diff --git a/Chapter6_Priorities/Priors.ipynb b/Chapter6_Priorities/Priors.ipynb index 934fb4d9..1ce5a59a 100644 --- a/Chapter6_Priorities/Priors.ipynb +++ b/Chapter6_Priorities/Priors.ipynb @@ -1,6 +1,6 @@ { "metadata": { - "name": "Priors" + "name": "" }, "nbformat": 3, "nbformat_minor": 0, @@ -85,14 +85,16 @@ "output_type": "stream", "stream": "stdout", "text": [ - "\n", - "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", - "For more information, type 'help(pylab)'.\n" + "Populating the interactive namespace from numpy and matplotlib\n" ] }, { + "metadata": {}, "output_type": "display_data", - "png": 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bSWylpaUS3Z+iKIqiKEoSaBJeB39/f9jb22PcuHHw9/cX2ubp6YnFixfDxcUF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\nRBVVta5qK4Hs7GzzbPSNpDcnJ4erV69y9OhRGjd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NmowbN87SoVillJQUevfuzdatW7G1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\n" 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0TzglLdpvk6oL2l4oadG2QjU2moTXIi0tDbGxsejQoQNCQkKaOpxP9pmezSS1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\n3vO+E/VrP/0AAAAASUVORK5CYII=\n", + "text": [ + "" + ] } ], "prompt_number": 2 @@ -1389,11 +1391,109 @@ "\n", "2. There typically exist conjugate priors for simple, one dimensional problems. For larger problems, involving more complicated structures, hope is lost to find a conjugate prior. For smaller models, Wikipedia has a nice [table of conjugate priors](http://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions).\n", "\n", - "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. \n", - "\n", + "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "## Jefferys Priors\n", "\n", - "TODO." + "Earlier, we talked about objective priors rarely being *objective*. Partly what we mean by this is that we want a prior that doesn't bias our posterior estimates. The flat prior seems like a reasonable choice as it assigns equal probability to all values. \n", + "\n", + "But the flat prior is not transformation invariant. What does this mean? Suppose we have a random variable $ \\bf X $ from Bernoulli($\\theta$). We define the prior on $p(\\theta) = 1$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize( 12.5, 5 )\n", + "\n", + "x = linspace( 0.000 ,1, 150 )\n", + "y = linspace( 1.0, 1.0, 150 )\n", + "lines = plt.plot( x, y, color=\"#A60628\", lw = 3 )\n", + "plt.fill_between( x, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", + "plt.autoscale(tight=True)\n", + "plt.ylim( 0, 2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 12, + "text": [ + "(0, 2)" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, let's transform $\\theta$ with the function $\\psi = log \\frac{\\theta}{1-\\theta}$. This is just a function to stretch $\\theta$ across the real line. Now how likely are different values of $\\psi$ under our transformation." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize( 12.5, 5 )\n", + "\n", + "psi = linspace( -10 ,10, 150 )\n", + "y = exp(psi) / (1 + exp(psi))**2\n", + "lines = plt.plot( psi, y, color=\"#A60628\", lw = 3 )\n", + "plt.fill_between( psi, 0, y, alpha = 0.2, color = lines[0].get_color() )\n", + "plt.autoscale(tight=True)\n", + "plt.ylim( 0, 1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 17, + "text": [ + "(0, 1)" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oh no! Our function is no longer flat. It turns out flat priors do carry information in them after all. The point of Jeffreys Priors is to create priors that don't accidentally become informative when you transform the variables you placed them originally on.\n", + "\n", + "Jeffreys Priors are defined as:\n", + "\n", + "$$p_J(\\theta) \\propto \\mathbf{I}(\\theta)^\\frac{1}{2}$$\n", + "$$\\mathbf{I}(\\theta) = - \\mathbb{E}\\bigg[\\frac{d^2 \\text{ log } p(X|\\theta)}{d\\theta^2}\\bigg]$$\n", + "\n", + "$\\mathbf{I}$ being the *Fisher information*" ] }, {