{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "#%qtconsole" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "import json\n", "s = json.load( open(\"styles/bmh_matplotlibrc.json\") )\n", "matplotlib.rcParams.update(s)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Buffon's Needle " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem is to randomly drop a needle on the unit square and count the number of times that the needle touches (or \"cuts\") the edge of the square. This is a well-studied problem, but instead of the usual tack of going directly for the analytical result (see appendix), we instead write a quick simulation that we'll later refine to obtain more precise results more efficiently. This methodology is common in Monte Carlo methods and we will work through this example in careful detail.\n", "\n", "Buffon's needle is a classic problem that is easy to understand, and complex enough to be characteristic of much more difficult problems encountered in practice. The overall idea is that when the problem is too complex to analyze analytically (at least in the general case), we write representative computer models that can drive a numerical solution and motivate analytical solutions, even if only on special cases. \n" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Setting up the Simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following code-block sets up the random needle position and orientation and creates the corresponding matplotlib primitives to be drawn in the figure. As shown, the simulation chooses a random center point for the needle in the unit square and then chooses a random angle $\\theta \\in (0,\\pi)$ as the needle's orientation. Because the needle pivots at its center, we only need $\\theta$ in this range." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "from matplotlib.lines import Line2D\n", "from matplotlib.patches import Rectangle\n", "\n", "def needle_gen(L=0.5):\n", " '''Drops needle on unit square. Return dictionary describing needle position and \n", " orientation. The `cut` key in the dictionary is True when the needle intersects \n", " an edge of the unit square and is False otherwise.\n", " \n", " L := length of needle (default = 0.5)\n", " '''\n", " assert 0" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above is a good visual check of our simulation and helps motivate our reasoning. Now, we want to concentrate on counting the number of cuts and then use that to estimate the probability of a cut." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,axs = subplots(1,2)\n", "fig.set_size_inches((12,2))\n", "ax=axs[0]\n", "samples=np.array([[needle_gen(L)['cut'] for i in range(300)] for k in range(100)])\n", "\n", "ax.plot(np.mean(samples,axis=1),'o-',alpha=0.3)\n", "ax.axis(xmax=samples.shape[0])\n", "ax.set_xlabel(r'$trial$',fontsize=18)\n", "ax.set_ylabel('$\\mathbb{\\hat{P}}(cut)$',fontsize=18)\n", "ax.set_title('$\\overline{\\mathbb{\\hat{P}}}(cut) = %3.3f,\\hat{\\sigma}=%3.3f$'%\n", " (samples.mean(),(samples.mean(1)).std()))\n", "ax.grid()\n", "\n", "ax = axs[1]\n", "ax.hist( samples.mean(1));\n", "ax.set_title('Distribution of Mean Estimates');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAu0AAAC3CAYAAACmNGDfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPyoCbFGM1Q/sAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows some statistical history of our Monte Carlo simulation. The `samples` array in the prior code-block is a 100x300 matrix of True/False values indicating cut or no-cut. The overall average of this array is our estimate of the probability of a cut. In other words, we count the number of cuts and divide by the total number of needle drops to obtain the estimated probability (approximately 55% in this case of $L=1/2$). The plot on the left shows the average across each of the 300 columns. Thus, there are 100 such column-wise averages (recall the `samples` matrix is 100x300). The title shows the estimated standard deviation across these 100 columnwise averages. \n", "\n", "The plot on the right shows a histogram of the column-wise averages. Why did we partition the simulated samples like this and compute column-wise instead of just using all the data at once? Because we want to get a sense of the spread of the estimates by computing the standard error. If we used all our samples at once, we would not be able to do this even though we'll still use our average of these averages to get our ultimate probability of a cut!\n", "\n", "Naturally, if we wanted to improve the standard deviation of our ensemble of columnwise means, we could simply run a larger simulation, but remember that the standard error only improves at the rate of $\\sqrt{N}$ (where $N$ is the number of samples) so we'd need a sample run *four* times as large to improve the standard error by a factor of *two*. Furthermore, we need to understand the mechanics of this problem better per unit of computing time." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Relative Errors and Using Weighting for Better Efficiency" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There's nothing wrong with the way we have been using the simulation so far, but in the first figure all of those blue needles did not help us compute the probability we were after because they did not touch the edges of the square. Yes, we could reverse the reasoning and use the blue instead of the red for our estimation, but that does not escape the basic problem. For example, if the length of the needle were really short in comparison, then there would have been a lot of blue in our initial plot (try this using this IPython notebook!). In the extreme case, we could find ourselves in a situation where we run the simulation for a long time and not have a single cut! We want to use our valuable computer time to create samples that will improve our estimated solution.\n", "\n", "To recap, we computed a matrix of (100x300) cases of needle drops. Each of element of `samples` in the code above is a `True/False` value as to whether or not the needle touched the edge of the square. We averaged over the 300 columns to compute the estimated probability of a cut (the mean value of the boolean array in this case). The estimated standard deviation is taken over the ensemble of these estimated means. \n", "\n", "A common way to evaluate the quality of the simulated result is to compute the *relative error*, which is the ratio of the estimated standard deviation of the mean to the estimated mean using *all* of the samples ($R_e$). This is computed in the title of the figure below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "fig.set_size_inches(12,2)\n", "ax.plot(samples.mean(1))\n", "ax.set_title(r'$\\hat{\\sigma}=%2.3f,R_e=%2.3f$'% (samples.mean(1).std(),samples.mean(1).std()/samples.mean()), fontsize=18)\n", "ax.set_xlabel('sample history index',fontsize=16)\n", "ax.set_ylabel('$\\mathbb{\\hat{P}}(cut)$',fontsize=18);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAACyCAYAAAAZO5pSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "So far, our relative error is pretty good (the rule of thumb is below 5%), but let's see how we do when the needle length is smaller? The code-block below draws the corresponding figure for the simulation for this case." ] }, { "cell_type": "code", "collapsed": false, "input": [ "L=0.1\n", "\n", "samples_d=[needle_gen(L) for i in range(300*100)]\n", "samples = np.array([k['cut'] for k in samples_d]).reshape(100,300)\n", "\n", "def draw_sample_history(samples):\n", " fig,ax=subplots()\n", " fig.set_size_inches(12,2)\n", " mn = samples.mean(1)\n", " ax.plot(mn)\n", " ax.set_title(r'$\\hat{\\sigma}=%2.3f,R_e=%2.3f$'% (mn.std(),\n", " mn.std()/mn.mean()), fontsize=18)\n", " ax.set_xlabel('sample history index',fontsize=16)\n", " ax.set_ylabel('$\\mathbb{\\hat{P}}(cut)$',fontsize=18);\n", "\n", "draw_sample_history(samples) " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAACyCAYAAAAZO5pSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCFu7P8BCS3oJmwq/KsAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows that for shorter needles, we did *not* do so well for relative error. This situation is illustrated in the figure below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "draw_sim(samples_d[:500]) " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAUoAAAFSCAYAAACUrJbzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nY0wCFyVjjEngomSMMQlclIwxJuH/wDBailiDieYAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure shows there are very few cuts in our simulation with the short needle (red needles). To remedy this, we can alter the code to bias for randomly generating x-coordinates that are within needle length of an edge instead of uniformly random in the unit interval. The code-block below makes this change for the x-coordinate." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def needle_gen_b(L=0.5):\n", " '''Drops needle on unit square using a biased strategy. Return dictionary describing \n", " needle position and orientation. The `cut` key in the dictionary is True when the\n", " needle intersects an edge of the unit square and is False otherwise.\n", " \n", " L := length of needle (default = 0.5)\n", " '''\n", " assert 0" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows that the samples are now clustered at both vertical edges, and, compared with the unbiased simulation, there are more red needles, indicating that we now have more relevent samples.\n", "\n", "The next figure shows the sample history and relative error which is now **much** better than before." ] }, { "cell_type": "code", "collapsed": false, "input": [ "no_bias_samples = samples # save for later\n", "samples = np.array([k['cut'] for k in samples_b]).reshape(100,300)\n", "\n", "draw_sample_history(samples);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAACyCAYAAAAZO5pSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ntJsBy7p0ZQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, that we have a tighter result, we need to make sure we have not changed the result by correcting for the bias we introduced. The probability of being near the edges in the x-direction is $2 L$. We have to multiply our estimated probability by this *weighting* factor." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "fig.set_size_inches(10,3)\n", "ax.hist(no_bias_samples.mean(1),alpha=0.3,normed=1,label='unbiased')\n", "ax.hist(samples.mean(1)*2*L,alpha=0.3,normed=1,label='biased')\n", "ax.legend(loc=0)\n", "ax.set_title('Biased samples more efficiently produce useful samples')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlYAAADRCAYAAAAOj/xWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERERERkICysiIiIiA/l/Sgx8zlsm+3EAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The histogram above shows the spread of the biased samples is much tighter than before, which is what the relative error we just computed is getting at. Still, it's good to back this up with a quick plot." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we illustrated some basic concepts of Monte Carlo methods by examing the famous problem of Buffon's needle. We showed how to code up a quick simulation that visually reveals the key issues and then how to boil this down into a simulation to compute the estimated solution. We also showed how to create biased samples to improve the overall efficiency and precision of our result.\n", "\n", "I carefully used the word [*precision*](https://en.wikipedia.org/wiki/Accuracy_and_precision) as opposed to *accuracy* because we have created a tighter estimate (as measured by relative error), but how do we know that this is the *correct* (i.e. accurate) answer? We don't! In this case, we can solve for the analytical solution (shown in the appendix), but in general, this is *way* too hard to do, otherwise we wouldn't bother with the simulation in the first place.\n", "\n", "The reality is that we have to do what we can using Monte Carlo methods and then carefully consider their computed results using as much domain knowledge as we can muster. In this section, we made the extra effort to generate some visual results along the way as a sanity-check and doing so is *always* worth the extra effort, when feasible. Furthermore, this kind of intermediate result can sometimes suggest a narrow special case for which we *can* generate a related analytical solution that we can use to further develop our simulation.\n", "\n", "As usual, the IPython Notebook corresponding to this section is available for download [here](http://github.com/unpingco/Pig-in-the-Python/blob/master/Buffons_Needle_Sim.ipynb). Play around with the various parameters as suggested above on your own to see what else you can discover about this famouse problem." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Appendix: Analytical Results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this appendix, we carefully derive the analytical solution for our problem using excessive detail. Note that $x_c$ is the needle's center. The needle is entirely contained in the square (at least in the x-direction) when the following two conditions hold:\n", "\n", "$$ 0 < x_c - L/2 \\cos(\\theta) < 1 $$\n", "\n", "$$ 0 < x_c + L/2 \\cos(\\theta) < 1 $$\n", "\n", "combining these two into one big inequality gives:\n", "\n", "$$ \\max(-L/2 \\cos(\\theta) , L/2 \\cos(\\theta) ) < x_c < \\min(1-L/2 \\cos(\\theta) , 1+L/2 \\cos(\\theta) )$$\n", "\n", "In the case where $0< \\theta < \\pi/2 $, we additionally have the following:\n", "\n", "$$ L/2 \\cos(\\theta) < x_c < 1-L/2 \\cos(\\theta) $$\n", "\n", "Because $\\theta$ is uniformly distributed between $0$ and $\\pi$, for this domain of $\\theta$ and $x_c$, we have the probability of the needle being contained completely in the square (in the x-direction) as the following:\n", "\n", "$$ \\frac{1}{\\pi}\\int_0^{\\pi/2} \\int_{L/2 \\cos(\\theta)}^{1-L/2 \\cos(\\theta)} dx_c d\\theta = \\frac{1}{\\pi}\\int_0^{\\pi/2} 1-L \\cos(\\theta) d\\theta = \\frac{1}{2} - \\frac{L}{\\pi} $$ \n", "\n", "Now, we can consider the other half of the domain of $\\theta$, $ \\pi/2 < \\theta < \\pi $, where we have\n", "\n", "$$ -L/2 \\cos(\\theta) < x_c < 1+L/2 \\cos(\\theta)$$\n", "\n", "Then, following the same reasoning as before we obtain:\n", "\n", "$$ \\frac{1}{\\pi}\\int_{\\pi/2}^{\\pi} \\int_{-L/2 \\cos(\\theta)}^{1+L/2 \\cos(\\theta)} dx_c d\\theta = \\frac{1}{\\pi}\\int_{\\pi/2}^{\\pi} 1+L \\cos(\\theta) d\\theta = \\frac{1}{2} - \\frac{L}{\\pi} $$ \n", "\n", "Thus, combining these two results gives the probability of the needle **not** cutting the edge in the x-direction as the following:\n", "\n", "$$ \\mathbb{P}(\\text{no x-cut}) = 1 - \\frac{2 L}{\\pi}$$\n", "Now, we can pursue exactly the same line of reasoning for the y-direction, or, just recognize that by symmetry it would be exactly the same as for the x-direction. Nonetheless, let's be thorough and reproduce the reasoning for the y-direction, just to be on the safe side.\n", "\n", "As before, the condition in the y-direction for the needle being entirely contained in the square in the y-direction is the following:\n", "\n", "$$ \\max(-L/2 \\sin(\\theta) , L/2 \\sin(\\theta) ) < y_c < \\min(1-L/2 \\sin(\\theta) , 1+L/2 \\sin(\\theta) )$$\n", "\n", "which can be combined into one big inequality, given the restrictions on $\\theta \\in (0,\\pi)$ as shown:\n", "\n", "$$ L/2 \\sin(\\theta) < y_c < 1-L/2 \\sin(\\theta) $$\n", "\n", "Then, integrating this out as before, we obtain\n", "\n", "$$ \\frac{1}{\\pi}\\int_0^{\\pi} \\int_{L/2 \\sin(\\theta)}^{1-L/2 \\sin(\\theta)} dy_c d\\theta = \\frac{1}{\\pi}\\int_0^{\\pi} 1-L \\sin(\\theta) d\\theta = 1 - \\frac{2 L}{\\pi} $$ \n", "\n", "$$ \\mathbb{P}(\\text{no y-cut}) = 1 - \\frac{2 L}{\\pi}$$\n", "\n", "which is exactly what we got for the x-direction. It's usually worth the extra work to check things like this instead of trying to be too clever too early.\n", "\n", "Then, combining the x-direction and y-direction results, we obtain,\n", "\n", "$$ \\mathbb{P}(\\text{no cut}) = \\left(1 - \\frac{2 L}{\\pi}\\right)^2$$\n", "\n", "so that\n", "\n", "$$ \\mathbb{P}(\\text{cut}) =1-\\mathbb{P}(\\text{no cut}) = 1-\\left(1 - \\frac{2 L}{\\pi}\\right)^2$$\n", "\n", "which we code next." ] }, { "cell_type": "code", "collapsed": false, "input": [ "prob_cut= lambda l:(1-(1-2*l/pi)**2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use this result later to check or Monte Carlo estimates. Try it!" ] } ], "metadata": {} } ] }