python Library Reference Release 2.6.5., (2010). URL http://docs.python.org/library/.\n", "\n", "Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D. (1987) “Hybrid Monte Carlo”, Physics Letters, vol. 195, pp. 216-222.\n", "\n", "Stan Development Team. (2014). Stan: A C++ Library for Probability and Sampling, Version 2.5.0. http://mc-stan.org. \n", "\n", "Gamerman, D. Markov Chain Monte Carlo: statistical simulation for Bayesian inference. Chapman and Hall, 1997.\n", "\n", "Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. The Journal of Machine Learning Research, 30.\n", "\n", "Kucukelbir A, Ranganath R, Gelman A, and Blei DM. Automatic Variational Inference in Stan http://arxiv.org/abs/1506.03431, in prep.\n", "\n", "Vanderplas, Jake. \"Frequentism and Bayesianism IV: How to be a Bayesian in Python.\" Pythonic Perambulations. N.p., 14 Jun 2014. Web. 27 May. 2015. .\n", "\n", "R.G. Jarrett. A note on the intervals between coal mining disasters. Biometrika, 66:191–193, 1979.\n" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }