{ "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": 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XlQL1ZRg/zEz17BQKhUIZ1OzZs2egm3BWQccrPOh49T+DWtM+WIjWG5CbpQXL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"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": 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LSiAQCL6CGOs+gvGsx4cIAQDpEWYZjFQF2s+8yQNBfaepemtqeAC23jESz81NRbSIj8p2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\nV3dkZ2djzJgxXXquwMxtMQuBQICtW7di/PjxUKlUWLhwIaKjo7Ft2zY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"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": 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LiaLmfu7/G1V6aMjK8wUNCdgDkOK2fhjNDPZV92DANPpZJH/CNk2KVVoC9pw4S8BeOko6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\n47r8fduxYmTm38DS5EDMt+JVkIrGVuRcqUNarLfRqnC5ublITU21+P4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"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": 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4cytT4qc/VRkfL8Vmi1FfH8E97kO5fgP/1NHPc3lONMXO6vfcQEbegKA1EHXZ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"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": 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htlv/UKGLOliCw2YhNZTOFnP9pnckjB1aJErIDQXDnpkZjnHefNT2KPBreddo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"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": 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wZMgQrF69utL6Dg4OVW6n4rj98MMPVY4DcnJy0qk9hqJLHICqPxd1jTlwNxkaOHAgPv/8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\niIj0wCTKwIy1X7i5YPzUi7F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"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": {} } ] }