{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Bayesian Machine Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Preliminaries\n",
    "\n",
    "- Goals\n",
    "  - Introduction to Bayesian (i.e., probabilistic) modeling\n",
    "- Materials\n",
    "  - Mandatory\n",
    "    - These lecture notes\n",
    "  - Optional\n",
    "    - Bishop pp. 68-74 (on the coin toss example)\n",
    "    - [Ariel Caticha - 2012 - Entropic Inference and the Foundations of Physics](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Caticha-2012-Entropic-Inference-and-the-Foundations-of-Physics.pdf), pp.35-44 (section 2.9, on deriving Bayes rule for updating probabilities)\n",
    "    <!--- - [David Blei - 2014 - Build, Compute, Critique, Repeat: Data Analysis with Latent Variable Models](https://github.com/bertdv/BMLIP/blob/master/lessons/notebooks/files/Blei-2014-Build-Compute-Critique-Repeat.pdf), on the _Build-Compute-Critique-Repeat_ design model. --->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Challenge: Predicting a Coin Toss\n",
    "\n",
    "- **Problem**: We observe a the following sequence of heads (h) and tails (t) when tossing the same coin repeatedly $$D=\\{hthhtth\\}\\,.$$\n",
    "\n",
    "- What is the probability that heads comes up next?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- **Solution**: later in this lecture. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Bayesian Machine Learning Framework\n",
    "\n",
    "- Suppose that your application is to predict a future observation $x$, based on $N$ past observations $D=\\{x_1,\\dotsc,x_N\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The Bayesian design approach to solving this task involves four stages: \n",
    "\n",
    "<div style=\"background-color:rgba(0, 0, 0, 0.0470588); padding:10px 0;font-family:monospace;\">\n",
    "<font color = \"red\">REPEAT</font></br>\n",
    "&nbsp; 1- Model specification</br>\n",
    "&nbsp; 2- Parameter estimation</br>\n",
    "&nbsp; 3- Model evaluation</br>\n",
    "<font color = \"red\">UNTIL model performance is satisfactory</font></br>\n",
    "&nbsp; 4- Apply model\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Intosses principle, based on the model evaluationtosses results, you may want to re-specify your model and _repeat_ the design process (a few times), until model performance is acceptable. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "  \n",
    "- Next, we discuss these four stages in a bit more detail."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### (1) Model specification\n",
    "\n",
    "- Your first task is to propose a probabilistic model ($m$) for generating the observations $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- A probabilistic model $m$ consists of a joint distribution $p(x,\\theta|m)$ that relates observations $x$ to model parameters $\\theta$. Usually, the model is proposed in the form of a data generating  distribution $p(x|\\theta,m)$ and a prior $p(\\theta|m)$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- _You_ are responsible to choose the data generating distribution $p(x|\\theta)$ based on your physical understanding of the data generating process. (For brevity, since we are working on one given model $m$, we drop the given dependency on $m$ from the notation)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- _You_ must also choose the prior $p(\\theta)$ to reflect what you know about the parameter values before you see the data $D$.\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### (2) Parameter estimation\n",
    "\n",
    "- Note that, for a given data set $D=\\{x_1,x_2,\\dots,x_N\\}$ with _independent_ observations $x_n$, the likelihood factorizes as \n",
    "$$ p(D|\\theta) = \\prod_{n=1}^N p(x_n|\\theta)\\,,$$\n",
    "so usually you select a model for generating one observation $x_n$ and then use (in-)dependence assumptions to combine these models into a likelihood function for the model parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The likelihood and prior both contain information about the model parameters. Next, you use Bayes rule to fuse these two information sources into a posterior distribution for the parameters:\n",
    "$$\n",
    "\\underbrace{p(\\theta|D) }_{\\text{posterior}} = \\frac{p(D|\\theta) p(\\theta)}{p(D)} \\propto \\underbrace{p(D|\\theta)}_{\\text{likelihood}} \\cdot \\underbrace{p(\\theta)}_{\\text{prior}}\n",
    "$$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Note that there's **no need for you to design some clever parameter estimation algorithm**. Bayes rule _is_ the parameter estimation algorithm. The only complexity lies in the computational issues! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- This \"recipe\" works only if the right-hand side (RHS) factors can be evaluated; the computational details can be quite challenging and this is what machine learning is about.     \n",
    "  \n",
    "- $\\Rightarrow$ **Machine learning is EASY, apart from computational details :)**\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  (3) Model Evaluation \n",
    "\n",
    "- In the framework above, parameter estimation was executed by \"perfect\" Bayesian reasoning. So is everything settled now? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- No, there appears to be one remaining problem: how good really were our model assumptions $p(x|\\theta)$ and $p(\\theta)$? We want to \"score\" the model performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Note that this question is only interesting in practice if we have alternative models to choose from. After all, if you don't have an alternative model, any value for the model evidence would still not lead you to switch to another model.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Let's assume that we have more candidate models, say $\\mathcal{M} = \\{m_1,\\ldots,m_K\\}$ where each model relates to specific prior $p(\\theta|m_k)$ and likelihood $p(D|\\theta,m_k)$? Can we evaluate the relative performance of a model against another model from the set?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Start again with **model specification**. _You_ must now specify a prior $p(m_k)$ (next to the likelihood $p(D|\\theta,m_k)$ and prior $p(\\theta|m_k)$) for each of the models and then solve the desired inference problem:      \n",
    "$$\\begin{align*} \n",
    "\\underbrace{p(m_k|D)}_{\\substack{\\text{model}\\\\\\text{posterior}}} &= \\frac{p(D|m_k) p(m_k)}{p(D)} \\\\\n",
    "  &\\propto p(m_k) \\cdot p(D|m_k) \\\\\n",
    "  &= p(m_k)\\cdot \\int_\\theta p(D,\\theta|m_k) \\,\\mathrm{d}\\theta\\\\\n",
    "  &= \\underbrace{p(m_k)}_{\\substack{\\text{model}\\\\\\text{prior}}}\\cdot \\underbrace{\\int_\\theta \\underbrace{p(D|\\theta,m_k)}_{\\text{likelihood}} \\,\\underbrace{p(\\theta|m_k)}_{\\text{prior}}\\, \\mathrm{d}\\theta }_{\\substack{\\text{evidence }p(D|m_k)\\\\\\text{= model likelihood}}}\\\\\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "- Note that, to evaluate the posterior for a model, you must calculate the \"evidence\", which can be interpreted as a likelihood function for the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- You can now compare posterior distributions $p(m_k|D)$ for a set of models $\\{m_k\\}$ and decide on the merits of each model relative to alternative models. This procedure is called **Bayesian model comparison**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\Rightarrow$ In a Bayesian framework, **model estimation** follows the same recipe as parameter estimation; it just works at one higher hierarchical level. Compare the required calulations:\n",
    "\n",
    "$$\\begin{align*}\n",
    "p(\\theta|D) &\\propto p(D|\\theta) p(\\theta) \\; &&\\text{(parameter estimation)} \\\\\n",
    "p(m_k|D) &\\propto p(D|m_k) p(m_k) \\; &&\\text{(model comparison)}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Again, **no need to invent a special algorithm for estimating the performance of your model**. Straightforward application of probability theory takes care of all that. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In principle, you could proceed with asking how good your choice for the candidate model set $\\mathcal{M}$ was. You would have to provide a set of alternative model sets $\\{\\mathcal{M}_1,\\mathcal{M}_2,\\ldots,\\mathcal{M}_M\\}$ with priors $p(\\mathcal{M}_m)$ for each set and compute posteriors $p(\\mathcal{M}_m|D)$. And so forth ...  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- With the (relative) performance evaluation scores of your model in hand, you could now re-specify your model (hopefully an improved model) and _repeat_ the design process until the model performance score is acceptable. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- As an aside, in the (statistics and machine learning) literature, performance comparison between two models is often reported by the [Bayes Factor](https://en.wikipedia.org/wiki/Bayes_factor), which is defined as the ratio of model evidences: \n",
    "$$\\begin{align*}\n",
    "\\underbrace{\\frac{p(D|m_1)}{p(D|m_2)}}_{\\text{Bayes Factor}} &= \\frac{\\frac{p(D,m_1)}{p(m_1)}}{\\frac{p(D,m_2)}{p(m_2)}}  \\\\\n",
    "&= \\frac{p(D,m_1)}{p(m_1)} \\cdot \\frac{p(m_2)}{p(D,m_2)} \\\\\n",
    "&= \\frac{p(m_1|D) p(D)}{p(m_1)} \\cdot \\frac{p(m_2)}{p(m_2|D) p(D)} \\\\\n",
    "&= \\underbrace{\\frac{p(m_1|D)}{p(m_2|D)}}_{\\substack{\\text{posterior} \\\\ \\text{ratio}}} \\cdot \\underbrace{\\frac{p(m_2)}{p(m_1)}}_{\\substack{\\text{prior} \\\\ \\text{ratio}}}\n",
    "\\end{align*}$$\n",
    "  - Hence, for equal model priors ($p(m_1)=p(m_2)=0.5$), the Bayes Factor reports the posterior probability ratio for the two models. \n",
    "\n",
    "- In principle, any decision about which is the better model has accepted some ad hocery, but [Jeffreys (1961)](https://www.amazon.com/Theory-Probability-Classic-Physical-Sciences/dp/0198503687/ref=sr_1_1?qid=1663516628&refinements=p_27%3Athe+late+Harold+Jeffreys&s=books&sr=1-1&text=the+late+Harold+Jeffreys) advises the following interpretation of the log-Bayes factor $log_{10} B_{12} =\\log_{10}\\frac{p(D|m_1)}{p(D|m_2)}$:\n",
    "\n",
    "<table width=\"60%\" align=\"center\" text-align=\"center\">\n",
    "<tr><td> $\\log_{10} B_{12}$</td><td > <b>Evidence for $m_1$ </b></td></tr>\n",
    "<tr><td>0 to 0.5</td><td>not worth mentioning</td></tr>\n",
    "<tr><td>0.5 to 1</td><td>substantial</td></tr>\n",
    "<tr><td>1 to 2</td><td>strong</td></tr>\n",
    "<tr><td> >2</td><td>decisive</td></tr>\n",
    "</table> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### (4) Prediction\n",
    "\n",
    "- Once we are satisfied with the evidence for a (trained) model, we can apply the model to our prediction/classification/etc task."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Given the data $D$, our knowledge about the yet unobserved datum $x$ is captured by (everything is conditioned on the selected model)\n",
    "$$\\begin{align*}\n",
    "p(x|D) &\\stackrel{s}{=} \\int p(x,\\theta|D) \\,\\mathrm{d}\\theta\\\\\n",
    " &\\stackrel{p}{=} \\int p(x|\\theta,D) p(\\theta|D) \\,\\mathrm{d}\\theta\\\\\n",
    " &\\stackrel{m}{=} \\int \\underbrace{p(x|\\theta)}_{\\text{data generation dist.}} \\cdot \\underbrace{p(\\theta|D)}_{\\text{posterior}} \\,\\mathrm{d}\\theta\\\\\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In the last equation, the simplification $p(x|\\theta,D) = p(x|\\theta)$ follows from our model specification. We assumed a _parametric_ data generating distribution $p(x|\\theta)$ with no explicit dependency on the data set $D$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Again, **no need to invent a special prediction algorithm**. Probability theory takes care of all that. The complexity of prediction is just computational: how to carry out the marginalization over $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Note that the application of the learned posterior $p(\\theta|D)$ not necessarily has to be a prediction task. We use it here as an example, but other applications (e.g., classification, regression etc.) are of course also possible. \n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "##### Prediction with multiple models\n",
    "\n",
    "- When you have a posterior $p(m_k|D)$ for the models, you don't *need* to choose one model for the prediction task. You can do prediction by **Bayesian model averaging**, which combines the predictive power from all models:\n",
    "$$\\begin{align*}\n",
    "p(x|D) &= \\sum_k \\int p(x,\\theta,m_k|D)\\,\\mathrm{d}\\theta \\\\\n",
    " &= \\sum_k \\int  p(x|\\theta,m_k) \\,p(\\theta|m_k,D)\\, p(m_k|D) \\,\\mathrm{d}\\theta \\\\\n",
    "  &= \\sum_k \\underbrace{p(m_k|D)}_{\\substack{\\text{model}\\\\\\text{posterior}}} \\cdot \\int \\underbrace{p(\\theta|m_k,D)}_{\\substack{\\text{parameter}\\\\\\text{posterior}}} \\, \\underbrace{p(x|\\theta,m_k)}_{\\substack{\\text{data generating}\\\\\\text{distribution}}} \\,\\mathrm{d}\\theta\n",
    "\\end{align*}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Alternatively, if you do need to work with one model (e.g. due to computational resource constraints), you can for instance select the model with largest posterior $p(m_k|D)$ and use that model for prediction. This is called **Bayesian model selection**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "- Bayesian model averaging is the principal way to apply PT to machine learning. You don't throw away information by discarding lesser performant models, but rather use PT (marginalization of models) to compute $$p(\\text{what-I-am-interested-in} \\,|\\, \\text{all available information})$$ exactly. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We're Done!\n",
    "\n",
    "- In principle, you now have the recipe in your hands now to solve all your prediction/classification/regression etc problems by the same method:\n",
    "\n",
    "  1. specify a model\n",
    "  2. train the model (by PT)\n",
    "  3. evaluate the model (by PT); if not satisfied, goto 1\n",
    "  4. apply the model (by PT)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Crucially, there is no need to invent clever machine learning algorithms, and there is no need to invent a clever prediction algorithm nor a need to invent a model performance criterion. Instead, you propose a model and, from there on, you let PT reason about everything that you care about. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Your problems are only of computational nature. Perhaps the integral to compute the evidence may not be analytically tractable, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayesian Evidence as a Model Performance Criterion\n",
    "\n",
    "- I'd like to convince you that <a id=\"Bayesian-model-evidence\">Bayesian model evidence</a> is an excellent criterion for assessing your model's performance. To do so, let us consider a decomposition that relates model evidence to other valued criteria such as **accuracy** and **model complexity**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Consider a model $p(x,\\theta|m)$ and a data set $D = \\{x_1,x_2, \\ldots,x_N\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Given the data set $D$, the log-evidence for model $m$ decomposes as follows (please check the derivation):\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\underbrace{\\log p(D|m)}_{\\text{log-evidence}} &= \\log \\frac{p(D|\\theta,m) p(\\theta|m)}{p(\\theta|D,m)} \\qquad \\text{(use Bayes rule)} \\\\\n",
    " &=  \\underbrace{\\log \\frac{p(D|\\theta,m) p(\\theta|m)}{p(\\theta|D,m)}}_{\\substack{\\text{evaluates to } \\log p(D|m) \\\\ \\text{therefore independent of }\\theta}} \\cdot \\underbrace{\\int p(\\theta|D,m)\\mathrm{d}\\theta}_{\\text{evaluates to }1} \\\\\n",
    "  &= \\int p(\\theta|D,m)  \\cdot \\underbrace{\\log \\frac{p(D|\\theta,m) p(\\theta|m)}{p(\\theta|D,m)}}_{= \\log p(D|m)} \\mathrm{d}\\theta \\qquad \\text{(move $\\log p(D|m)$ into the integral)} \\\\\n",
    "  &= \\underbrace{\\int p(\\theta|D,m) \\log p(D|\\theta,m) \\mathrm{d}\\theta}_{\\text{accuracy (a.k.a. data fit)}} - \\underbrace{\\int p(\\theta|D,m) \\log  \\frac{p(\\theta|D,m)}{p(\\theta|m)} \\mathrm{d}\\theta}_{\\text{complexity}}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The first term (data fit, also known as accuracy) measures how well the model predicts the data set $D$ (as measured by $\\log p(D|\\theta,m)$), after having learned from the data (because we marginalize $\\theta$ with the posterior $p(\\theta|D,m)$). We want this term to be large (although only focussing on this term could lead to *overfitting*)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The second term (complexity) quantifies the amount of information that the model absorbed through learning, i.e., by moving parameter beliefs from $p(\\theta|m)$ to $p(\\theta|D,m)$. Technically, this term is the [Kullback-Leibler divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence) between posterior and prior. We want this term to be small.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The complexity term regularizes the Bayesian learning process automatically. If you prefer models with high Bayesian evidence, then you prefer models that get a good data fit without need to learn much from the data set. These types of models are said to *generalize* well, since they can be applied to different data sets without specific adaptations for each data set. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\Rightarrow$ Bayesian learning automatically leads to models that generalize well. **There is no need for early stopping or validation data sets**. Just learn on the full data set and all behaves well.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayesian Machine Learning and the Scientific Method Revisited\n",
    "\n",
    "- The Bayesian design process provides a unified framework for the Scientific Inquiry method. We can now add equations to the design loop. (Trial design to be discussed in [Intelligent Agent lesson](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Intelligent-Agents-and-Active-Inference.ipynb).) \n",
    "\n",
    "<p style=\"text-align:center;\"><img src=\"./figures/scientific-inquiry-loop-w-BML-eqs.png\" width=\"600px\"></p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Now Solve the Example Problem: Predicting a Coin Toss\n",
    "\n",
    "- We observe a the following sequence of heads ($h$) and tails ($t$) when tossing the same coin repeatedly $$D=\\{hthhtth\\}\\,.$$\n",
    "\n",
    "- What is the probability that heads comes up next? We solve this in the next slides ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Coin toss example (1): Model Specification\n",
    "\n",
    "- We observe a sequence of $N$ coin tosses $D=\\{x_1,\\ldots,x_N\\}$ with $n$ heads. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Let us denote outcomes by \n",
    "$$x_k = \\begin{cases} h & \\text{if heads comes up} \\\\\n",
    "  t & \\text{if tails} \\end{cases}\n",
    "  $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "##### Likelihood\n",
    "\n",
    "- Assume a [**Bernoulli** distributed](https://en.wikipedia.org/wiki/Bernoulli_distribution) variable $p(x_k=h|\\mu)=\\mu$ for a single coin toss, leading to \n",
    "$$p(x_k|\\mu)=\\mu^{x_k} (1-\\mu)^{1-x_k} \\,.$$\n",
    "\n",
    "- Assume $n$ times heads were thrown out of a total of $N$ throws. The likelihood function then follows a a [**binomial** distribution](https://en.wikipedia.org/wiki/Binomial_distribution) :\n",
    "$$   \n",
    "p(D|\\mu) = \\prod_{k=1}^N p(x_k|\\mu) = \\mu^n (1-\\mu)^{N-n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "##### <a id=\"beta-prior\">Prior</a>\n",
    "\n",
    "-  Assume the prior beliefs for $\\mu$ are governed by a [**beta distribution**](https://en.wikipedia.org/wiki/Beta_distribution)\n",
    "\n",
    "$$\n",
    "p(\\mu) = \\mathrm{Beta}(\\mu|\\alpha,\\beta) = \\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\mu^{\\alpha-1}(1-\\mu)^{\\beta-1}\n",
    "$$\n",
    "where the Gamma function is sort of a generalized factorial function. In particular, if $\\alpha,\\beta$ are integers, then $$\\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)(\\Gamma(\\beta)} = \\frac{(\\alpha+\\beta-1)!}{(\\alpha-1)!\\,(\\beta-1)!}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- A _what_ distribution? Yes, the **beta distribution** is a **conjugate prior** for the binomial distribution, which means that \n",
    "$$\n",
    "\\underbrace{\\text{beta}}_{\\text{posterior}} \\propto \\underbrace{\\text{binomial}}_{\\text{likelihood}} \\times \\underbrace{\\text{beta}}_{\\text{prior}}\n",
    "$$\n",
    "so we get a closed-form posterior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- $\\alpha$ and $\\beta$ are called **hyperparameters**, since they parameterize the distribution for another parameter ($\\mu$). E.g., $\\alpha=\\beta=1$ (uniform).\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"./figures/B-fig-2.2.png\" width=\"600px\">\n",
    "\n",
    "- (Bishop Fig.2.2). Plots of the beta distribution $\\mathrm{Beta}(\\mu|a, b)$ as a function of $\\mu$ for various values of the hyperparameters $a$ and $b$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Coin toss example (2): Parameter estimation\n",
    "\n",
    "- Infer posterior PDF over $\\mu$ (and evidence) through Bayes rule\n",
    "\n",
    "$$\\begin{align*}\n",
    "p(\\mu&|D) \\cdot p(D) = p(D|\\mu)\\cdot p(\\mu)  \\\\\n",
    "  &=  \\left[ \\mu^n (1-\\mu)^{N-n}\\right] \\cdot \\left[ \\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\mu^{\\alpha-1}(1-\\mu)^{\\beta-1} \\right] \\\\\n",
    "  &= \\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\mu^{n+\\alpha-1} (1-\\mu)^{N-n+\\beta-1} \\\\\n",
    "        &= \\underbrace{\\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\frac{\\Gamma(N+\\alpha) \\Gamma(N-n+\\beta)}{\\Gamma(N+\\alpha+\\beta)}}_{\\text{evidence }p(D)} \\cdot \\left[ \\underbrace{\\frac{\\Gamma(N+\\alpha+\\beta)}{\\Gamma(n+\\alpha)\\Gamma(N-n+\\beta)} \\mu^{n+\\alpha-1} (1-\\mu)^{N-n+\\beta-1}}_{\\text{posterior }p(\\mu|D)=\\mathrm{Beta}(\\mu|n+\\alpha, N-n+\\beta)}\\right]\n",
    "\\end{align*}$$\n",
    "\n",
    "\n",
    "hence the posterior is also beta-distributed as\n",
    "\n",
    "$$\n",
    "p(\\mu|D) = \\mathrm{Beta}(\\mu|\\,n+\\alpha, N-n+\\beta)\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Coin toss example (3): Model Evaluation\n",
    "\n",
    "- It follow from the above calculation that the evidence for model $m$ can be analytically expressed as\n",
    "\n",
    "$$\n",
    "p(D|m) = \\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\frac{\\Gamma(N+\\alpha) \\Gamma(N-n+\\beta)}{\\Gamma(N+\\alpha+\\beta)}\n",
    "$$\n",
    "\n",
    "- The model evidence is a scalar. The absolute value is not important. However, you may want to compare the model evidence of this model to the evidence for another model on the same data set.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Coin Toss Example (4): Prediction\n",
    "\n",
    "- Once we have accepted a model, let's apply it to the application, in this case, predicting future observations. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Marginalize over the parameter posterior to get the predictive PDF for a new coin toss $x_\\bullet$, given the data $D$,\n",
    "\n",
    "$$\\begin{align*}\n",
    "p(x_\\bullet=h|D)  &= \\int_0^1 p(x_\\bullet=h|\\mu)\\,p(\\mu|D) \\,\\mathrm{d}\\mu \\\\\n",
    "  &= \\int_0^1 \\mu \\times  \\mathrm{Beta}(\\mu|\\,n+\\alpha, N-n+\\beta) \\,\\mathrm{d}\\mu  \\\\\n",
    "  &= \\frac{n+\\alpha}{N+\\alpha+\\beta}\n",
    "\\end{align*}$$\n",
    "\n",
    "- This result is known as [**Laplace's rule of succession**](https://en.wikipedia.org/wiki/Rule_of_succession)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The above integral computes the mean of a beta distribution, which is given by $\\mathbb{E}[x] = \\frac{a}{a+b}$ for $x \\sim \\mathrm{Beta}(a,b)$, see [wikipedia](https://en.wikipedia.org/wiki/Beta_distribution)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Finally, we're ready to solve our example problem: for $D=\\{hthhtth\\}$ and uniform prior ($\\alpha=\\beta=1$), we get\n",
    "\n",
    "$$ p(x_\\bullet=h|D)=\\frac{n+1}{N+2} = \\frac{4+1}{7+2} = \\frac{5}{9}$$\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Coin Toss Example: What did we learn?\n",
    "\n",
    "- What did we learn from the data? Before seeing any data, we think that $$p(x_\\bullet=h)=\\left. p(x_\\bullet=h|D) \\right|_{n=N=0} = \\frac{\\alpha}{\\alpha + \\beta}\\,.$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Hence, $\\alpha$ and $\\beta$ are prior pseudo-counts for heads and tails respectively. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- After the $N$ coin tosses, we think that $p(x_\\bullet=h|D) = \\frac{n+\\alpha}{N+\\alpha+\\beta}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Note the following decomposition\n",
    "\n",
    "$$\\begin{align*}\n",
    "    p(x_\\bullet=h|\\,D) &= \\frac{n+\\alpha}{N+\\alpha+\\beta} = \\frac{n}{N+\\alpha+\\beta} + \\frac{\\alpha}{N+\\alpha+\\beta} \\\\\n",
    "        &= \\frac{N}{N+\\alpha+\\beta}\\cdot \\frac{n}{N} + \\frac{\\alpha+\\beta}{N+\\alpha+\\beta} \\cdot \\frac{\\alpha}{\\alpha+\\beta} \\\\\n",
    "        &= \\underbrace{\\frac{\\alpha}{\\alpha+\\beta}}_{\\substack{\\text{prior}\\\\\\text{prediction}}} + \\underbrace{\\underbrace{\\frac{N}{N+\\alpha+\\beta}}_{\\text{gain}}\\cdot \\underbrace{\\big( \\underbrace{\\frac{n}{N}}_{\\substack{\\text{data-based}\\\\\\text{prediction}}} - \\underbrace{\\frac{\\alpha}{\\alpha+\\beta}}_{\\substack{\\text{prior}\\\\\\text{prediction}}} \\big)}_{\\text{prediction error}}}_{\\text{correction}}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Note that, since $0\\leq \\underbrace{\\frac{N}{N+\\alpha+\\beta}}_{\\text{gain}} \\lt 1$, the Bayesian prediction lies between (fuses) the prior and data-based predictions. The data plays the role of \"correcting\" the prior prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- For large $N$, the gain goes to $1$ and $\\left. p(x_\\bullet=h|D)\\right|_{N\\rightarrow \\infty} \\rightarrow \\frac{n}{N}$ goes to the data-based prediction (the observed relative frequency)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Code Example: Bayesian evolution for the coin toss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "- Next, we code an example for a sequence of coin tosses, where we assume that the true coin generates data $x_n \\in \\{0,1\\}$ by a Bernoulli distribution:\n",
    "$$\n",
    "p(x_n|\\mu=0.4)=0.4^{x_n} \\cdot 0.6^{1-x_n}\n",
    "$$\n",
    "\n",
    "- So, this coin is biased!\n",
    "\n",
    "- In order predict the outcomes of future coin tosses, we'll use two models $m_1$ and $m_2$.\n",
    "\n",
    "- Both models have the same data generating distribution (also Bernoulli)\n",
    "$$\n",
    "p(x_n|\\mu,m_1) = p(x_n|\\mu,m_2) = \\mu^{x_n} (1-\\mu)^{1-x_n}\n",
    "$$\n",
    "but they have different priors:\n",
    "$$\\begin{aligned}\n",
    "p(\\mu|m_1) &= \\mathrm{Beta}(\\mu|\\alpha=1,\\beta=1) \\\\\n",
    "p(\\mu|m_2) &= \\mathrm{Beta}(\\mu|\\alpha=15,\\beta=1)\n",
    "\\end{aligned}$$\n",
    "\n",
    "- Which model is better?\n",
    "\n",
    "- For both models, we will report as a function of the total number of coin tosses, the posteriors \n",
    "$$p(\\mu|D,m_1) \\text{  and  }p(\\mu|D,m_2) \\,,$$\n",
    "and the Bayes factor in decibels\n",
    "$$\n",
    "B_{12} = log_{10}\\left( \\frac{p(D|m_1)}{p(D|m_2)} \\right) \\,.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# computes log10 of Gamma function\n",
    "function log10gamma(int)\n",
    "    if int == 1 || int == 2\n",
    "        return 1\n",
    "    end\n",
    "    return sum(log10(ii) for ii in 2:int-1)\n",
    "end\n",
    "\n",
    "# compute posterior and log-evidence\n",
    "function execute_bayes(N,n,α,β)\n",
    "# N, n is total # tosses and heads counts\n",
    "# \\alpha, \\beta are parameters for Beta prior\n",
    "    posterior = Beta( α + n, β + (N-n) )\n",
    "    logevidence = log10gamma(α+β) - log10gamma(α) - log10gamma(β) + log10gamma(N+α) + log10gamma(N-n+β) - log10gamma(N+α+β)\n",
    "    return posterior, logevidence\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Distributions\n",
    "\n",
    "# specify model parameters\n",
    "μ  = 0.4;\n",
    "α_m1 = 1; β_m1 = 1;\n",
    "α_m2 = 15; β_m2 = 1;\n",
    "\n",
    "# do experiment and update model\n",
    "max_ntosses = 192\n",
    "samples = rand(max_ntosses) .<= μ # Flip 192 coins\n",
    "\n",
    "posterior_m1 = Array{Distribution}(undef,max_ntosses)\n",
    "posterior_m2 = Array{Distribution}(undef,max_ntosses)\n",
    "logevidence_m1 = Array{Float64}(undef,max_ntosses)\n",
    "logevidence_m2 = Array{Float64}(undef,max_ntosses)\n",
    "logBF12 = Array{Float64}(undef,max_ntosses)\n",
    "\n",
    "for ntosses = 1:1:max_ntosses\n",
    "    nheads = sum(samples[1:ntosses]) # Count number of heads in first N flips\n",
    "    posterior_m1[ntosses], logevidence_m1[ntosses] = execute_bayes( ntosses, nheads, α_m1, β_m1 )\n",
    "    posterior_m2[ntosses], logevidence_m2[ntosses] = execute_bayes( ntosses, nheads, α_m2, β_m2 )\n",
    "    logBF12[ntosses] = logevidence_m1[ntosses] - logevidence_m2[ntosses]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1100x1100 with 4 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using PyPlot\n",
    "\n",
    "fig = figure(\"Posterior distributions\", figsize=(11,11));\n",
    "range_grid = range(0.0, stop=1.0, length=100)\n",
    "ax1 = fig.add_subplot(2,2,1);\n",
    "ax2 = fig.add_subplot(2,2,2);\n",
    "ax3 = fig.add_subplot(2,2,3);\n",
    "ax4 = fig.add_subplot(2,2,4);\n",
    "\n",
    "function plot_distribution(position, ntosses, posterior_m1, posterior_m2, logBF12)\n",
    "    plt.subplot(position); \n",
    "    plot(range_grid,pdf.(posterior_m1[ntosses],range_grid), \"b-\");\n",
    "    plt.subplot(position); \n",
    "    plot(range_grid,pdf.(posterior_m2[ntosses],range_grid), \"k--\");\n",
    "    \n",
    "    xlabel(L\"\\mu\"); ylabel(L\"p(\\mu|\\mathcal{D})\"); grid()\n",
    "    title(L\"p(\\mu|\\mathcal{D})\"*\" for N=$(ntosses), n=$(sum(samples[1:ntosses])) (real \\$\\\\mu\\$=$(μ))\")\n",
    "    legend([\"model 1 \"*L\"B(\"*string(α_m1)*\",\"*string(β_m1)*\")\",\"model 2 \"*L\"B(\"*string(α_m2)*\",\"*string(β_m2)*\")\"], loc=4)\n",
    "    ymax = max(maximum((pdf.(posterior_m1[ntosses],range_grid))),maximum((pdf.(posterior_m2[ntosses],range_grid))))\n",
    "    text(0, ymax-.5,\"model 1 with prior \"*L\"B(\"*string(α_m1)*\",\"*string(β_m1)*\")\\n\")\n",
    "    text(0, ymax-1, \"model 2 with prior \"*L\"B(\"*string(α_m2)*\",\"*string(β_m2)*\")\\n\")\n",
    "    text(0, ymax-1.5, \"log B12 = $(round(logBF12[ntosses], digits=2))\\n\")\n",
    "end\n",
    "\n",
    "function plot_all_distributions(posterior_m1,posterior_m2,logBF12)\n",
    "    ntosses = [3,10,50,190];\n",
    "    plot_distribution(221, ntosses[1], posterior_m1, posterior_m2, logBF12)\n",
    "    plot_distribution(222, ntosses[2], posterior_m1, posterior_m2, logBF12)\n",
    "    plot_distribution(223, ntosses[3], posterior_m1, posterior_m2, logBF12)\n",
    "    plot_distribution(224, ntosses[4], posterior_m1, posterior_m2, logBF12)\n",
    "end\n",
    "\n",
    "plot_all_distributions( posterior_m1, posterior_m2, logBF12 );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$\\Rightarrow$ With more data, the relevance of the prior diminishes!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### From Posterior to Point-Estimate\n",
    "\n",
    "- In the example above, Bayesian parameter estimation and prediction were tractable in closed-form. This is often not the case. We will need to approximate some of the computations. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Recall Bayesian prediction\n",
    "\n",
    "$$\n",
    "p(x|D) = \\int p(x|\\theta)p(\\theta|D)\\,\\mathrm{d}{\\theta}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- If we approximate posterior $p(\\theta|D)$ by a delta function for one 'best' value $\\hat\\theta$, then the predictive distribution collapses to\n",
    "\n",
    "$$\n",
    "p(x|D)= \\int p(x|\\theta)\\,\\delta(\\theta-\\hat\\theta)\\,\\mathrm{d}{\\theta} = p(x|\\hat\\theta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- This is just the data generating distribution $p(x|\\theta)$ evaluated at $\\theta=\\hat\\theta$, which is easy to evaluate.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The next question is how to get the parameter estimate $\\hat{\\theta}$? (See next slide)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Some Well-known Point-Estimates\n",
    "\n",
    "- **Bayes estimate** (the mean of the posterior)\n",
    "\n",
    "$$\n",
    "\\hat \\theta_{bayes}  = \\int \\theta \\, p\\left( \\theta |D \\right)\n",
    "\\,\\mathrm{d}{\\theta}\n",
    "$$\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- **Maximum A Posteriori** (MAP) estimate \n",
    "$$\n",
    "\\hat \\theta_{\\text{map}}=  \\arg\\max _{\\theta} p\\left( \\theta |D \\right) =\n",
    "\\arg \\max_{\\theta}  p\\left(D |\\theta \\right) \\, p\\left(\\theta \\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- **Maximum Likelihood** (ML) estimate\n",
    "$$\n",
    "\\hat \\theta_{ml}  = \\arg \\max_{\\theta}  p\\left(D |\\theta\\right)\n",
    "$$\n",
    "  - Note that Maximum Likelihood is MAP with uniform prior\n",
    "  - ML is the most common approximation to the full Bayesian posterior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bayesian vs Maximum Likelihood Learning\n",
    "\n",
    "Consider the task: predict a datum $x$ from an observed data set $D$.\n",
    "\n",
    "<table>\n",
    "<tr><td></td><td style=\"text-align:center\"> <b>Bayesian</b></td><td style=\"text-align:center\"> <b>Maximum Likelihood </b></td></tr>\n",
    "<tr><td>1. <b>Model Specification</b></td><td>Choose a model $m$ with data generating distribution $p(x|\\theta,m)$ and parameter prior $p(\\theta|m)$</td><td>Choose a model $m$ with same data generating distribution $p(x|\\theta,m)$. No need for priors.</td></tr>\n",
    "<tr><td>2. <b>Learning</b></td><td>use Bayes rule to find the parameter posterior,\n",
    "$$\n",
    "p(\\theta|D) \\propto p(D|\\theta) p(\\theta)\n",
    "$$  </td><td>By Maximum Likelihood (ML) optimization,\n",
    "$$ \n",
    "    \\hat \\theta  = \\arg \\max_{\\theta}  p(D |\\theta)\n",
    "$$</td></tr>\n",
    "<tr><td>3. <b>Prediction</b></td><td>$$\n",
    "p(x|D) = \\int p(x|\\theta) p(\\theta|D) \\,\\mathrm{d}\\theta\n",
    "$$</td><td>\n",
    "$$ \n",
    "    p(x|D) =  p(x|\\hat\\theta)\n",
    "$$</td></tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Report Card on Maximum Likelihood Estimation\n",
    "\n",
    "- Maximum Likelihood (ML) is MAP with uniform prior. MAP is sometimes called a 'penalized' ML procedure:\n",
    "\n",
    "$$\n",
    "\\hat \\theta_{map}  = \\arg \\max _\\theta  \\{ \\underbrace{\\log\n",
    "p\\left( D|\\theta  \\right)}_{\\text{log-likelihood}} + \\underbrace{\\log\n",
    "p\\left( \\theta \\right)}_{\\text{penalty}} \\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- (good!). ML works rather well if we have a lot of data because the influence of the prior diminishes with more data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- (good!). Computationally often do-able. Useful fact that makes the optimization easier (since $\\log$ is monotonously increasing):\n",
    "\n",
    "$$\\arg\\max_\\theta \\log p(D|\\theta) =  \\arg\\max_\\theta p(D|\\theta)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- (bad). Cannot be used for model comparison! When doing ML estimation, the Bayesian model evidence always evalutes to zero because the prior probability mass under the likelihood function goes to zero. Therefore, when doing ML estimation, Bayesian model evidence cannot be used to evaluate model performance: \n",
    "$$\\begin{align*}\n",
    "\\underbrace{p(D|m)}_{\\substack{\\text{Bayesian}\\\\ \\text{evidence}}} &= \\int p(D|\\theta) \\cdot p(\\theta|m)\\,\\mathrm{d}\\theta \\\\\n",
    "  &= \\lim_{(b-a)\\rightarrow \\infty} \\int p(D|\\theta)\\cdot \\text{Uniform}(\\theta|a,b)\\,\\mathrm{d}\\theta \\\\\n",
    "  &= \\lim_{(b-a)\\rightarrow \\infty} \\frac{1}{b-a}\\underbrace{\\int_a^b p(D|\\theta)\\,\\mathrm{d}\\theta}_{<\\infty}  \\\\\n",
    "    &= 0\n",
    "\\end{align*}$$\n",
    "  - In fact, this is a serious problem because evidence is fundamentally the correct criterion that follows from straighforward PT. In practice, when estimating parameters by maximum likelihood, we evaluate model performance by an ad hoc performance measure such as mean-squared-error on a testing data set."
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    "$\\Rightarrow$ **ML estimation is an approximation to Bayesian learning**, but for good reason a very popular learning method when faced with lots of available data."
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