From 66a1218fbb6a167a1d3d8e27801184334e727d3d Mon Sep 17 00:00:00 2001 From: unknown Date: Tue, 26 Feb 2013 09:06:10 -0500 Subject: [PATCH] cosmetic changes --- .../Chapter1_Introduction.ipynb | 87 +++++++++++------ Chapter2_MorePyMC/MorePyMC.ipynb | 94 ++++++++++++++----- Chapter3_MCMC/IntroMCMC.ipynb | 32 +++++-- .../LawOfLargeNumbers.ipynb | 41 +++++--- Chapter5_LossFunctions/LossFunctions.ipynb | 40 +++++--- styles/custom.css | 18 +++- 6 files changed, 222 insertions(+), 90 deletions(-) diff --git a/Chapter1_Introduction/Chapter1_Introduction.ipynb b/Chapter1_Introduction/Chapter1_Introduction.ipynb index 7881d4b8..670f2e47 100644 --- a/Chapter1_Introduction/Chapter1_Introduction.ipynb +++ b/Chapter1_Introduction/Chapter1_Introduction.ipynb @@ -87,8 +87,8 @@ "metadata": {}, "source": [ "\n", - "Bayesian Inference in Practice\n", - "------ \n", + "###Bayesian Inference in Practice\n", + "\n", " If frequentist and Bayesian inference were computer programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, whereas the Bayesian function would return a *distribution*.\n", "\n", "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: a distribution over *YES* and *NO*. The function might return \n", @@ -139,7 +139,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "###Example\n", + "#####Example: Coding Horror\n", "______\n", "\n", "\n", @@ -269,8 +269,8 @@ "source": [ "_______\n", "\n", - "Probability Distributions\n", - "------\n", + "##Probability Distributions\n", + "\n", "\n", "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. There are three cases:\n", "\n", @@ -308,10 +308,10 @@ "lambda_ = [1.5, 4.25 ]\n", "colours = [\"#348ABD\", \"#A60628\"]\n", "\n", - "plt.bar( a, poi.pmf( a, lambda_[0]), color=colours[0],label = \"$\\lambda = %.1f$\"%lambda_[0], \n", - " alpha = 0.95)\n", - "plt.bar( a, poi.pmf( a, lambda_[1]), color=colours[1], label = \"$\\lambda = %.1f$\"%lambda_[1], \n", - " alpha = 0.60)\n", + "plt.bar( a, poi.pmf( a, lambda_[0]), color=colours[0],\n", + " label = \"$\\lambda = %.1f$\"%lambda_[0], alpha = 0.95)\n", + "plt.bar( a, poi.pmf( a, lambda_[1]), color=colours[1],\n", + " label = \"$\\lambda = %.1f$\"%lambda_[1], alpha = 0.60)\n", "\n", "plt.xticks( a + 0.4, a )\n", "plt.legend()\n", @@ -366,7 +366,8 @@ "lambda_ = [0.5, 1]\n", "colours = [ \"#A60628\", \"#348ABD\"]\n", "for l,c in zip(lambda_,colours):\n", - " plt.plot( a, expo.pdf( a, scale=1./l), lw=3, color=c, label = \"$\\lambda = %.1f$\"%l)\n", + " plt.plot( a, expo.pdf( a, scale=1./l), lw=3, \n", + " color=c, label = \"$\\lambda = %.1f$\"%l)\n", " plt.fill_between( a, expo.pdf( a, scale=1./l), color=c, alpha = .33)\n", " \n", "plt.legend()\n", @@ -397,8 +398,8 @@ "metadata": {}, "source": [ "\n", - "But what is $\\lambda \\;\\;$?\n", - "-----\n", + "###But what is $\\lambda \\;\\;$?\n", + "\n", "\n", "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We only see $Z$, and must go backwards to try and determine $\\lambda$. The problem is so difficult because there is not a one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is better! \n", "\n", @@ -412,7 +413,7 @@ "metadata": {}, "source": [ "\n", - "###Example\n", + "##### Example: Inferring behaviour from text-message data\n", "_____\n", "Let's try to model a more interesting example, concerning text-message rates:\n", "\n", @@ -654,23 +655,30 @@ "input": [ "figsize(12.5, 10)\n", "#histogram of the samples:\n", + "\n", "plt.subplot(311)\n", - "plt.hist( lambda_1_samples, histtype='stepfilled', bins = 70, \n", - " alpha = 0.85, label = \"positerior of $\\lambda_1$\", color = \"#A60628\",normed = True )\n", + "\n", + "plt.hist( lambda_1_samples, histtype='stepfilled', bins = 70, alpha = 0.85, \n", + " label = \"positerior of $\\lambda_1$\", color = \"#A60628\",normed = True )\n", "plt.legend()\n", - "plt.title(r\"Posterior distributions of the variables $\\lambda_1, \\;\\lambda_2, \\;\\tau$\")\n", + "plt.title(r\"Posterior distributions of the variables $\\lambda_1,\\;\\lambda_2,\\;\\tau$\")\n", + "\n", "\n", "plt.subplot(312)\n", + "\n", "plt.hist( lambda_2_samples,histtype='stepfilled', bins = 70, alpha = 0.85, \n", " label = \"positerior of $\\lambda_2$\",color=\"#7A68A6\", normed = True )\n", "plt.legend(loc = \"upper left\")\n", "\n", + "\n", "plt.subplot(313)\n", - "plt.hist( tau_samples, bins = n_count_data, alpha = 0.85, label = r\"positerior of $\\tau$\",\n", + "\n", + "plt.hist( tau_samples, bins = n_count_data, alpha = 0.85, \n", + " label = r\"positerior of $\\tau$\",\n", " color=\"#467821\", normed = True, histtype='stepfilled' )\n", "plt.legend(loc = \"upper left\")\n", "\n", - "print\n", + "\n", "\n" ], "language": "python", @@ -707,8 +715,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Why would I want samples from the posterior, anyways?\n", - "-------\n", + "###Why would I want samples from the posterior, anyways?\n", + "\n", "\n", "We will deal with this question for the remainder of the book, and it is an understatement to say we can perform amazingly useful things. For now, let's finishing with using posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le70$? Recall that the expected value of a Poisson is equal to its parameter $\\lambda$, then the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n", "\n", @@ -734,7 +742,8 @@ "expected_texts_per_day = np.zeros(n_count_data)\n", "for day in range(0, n_count_data):\n", " ix = day < tau_samples\n", - " expected_texts_per_day[day] = (lambda_1_samples[ix].sum() + lambda_2_samples[~ix].sum() ) /N\n", + " expected_texts_per_day[day] = (lambda_1_samples[ix].sum() \n", + " + lambda_2_samples[~ix].sum() ) /N\n", "\n", " \n", "plt.plot( range( n_count_data), expected_texts_per_day, lw =4, color = \"#E24A33\" )\n", @@ -753,9 +762,9 @@ "outputs": [ { "output_type": "pyout", - "prompt_number": 12, + "prompt_number": 23, "text": [ - "" + "" ] }, { @@ -763,7 +772,7 @@ "png": 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OVX4mAMArr7yCf/7znzh79iy2bNmC9957T2ufgLz3P5Ex4eguRLVQ6cgNqampWj+lli5d\nikuXLmHjxo0IDg7G1KlTMXbsWNy/f19rOytWrMCuXbtw6dIlTJ8+HXfv3sWMGTMAAK+//jqKioow\nZMgQHDt2DImJiTh27BgWLlyIqKgoAMC8efNw9epVjBs3DqdPn0Z8fDx++OEHREdHAwCaN2+O1NRU\nREdH486dO8jJyUGLFi0wadIkTJkyBZs2bcK1a9fwxx9/4Ouvv8bKlSsBlHxl3rFjR7z88ss4efIk\nzp49i3HjxtXIsHLW1tZ49tlnsXLlSpw7dw6nT5/GK6+8Ummjo7q+/vprbNmyBXFxcXj33XcRHR2N\nt956CwAwbtw4eHp6YsCAAdi3bx8SExPx+++/Y/ny5fj555+rtR8bGxvMmjULixcvxvbt2xEXF4dl\ny5YhPDwcCxYs0Fq2qrOQ7u7uMDExwa+//or09HTNsbJ06VKsWbMGy5Ytw/nz53HlyhXs2LFD01VF\nCIFXXnkF7dq1w+LFi7Fy5Uo0bNgQkyZN0my7vOOgMtU9Y1qvXj0sWLAACxYswOeff44rV67gwoUL\n2Lp1K+bPnw+gpPH84Ycf4sSJE0hOTkZERATOnTunGZZy1apV2Lx5My5cuICEhASsX78eZmZmmjPe\nrVu3xqZNm3D+/HmcPXsWY8aMQXFxsabWli1bYtCgQZg5cyaOHDmCixcv4rXXXkNWVpbmj46aqFMp\nJcfZjBkzUFxcjCFDhiAyMhIJCQnYuXOn1mhIj1PymQAA7du3R6dOnTBx4kRkZWVpjZIj+/1PZFT0\n3w2eiCozYcIEoVKpyvyYmJiIu3fviuPHjwtzc3Oxc+dOzTq5ubmiY8eOYvTo0UKI/10Q9ssvvwg/\nPz9haWkpvLy8xP79+7X2lZSUJMaNGycaNmwoLC0thbu7uxg/frzWRW0nTpwQffv2Fba2tsLOzk50\n795dnDx5UghRcuHc2LFjhbOzs1CpVJoLM4uKisTKlStFmzZthIWFhWjQoIHo3bu32L59u2a7iYmJ\nIigoSFhZWQlXV1exZs0a0bt37yovHDUxMdFc6FbKzMxMhIWFaabj4uJEr169hK2trWjVqpX46aef\nyr1w9Lvvvqt0O0IIYWVlpRmVIiEhQZiYmIhNmzaJ3r17CysrK9G8eXOxZcsWrXXu3r0rpk+fLpo2\nbSosLCxE06ZNRXBwsDh79mylz6M8BQUFYv78+ZpteXl5ldnfhAkTtEYYqcjKlStF06ZNhampqXjh\nhRc083fs2CG6d+8ubGxshL29vfDx8REffvihEEKI0NBQUb9+fa3RZ+Li4oSdnZ34/PPPNTWWdxyU\np7xaX331Va16hBBi2rRp4vnnn9ea99VXXwkfHx9hZWUlnJycRLdu3cS///1vIYQQFy5cEC+99JJw\ncXHRHMvz5s3TXKD6xRdfCD8/P2Fvby/q1asn/P39RXh4uGbbsbGxokePHsLa2lp4enqKdevWib59\n+4qJEydqlrl7964YMWKEsLGxEWq1Wrz77rti5MiRZS7q/it1Ks2stJ7KjjMhSl6rYcOGCQcHB2Fj\nYyN8fHy0Rnd58jhU8pkghBCffvqpUKlUIjg4uExdunr/E9U1KiHYCYzI2Bw6dAh9+vTBjRs30KRJ\nE9nlEBmloqIitGnTBkOHDsWqVatkl0NERkZv3V2WL18OLy8veHt7Y+zYscjLy0NGRgYCAwPRqlUr\nBAUF4d69e/oqh4iIqFqOHj2K7du3Iz4+HmfPnsWkSZOQnJyMCRMmyC6NiIyQXhrpiYmJ+PLLLxET\nE4PY2FgUFRVh69atCA0NRWBgIOLi4hAQEFAjQ4oRUYnqXpxHRJUrKirC0qVL4ePjgz59+iAxMREH\nDx6sdn9yIiIl9NLdJSMjA927d9cMdTVs2DDMmjULb7zxBg4fPgy1Wo3U1FT07t1bMy4uEREREVFd\npZchGJ2dnTF37ly4ubnB2toa/fr1Q2BgINLS0qBWqwGUDAVW3s1IIiIi9FEiEREREZFeBQQEVPiY\nXhrp8fHx+OSTT5CYmAgHBweMHDkSmzZt0lpGpVJV+PW8r6+vPsqkx6xYsQLvvPOO7DLqHOYuD7OX\ng7nLwdzlYO7y1MbsY2JiKn1cL33ST506hR49eqB+/fowMzNDcHAwoqKi4OLiohn7OSUlReuOdCRX\n6a2wSb+YuzzMXg7mLgdzl4O5y2OI2eulkd6mTRtER0cjJycHQgjs378f7dq1w6BBgxAWFgYACAsL\nw9ChQ/VRDhERERFRraaX7i4dO3bEK6+8gs6dO8PExAS+vr6YOnUqHjx4gFGjRmH9+vXw8PDAtm3b\n9FEOKfD4HeRIf5i7PMxeDuYuB3OXg7nLY4jZ1/qbGUVERLBPOhEREREZlZiYGPkXjuqCEALp6eko\nKirieNA6cP/+fTg4OMguo84QQsDU1BRXr17Fc889J7ucOunYsWPMXgLmLgdzl4O5y2OI2RtsIz09\nPR12dnawsbGRXYpRaty4sewS6pzs7GzY2trKLoOIiIhqAYPt7nLr1i00adJEQkVEusPjmoiIqG6o\nqruLXkZ30QV2cSFjxOOaiIiIAANupBMZo/v378suoc46duyY7BLqJOYuB3OXg7nLY4jZs5EuwcyZ\nM7Fs2TLZZVTLihUrMG3aNNll1CrJycmoX78+iouLZZdCRERERsZgLxwtz72cAtzPLdTZ9h2szOBo\nbf6Xt6NSqYyqW8OxY8cwbdo0nD9/vlZtyxBxRB15DO2qf2PB3OVg7nIwd3kMMXujaqTfzy3E+bRH\nOtt+e7VtjTTSgZIh93SpsLAQZmZG9fLqFfMjIiIimdjdRUeuXLmCQYMGwdPTEz169MDu3bu1Hr97\n9y6GDx8Od3d3DBo0CDdu3NA8tnDhQrRu3Rru7u547rnncPnyZQBAXl4eFi9ejA4dOqBNmzaYO3cu\ncnNzAZScgW7fvj3WrFmDtm3b4o033kD37t2xd+9ezXYLCwvRsmVLxMbGAgBOnjyJfv36wdPTEz17\n9sTx48c1yyYlJWHgwIFwd3fH8OHDkZGRUe7zfPToEUaNGoXU1FS4ubnB3d0daWlpEELgk08+gZ+f\nH1q0aIFJkybh3r17AIC5c+diwoQJmm28//77GDZsGLKzs8vd1unTp9GnTx+4u7ujTZs2WLRoUbm1\nlGawevVqtGzZEj4+Pti+fbvm8erkN2vWrDLbLy4uxuLFi9GyZUv4+vpqZQsA3333Hbp37w53d3f4\n+voiLCxM81iPHj2wZ88ezXRBQQFatGhR5hsD9kmXxxD7KxoD5i4Hc5eDuctjiNmzka4DBQUFGDt2\nLAICAnD16lWsWLECr732Gq5duwag5Cz69u3b8fe//x1Xr16Ft7c3pk6dCqBkyMmoqCicPHkSSUlJ\n2LBhA5ycnAAAS5YsQUJCAo4ePYpTp04hJSUFq1at0uw3PT0d9+7dw7lz57B69WoEBwfjxx9/1Dx+\n4MABNGjQAN7e3rh16xbGjBmDefPmISEhAUuWLEFISIimMT5lyhR06tQJ165dw9tvv42tW7eW20XH\n1tYWP/zwA1xcXJCcnIykpCSo1Wp88cUX2LVrF3bu3IlLly7B0dERf//73wEA//jHP3Dx4kVs2bIF\nUVFR+O677/D555/Dxsam3G393//9H6ZPn46kpCTExMRg6NChFWafnp6OjIwMXLx4EZ9//jnmzJmj\nyb06+X388cdlth0WFoZ9+/bh8OHDOHDgAMLDw7UyadSoEbZu3YqkpCSsXbsWCxcuxLlz5wCU3I54\n27ZtmmX37duHxo0bo3379hU+FyIiIqq72EjXgVOnTiE7OxuzZ8+GmZkZnn/+eQQFBWk1mIOCgtCt\nWzdYWFhg4cKFOHnyJG7dugULCws8fPgQcXFxKC4uRsuWLaFWqyGEwLfffot//OMfcHBwQL169TBn\nzhz89NNPmm2amJhg/vz5MDc3h5WVFUaMGIHdu3drzhZv374dw4cPBwD88MMPCAwM1IzP2bt3b/j4\n+GDv3r24ceMGzp49iwULFsDc3Bzdu3dHv379KuyiU978sLAwLFy4EI0bN4a5uTnmzZuH8PBwFBcX\nw9raGuvWrcPChQsxbdo0rFy5UnPzpPK2ZWFhgT///BN3796FjY0NOnfuXGn+pXX36NEDgYGB2LFj\nx1Pl96QdO3Zg+vTpaNKkCRwdHTFnzhytegMDA+Hu7g6g5Mz5Cy+8gKioKADAiBEjsG/fPjx8+BAA\nsG3bNowePbrMPtgnXR5D7K9oDJi7HMxdDuYujyFmz063OpCamoqmTZtqzXN1dUVqaiqAkgtHH79h\nja2tLZycnJCamornn38er776KubNm4fr169j4MCBWLJkCXJzc5GdnY0XXnhBs54QQquR2KBBA1hY\nWGimPT090apVK+zevRtBQUHYs2cPFixYAAC4fv06fv75Z61uOEVFRejZsydSUlLg6OgIa2trrfpv\n3rypOIPk5GSMHz8eJib/+zvQzMwM6enpcHFxgZ+fHzw8PHD37l0MGTKk0m2tWbMGy5cvR7du3eDu\n7o558+YhKCio3GXLqzstLQ13796tdn5PSktL03pdmzVrpvX4/v37sXLlSsTHx6O4uBg5OTnw8vIC\nUHIHV39/f4SHh2PAgAGIiIhAaGhopc+biIiI6i6eSdcBFxcX3Lx5U6sBeP36da2zxY83eB8+fIjM\nzEy4uLgAAKZOnYoDBw4gKioK8fHxWLt2LRo0aABra2tERUUhISEBCQkJSExMRFJSUqW1lHZ52bVr\nF1q3bg0PDw8AJQ3MUaNGabaVkJCA5ORkzJo1Cy4uLrh37x6ys7O16q9oRJry5jdr1gzbt2/X2v7N\nmzc1z/Grr75Cfn4+XFxcsGbNmkq31bx5c3z55Ze4evUqZs2ahQkTJiAnJ6fcWsqr28XFBfXr13+q\n/B6nVqu1rh14/P95eXkICQnBG2+8gbi4OCQkJCAwMFDrGBgzZgx++OEH/Pzzz/D399dk8Tj2SZfH\nEPsrGgPmLgdzl4O5y2OI2bORrgOdO3eGtbU11qxZg4KCAhw7dgx79+5FcHCwZpl9+/bh999/R35+\nPpYvX44uXbqgSZMmOHPmDE6dOoWCggJYW1vD0tISJiYmUKlUeOWVV7BgwQLcuXMHQMkt5A8cOFBp\nLcHBwThw4AA2bNiAESNGaOaPHDkSe/bswYEDB1BUVITc3FwcO3YMt27dgqurK3x8fBAaGoqCggJE\nR0drXfT4pIYNGyIzMxNZWVmaeRMmTMCHH36oacjeuXMHu3btAgBcu3YNy5Ytw3/+8x+sW7cOa9as\n0VxAWd62tm3bpnnO9vb2UKlUWmfon1Rad1RUFPbt24chQ4Y8dX6PGzp0KL744gvcunUL9+7dw6ef\nfqp5LD8/H/n5+ahfvz5MTEywf/9+HDx4UGv9AQMG4I8//sAXX3xRblcXIiIiolJG1d3FwcoM7dW2\nOt2+Eubm5ti8eTP+/ve/Y/Xq1WjSpAnWrVuHFi1aACg5Wzxy5EisXLkSJ0+eRMeOHfHFF18AAB48\neICFCxciKSkJlpaWCAgIwBtvvAEAeO+997Bq1SoEBQXh7t27aNKkCSZNmoQ+ffpotvsktVoNf39/\nREZGYsOGDZr5TZs2xaZNm/D+++9jypQpMDU1hZ+fH/75z38CAL788kvMmDEDzzzzDLp06YIxY8ZU\neJa3VatWGD58OHx9fVFcXIyoqChMmzYNQggMHz4cqampaNCgAYKDgxEUFITp06dj9uzZaNeuHQBg\n8eLFmDZtGg4ePFhmW5GRkThw4AAWL16MnJwcuLq64quvvoKlpWW5tTRq1AiOjo5o164dbGxs8PHH\nH2tyf5r8HvfKK6/g2rVr6NmzJ+zt7TFz5kzNX+Z2dnYIDQ3FpEmTkJeXhxdffBH9+/fXWt/KygoD\nBw7Ejh07MHDgwHL3wT7p8hhif0VjwNzlYO5yMHd5DDF7ldD1gN1/UUREBHx9fcvMT0lJ0XQfIQIM\n40ZIq1atwp9//ol169aV+ziPayIiorohJiZGM4BHedjdhUhPMjMz8d133yEkJKTCZWT0Sb+XU4Ck\nzJxyf+7lFOi9HlkMsb+iMWDucjB3OZi7PIaYvVF1dyGqqsuKLN9++y0WLlyI0aNHo1u3brLL0VLZ\nnXpr8i7YSu+aAAAgAElEQVS7REREpBy7uxDVIjKO66TMnEob6e5O1uU+RkRERE+vVnR3uXLlCjp1\n6qT5cXBwwJo1a5CRkYHAwEC0atUKQUFBmtvGExERERHVZXpppLdu3RpnzpzBmTNncPr0adjY2GDY\nsGEIDQ1FYGAg4uLiEBAQUK2bu9TyLwCInkpmZqbsEuosQ+yvaAyYuxzMXQ7mLo8hZq/3C0f379+P\nFi1awNXVFeHh4ZqL6EJCQrBjxw7F2zE1NdW6aQ2RocvOzkZeXp7sMoiIiKgW0PuFo1u3bsWYMWMA\nlNxmXa1WAygZzzstLa3cdWbOnAk3NzcAJTez8fb2xrPPPov09HQkJibCxMREM7506egYnOa0IU3b\n29vD1NQUjx49wrFjxzTjuZb+5a/L6bQHebDy7AgAuBTzOwCgrW9XAMCp6Ehct7PUaz2ypp977rla\nVU9dmi5VW+pROr074hAe5Rehc7ceAEreLwDQuVsPOFiZ4fzp32tVvTzea8d0qdpST12ZLp0ns57Y\n2FjNzRqTk5MxefJkVEavF47m5+ejadOmuHjxIho2bAgnJyetr/ednZ2RkZGhtU5FF44SUc3ghaNE\nT4fvHSL6K2rFhaOldu3aBT8/PzRs2BBAydnz1NRUACWjWjRq1Eif5VAlDLHvljFg7vIwezmYuxzM\nXQ7mLo8hZq/XRvqWLVs0XV0AYPDgwQgLCwMAhIWFYejQofosh4iIiIioVlLU3WXz5s3w8fFBu3bt\ncOXKFUyZMgWmpqZYt24d2rRpo2hHjx49gru7OxISEmBnZwcAyMjIwKhRo5CcnAwPDw9s27YNjo6O\nWuuxuwuRbvEre6Knw/cOEf0VVXV3UXTh6KJFixAVFQUAmDt3Lvz9/WFra4sZM2bgwIEDigqxtbXF\nnTt3tOY5Oztj//79itYnIiIiIqorFHV3uXPnDtRqNXJycnD8+HEsXboU7733Hs6cOaPr+kgSQ+y7\nZQyYuzzMXg7mLgdzl4O5y2OI2Ss6k96wYUNcvXoVsbGx6NKlCywtLfHo0SPeUIiIiIiISAcUNdIX\nL16Mzp07w8TEBN9//z2AkpsS+fj46LQ4kufxcUVJf5i7PMxeDuYuB3OXg7nLY4jZK2qkT5gwASNH\njoRKpYKNjQ0AoHv37ujatatOiyMiIiIiqosUD8GYm5uL7du3Y+XKlQCAgoICFBYW6qwwkssQ+24Z\nA+YuD7OXg7nLwdzlYO7yGGL2ihrphw8fRuvWrbF582Z8+OGHAICrV69i+vTpOi2OiIiIiKguUjRO\nuo+PD/75z3+ib9++cHJyQmZmJnJzc+Hm5ob09HSdFshx0ol0i2M9Ez0dvneI6K+oapx0RWfSk5KS\n0LdvX6155ubmKCoq+mvVERERERFRGYoa6W3btsXu3bu15kVERMDb21snRZF8hth3yxgwd3mYvRzM\nXQ7mLgdzl8cQs1c0usvHH3+MgQMH4qWXXkJubi6mTp2KX375BT///LOu6yMiIiIiqnMU9UkHgJs3\nb2LTpk1ISkqCm5sbXn75ZTRr1kzX9bFPOpGOsV8t0dPhe4eI/oqq+qQrOpMOAE2bNsU777xTI0UR\nEREREVHFFDXSx48fD5VKBQAQQmj+b2FhAVdXVwwdOhQdO3bUXZWkd8eOHTPIu3MZOuYuD7OXg7nL\nwdzlYO7yGGL2ii4ctbe3x88//wwhBJo1a4bi4mKEh4fD1NQUFy9eRLdu3RAWFqbrWomIiIiI6gRF\nZ9Lj4uLw22+/4dlnn9XMi4qKwuLFi7F//37s2rULc+bMQUhIiM4KJf0ytL82jQVzl4fZy8Hc5WDu\ncjB3eQwxe0Vn0n///Xd07dpVa17nzp1x4sQJAEC/fv1w/fr1mq+OiIiIiKgOUtRI9/HxwYIFC5Cb\nmwsAyMnJwaJFi+Dj4wMASEhIQP369XVXJemdIY4nagyYuzzMXg7mLgdzl4O5y2OI2StqpIeFheHo\n0aOws7ODWq2Gvb09jhw5gm+++QYAkJmZic8//1yXdRIRERER1RmKx0kHgOTkZNy6dQuNGzeGu7t7\ntXZ07949vPrqq7hw4QJUKhU2bNiAli1bYvTo0UhKSoKHhwe2bdsGR0dHrfU4TjqRbnGsZ6Knw/cO\nEf0VVY2TruhMeik3Nzd07doVrq6uKC4uRnFxseJ133zzTbz00ku4dOkSzp07hzZt2iA0NBSBgYGI\ni4tDQEAAQkNDq1MOEREREZFRUtRIv3nzJoYNGwZnZ2eYmZlpfszNzRXt5P79+zh69CgmTZoEADAz\nM4ODgwPCw8M1I8KEhIRgx44dT/k0qKYZYt8tY8Dc5WH2cjB3OZi7HMxdHkPMXtEQjNOmTYO1tTUO\nHDiAXr164fDhw/jggw/Qv39/RTtJSEhAw4YNMXHiRPzxxx/w8/PDJ598grS0NKjVagCAWq1GWlpa\nuevPnDkTbm5uAErGbPf29tYMpVMaOqdrdrpUbamnrkzHxsbqff9pD/Jg5VlyM7JLMb8DANr6lozm\ndCo6EtftLGtNPpw2vunY2NhaVU91pk9FRyIhM1fzfnny/SO7Pk7XvmlDPt4NfVrG79cnp2NjY5GV\nlQWgpAv55MmTURlFfdKdnZ2RnJyMevXqwcHBAffv30dGRgZ69OiBy5cvV7U6Tp06he7duyMyMhJd\nunTB7NmzYWdnh7Vr1yIzM1NrPxkZGVrrsk86kW6xXy3R0+F7h4j+ihrpk17avQUAnJyckJ6eDltb\nW9y8eVNREc2aNUOzZs3QpUsXAMCIESMQExMDFxcXpKamAgBSUlLQqFEjRdsjIiIiIjJmihrp/v7+\n2LVrF4CSGxeNHj0aw4YNQ+fOnRXtxMXFBa6uroiLiwMA7N+/H15eXhg0aBDCwsIAlAzzOHTo0Kd5\nDqQDpV/TkH4xd3mYvRzMXQ7mLgdzl8cQszdTstDGjRtR2itm9erV+Oijj/Dw4UPMnj1b8Y4+++wz\njBs3Dvn5+XjmmWewYcMGFBUVYdSoUVi/fr1mCEYiIiIiorquWuOky8A+6US6xX61RE+H7x0i+itq\npE/6Rx99hDNnzgAAoqOj4ebmBk9PT0RGRtZMlUREREREpKGokb569Wo0b94cADB//ny89dZbWLRo\nEebMmaPT4kgeQ+y7ZQyYuzzMXg7mLgdzl4O5y2OI2Svqk56VlQUHBwdkZWXh3LlziIiIgKmpKd56\n6y1d10dEREREVOcoaqS7urri+PHjuHDhAnr27AlTU1Pcv38fpqamuq6PJCkdfF9f7uUU4H5uYYWP\nO1iZwdFa2R1uDZm+c6f/YfZyMHc5mLsczF0eQ8xeUSN91apVGDFiBCwsLPDjjz8CAHbu3ImuXbvq\ntDiqO+7nFlZ4ARZQchFWXWikExEREQEK+6S/9NJLSElJQVJSkmZs9FGjRiE8PFynxZE8hth3yxgw\nd3mYvRzMXQ7mLgdzl8cQs1fUSL9w4YLmzqAPHjzAu+++i2XLlqGgoECnxRERERER1UWKGuljxozB\n/fv3AQBvv/02jh49iujoaLz22ms6LY7kMcS+W8aAucvD7OVg7nIwdzmYuzyGmL2iPulJSUlo3bo1\niouL8dNPP+HixYuwsbGBh4eHjssjIiIiIqp7FJ1Jt7KyQlZWFk6ePAl3d3c0bNgQFhYWyM3N1XV9\nJIkh9t0yBsxdHmYvB3OXg7nLwdzlMcTsFZ1JHzt2LPr06YMHDx7g9ddfB1ByK9PSGxwREREREVHN\nUQkhhJIF9+zZAwsLC7zwwgsAgFOnTiErKwt9+vTRaYERERHw9fXV6T5IvqTMnCqHYHR3stZjRXVH\nZdkzd6KK8b1DRH9FTEwMAgICKnxc0Zl0AOjXrx+Sk5MRHR2Nbt26aYZiJCIiIiKimqWoT3pycjKe\nffZZtG3bVtPi/+GHH/Dqq6/qtDiSxxD7bhkD5i4Ps5eDucvB3OVg7vIYYvaKzqRPnToVL730Eo4e\nPYr69esDAIKCgjB37lydFkdEREQl7uUU4H5uYYWPO1iZ8c7MREZEUSP9xIkT+O2332Bi8r8T7w4O\nDpqx08n4GOJ4osaAucvD7OVg7srdzy2s8todpY105i4Hc5fHELNX1N3FxcUFV69e1Zp38eJFuLu7\n66QoIiIiIqK6TFEj/e2338bAgQPx9ddfo7CwEFu2bMHo0aMxb948XddHkhhi3y1jwNzlYfZyMHc5\nmLsczF0eQ8xeUXeXSZMmoX79+vj3v/8NV1dXhIWF4cMPP8TQoUN1XR8RERERUZ2jeAjGIUOGYMiQ\nIU+9Iw8PD9jb28PU1BTm5uY4ceIEMjIyMHr0aCQlJcHDwwPbtm2Do6PjU++Dao4h9t0yBsxdHmYv\nB3OXg7nLwdzlMcTsFTfSjxw5grNnz+Lhw4cAACEEVCoVFixYoGh9lUqFQ4cOwdnZWTMvNDQUgYGB\nmDdvHlasWIHQ0FCEhoZW8ykQERERERkXRX3S33jjDYwcORJHjhzBpUuXcOnSJVy+fBmXLl2q1s6e\nvLlpeHg4QkJCAAAhISHYsWNHtbZHumOIfbeMAXOXh9nLwdzlYO5yMHd5DDF7RWfSN23ahAsXLqBJ\nkyZPvSOVSoW+ffvC1NQUr732GqZMmYK0tDSo1WoAgFqtRlpaWrnrzpw5E25ubgAAe3t7eHt7a762\nKA2d0zU7XUpf+3P18gMAXIr5HQDQ1rer1nT7/n1qVT66mo6NjdX7/tMe5MHKsyOAsvmfio7EdTvL\nWpMPp41vOjY2tlbVU53pU9GRSMjMLfN5VTqt7/3x/Vr7pw35eDf0aRm/X5+cjo2NRVZWFoCSG4VO\nnjwZlVGJJ09vl6NDhw44cOAAGjRoUNWiFUpJSUHjxo1x+/ZtBAYG4rPPPsPgwYORmZmpWcbZ2RkZ\nGRla60VERMDX1/ep90uGISkzp8rxf92drPVYUd1RWfbMnahi+n7v8HOSyLjExMQgICCgwsfNlGxk\n/fr1mDJlCsaOHas5812qZ8+eigpp3LgxAKBhw4YYNmwYTpw4AbVajdTUVLi4uCAlJQWNGjVStC0i\nIiIiImOmqE/66dOn8dtvv2H69OkYN26c1o8S2dnZePDgAQDg0aNH2Lt3L7y9vTF48GCEhYUBAMLC\nwjikYy1S+jUN6Rdzl4fZy2Hsud/LKUBSZk6FP/dyCqTUZey511bMXR5DzF7RmfSFCxdi586dCAwM\nfKqdpKWlYdiwYQCAwsJCjBs3DkFBQejcuTNGjRqF9evXa4ZgJCIiMhb3cwur7KLiaG2ux4qIyFAo\naqTb2tqiV69eT70TT09PnD17tsx8Z2dn7N+//6m3S7pTeqED6Rdzl4fZy8Hc5WDucjB3eQwxe0Xd\nXZYsWYLZs2cjJSUFxcXFWj9ERERERFSzFDXSJ02ahH//+99o2rQpzMzMND/m5vyKzlgZYt8tY8Dc\n5WH2cjB3OZi7HMxdHkPMXlF3lz///FPXdRARERER0f+nqJHu4eGh+f+NGzfQrFkzXdVDtYQh9t0y\nBsxdHmYvB3OXg7nLwdzlMcTsFXV3eVy7du10UQcREREREf1/1W6kK7hBKRkBQ+y7ZQyYuzzMXg7m\nLgdzl4O5y2OI2bORTkRERERUyyhqpKempmr+//Dhw3Lnk3ExxL5bxoC5y8Ps5WDucjB3OZi7PIaY\nvaJGeqtWrcqdz/7pREREREQ1T1EjvbwuLllZWTAxqXZvGTIQhth3yxgwd3mYvRzMXQ7mLgdzl8cQ\ns690CEZXV1cAQHZ2tub/pe7evYsxY8borjIiIiIiojqq0kb6xo0bAQD9+/fHpk2bNGfUVSoV1Go1\n2rRpo/sKSQpD7LtlDJi7PMxeDuYuB3OXg7nLY4jZV9pI7927N4CSs+Y2NjZlHi8oKIC5ublOCiMi\nIiIiqqsUdSofPHgwbt26pTXvjz/+gJ+fn06KIvkMse+WMWDu8jB7OZi7HMxdDuYujyFmr6iR7ufn\nh44dO+L7779HcXExQkND8cILL2DGjBm6ro+IiIiIqM6ptLtLqRUrVmDgwIEYP3483nnnHTRp0gQn\nTpxAixYtdF0fSWKIfbeMAXOXh9nLwdzlYO5yMHd5DDF7xWMo/vnnn8jKykKDBg3w8OFD5OTk6LIu\nIiIiIqI6S1EjfcSIEVi2bBl2796NU6dO4bXXXkOvXr2wcuVKXddHkhhi3y1jwNzlYfZyMHc5mLsc\nzF0eQ8xeUSO9YcOGOHv2LPz9/QEAM2fORHR0NH788UedFkdEREREVBcpaqSvW7cO1tbWKC4uRkpK\nCgCgVatWiIyMrNbOioqK0KlTJwwaNAgAkJGRgcDAQLRq1QpBQUG4d+9eNcsnXTHEvlvGgLnLw+zl\nYO5yMHc5mLs8hpi9okZ6ZmYmxo4dCysrKzzzzDMAgPDwcLz33nvV2tmnn36Kdu3aQaVSAQBCQ0MR\nGBiIuLg4BAQEIDQ0tJrlExEREREZH0WN9GnTpsHe3h5JSUmwtLQEAHTv3h1bt25VvKMbN27gt99+\nw6uvvqq5c2l4eDhCQkIAACEhIdixY0d16ycdMcS+W8aAucvD7OVg7nIwdzmYuzyGmL2iIRgjIiKQ\nkpKidXfRhg0bIj09XfGO5syZg1WrViErK0szLy0tDWq1GgCgVquRlpZW7rozZ86Em5sbAMDe3h7e\n3t6ary1KQ+d0zU6X0tf+XL1Kbox1KeZ3AEBb365a0+3796lV+ehqOjY2Vu/7T3uQByvPjgDK5n8q\nOhLX7SxrTT6cNr7p2NjYWlVPdaZPRUciITO3zOdV6XRV769LMb8j18kK7v0DamR/fL/W/mlDPt4N\nfVrG79cnp2NjYzXt4OTkZEyePBmVUYnS09qVaNGiBY4cOYImTZrAyckJmZmZSE5ORlBQEC5fvlzV\n6ti5cyd27dqFf/3rXzh06BA++ugj/PLLL5ptlXJ2dkZGRobWuhEREfD19a1yH2TYkjJzcD7tUYWP\nt1fbwt3JWo8V1R2VZc/ciSqm5L1Tk59t/JwkMi4xMTEICAio8HFF3V1effVVjBgxAgcOHEBxcTGi\noqIQEhKC1157TVERkZGRCA8Ph6enJ8aMGYMDBw5g/PjxUKvVSE1NBQCkpKSgUaNGirZHRERERGTM\nFDXS33nnHYwePRqvv/46CgoKMHHiRAwZMgSzZ89WtJNly5bh+vXrSEhIwNatW9GnTx9s3LgRgwcP\nRlhYGAAgLCwMQ4cOffpnQjWq9Gsa0i/mLg+zl4O5y8Hc5WDu1XMvpwBJmTnl/tzLKajWtgwxezMl\nC6WlpeHNN9/Em2++qTU/NTUVLi4u1d5p6egu8+fPx6hRo7B+/Xp4eHhg27Zt1d4WERERERmf+7mF\nlXYpc7Q2L/cxY6Gokd6qVSutCz5LtWvXrkwf8qr06tULvXr1AlDSB33//v3VWp/0o/RCB9Iv5i4P\ns5eDucvB3OVg7vIYYvaKuruUd21pVlYWTEwUrU5ERERERNVQaSvb1dUVrq6uyM7O1vy/9MfFxQVD\nhgzRV52kZ4bYd8sYMHd5mL0czF0O5i4Hc5fHELOvtLvLxo0bAQD9+/fHpk2bNGfUVSoV1Go12rRp\no/sKiYiIiIjqmEob6b179wYA3LlzB7a2tvqoh2oJQ+y7ZQyYuzzMXg7mLgdzl4O517x7OQW4n1tY\n4eMOVmZwtDY3yOwVXTjKBjoRERER1TaVjQADGPYoMLzyk8pliH23jAFzl4fZy8Hc5WDucjB3eQwx\nezbSiYiIiIhqGTbSqVyG2HfLGDB3eZi9HMxdDuYuB3OXxxCzV9QnHQC8vb0RGxuL06dPw8/PT5c1\nGY3KLmYovZCBiIiI5FB60SGRDJWeSZ87dy42b96MS5cu4caNGwCAvn376qUwY1B6MUN5P5V9KNQG\nhth3yxgwd3mYvRzMXQ7mXqKy39O6+F3N3OUxxOwrbaR7eXnh+PHjmDhxIh48eIDXX38dRUVFyM/P\n11d9RERERER1TqWN9EmTJuFf//oXoqOjYWdnh2effRa5ublwc3NDp06dMGXKFH3VSXpmiH23jAFz\nl4fZy8Hc5WDucjB3eQwx+0r7pLu5ucHX1xe+vr4oKipCcHAwZsyYgdTUVCQkJODMmTP6qpOIiIiI\nqM6o9Ez6xYsXMXfuXNjZ2SEvLw8dOnRATk4Ovv/+exQWFiI4OFhfdZKeGWLfLWPA3OVh9nIwdzmY\nuxzMXR5DzL7SRnq9evXw/PPPY86cObCxsUF0dDTMzMxw6NAhjB07Fmq1Wl91EhERERHVGYqHYBw+\nfDicnJxgbm6OdevWAQAKCgp0VhjJZYh9t4wBc5eH2cvB3OVg7nIwd3kMMXvFNzP66quvAABhYWGa\neebmHDuUiIiIiKimVfuOo4MHD9ZFHVTLGGLfLWNQW3O/l1OApMycCn/u5Rj+t2q1NXtjx9zlYO5y\nMHd5DDF7xd1diKjuKr3hR0Xaq215Vz4iIqIapJdGem5uLnr16oW8vDzk5+djyJAhWL58OTIyMjB6\n9GgkJSXBw8MD27Ztg6Ojoz5KoioYYt8tY8Dc5WH2cjB3OZTkfi+noNI7bjpYmfGP82qScbxX9jrW\npdfQED9r9NJIt7KywsGDB2FjY4PCwkI899xzOHbsGMLDwxEYGIh58+ZhxYoVCA0NRWhoqD5KIiIi\nokrwGzTjUNnryNewdqt2n/SnZWNjAwDIz89HUVERnJycEB4ejpCQEABASEgIduzYoa9yqAqG2HfL\nGDB3eZi9HMxdDuYuB3OXxxCzr/BM+vPPP681rVKpIITQmgaAI0eOKNpRcXExfH19ER8fj+nTp8PL\nywtpaWmasdbVajXS0tLKXXfmzJlwc3MDANjb28Pb21vztUVp6LV1+lLM7wCAtr5dtabb9+9TK+qr\naLqUvvbn6uVn0HnV1HRsbKze95/2IA9Wnh0BlM3/VHQkrttZ8vXhtM6mY2Nja1U91Zk+FR2JhMzc\nMu+H0umq3l+XYn5HrpMV3PsH1Mj+St+v+np+Nb0/GdM1+frU1uO9ss/v0ud3L6cAEYdK2nOdu/UA\nUPL6lk47WJnh/Onf9VKvrn4/yfj9+uR0bGwssrKyAADJycmYPHkyKqMSj7e8H/PNN99o/h8fH48N\nGzYgJCQEbm5uSE5ORlhYGCZNmoQlS5ZUuoMn3b9/H/369cPy5csRHByMzMxMzWPOzs7IyMjQWj4i\nIgK+vr7V2kdtkZSZU+lXTO5O1nquqPaqLCuAeemSkuOUrw9RWfp+7+j7fVgX3vd1/TnW9s94Q65d\niZiYGAQEBFT4uFlFD0yYMEHz/65du2LPnj3w8vLSzBs3btxTNdIdHBwwYMAAnD59Gmq1GqmpqXBx\ncUFKSgoaNWpUrW0RERERERkjRX3SL1++jObNm2vN8/T0xKVLlxTt5M6dO7h37x4AICcnB/v27UOn\nTp0wePBgzc2RwsLCMHTo0OrUTjr0ZLcXY1TZ2N+yxv2uC7nXVsxeDuYuB3OXg7nLY4jZV3gm/XG9\nevXCxIkTsWTJEri6uiI5ORnvv/8+evbsqWgnKSkpCAkJQXFxMYqLizF+/HgEBASgU6dOGDVqFNav\nX68ZgpFIX3jFOxEREdVWihrpGzZswMyZM9G+fXsUFhbCzMwMwcHB2LBhg6KdeHt7IyYmpsx8Z2dn\n7N+/v3oVk16UXuhA+sXc5WH2cjB3OZi7HMxdHkPMXlEjvX79+ti6dSuKiopw584dNGjQAKamprqu\njYiIiIioTlI8TvqlS5ewdOlSLFmyBKamprh8+TLOnTuny9pIIkPsu2UMmLs8zF4O5i4Hc5eDuctj\niNkraqT/8MMP6NmzJ27evIlvv/0WAPDgwQO89dZbOi2OiEhfHuYV1roLiYmIDE1tHJTBUCnq7rJ4\n8WLs27cPPj4+mos7fXx8cPbsWZ0WR/IYYt8tY8Dc5Wnr25UXEkvAY14O5i5HXci9tg7KYIjZKzqT\nfvv2bXTo0KHsyiaKe8sQEREREZFCilrZvr6+2Lhxo9a877//Hv7+/jopiuQzxL5bxoC5y1N6C2zS\nLx7zcjB3OZi7PIaYvaLuLp999hkCAwOxfv16ZGdnIygoCHFxcdi7d6+u6yMiIiIiqnMUNdLbtGmD\ny5cvY+fOnRg4cCDc3NwwcOBA1KtXT9f1kSSG2HfLGDB3eTp361FhP0rSHR7zcjB3OZi7PIaYvaJG\n+qxZs7BmzRqMHj1aa/7s2bPxySef6KQwIiIiIqK6SlGf9IruLFo6HCMZH0Psu2UMmLs87JMuB495\nOZi7HMxdHkPMvtIz6evXrwcAFBYW4uuvv4YQAiqVCgAQHx+Phg0b6r5CIiIiIqI6ptJG+saNG6FS\nqVBQUKA1uotKpYJarUZYWJjOC1TiXk4B7ucWVvi4g5WZ4nE5a3JbhswQ+24ZA+YuD/uky8FjXg7m\nLgdzl8cQs6+0kX7o0CEAwMKFC7F06VJ91PNUKhs4H6je4Pk1uS0iIiIioqeh6MLRnj174sqVK2jd\nurVm3pUrV5CcnIzAwECdFUfyHDt2zCD/6jR0zF2eU9GRsPLsKLuMOsdQj/nizLuw2r8bLa/fKPdx\nWxtz5FqawjavCC2zK74VeulyStTktiKvJaJHCw+97a+20vdzVJJ7TavsOer7OK1unjVZu4zsAcDE\nwRkWweOfal1FjfSZM2fiyJEjWvPq1auHGTNm4OrVq0+1YyIifWAXNqpphTFRyP3PKtg+fADbypYD\nYAWgSVXbU7jfmtxW0d0HKEw6r7f91Vb6fo5Kcq9pVT1HfR+n1cmzJmuXkT0AqJq46baRfvv2bTRp\noh1B48aNkZaW9lQ7pdrPEM9sGQPmXvOUdmFjn3Q5DOmYFwX5yN/6FQr2/Fd2KX9Z9/p2skuok5i7\nPIaYvaJGuqenJyIiIhAQEKCZd+jQIXh6euqsMJJLydlHADxDWcN41peodipOvYHctctQnMhvj4lI\nuYJigaTMHK15Sn+XK2qkf/DBBxg+fDgmT56MZ555BteuXcOGDRsqHD+dDF/EoSOV9s9try75kpcX\n2aTfFXwAABmMSURBVNYsJbkzU91gn3Q5DKFPesHx/cjbsAbI1f5FK0xMcb3bAOQ6NCizThM7C9S3\nscDd7HzcepBf4bZLl1NC6bYqW650meMXLuFZr7Y1sj9Dpq/Xpzq51zQldek7B6VqsnZ9Z19aV6GV\nLW4/0VZS+rtcUSN9yJAh2Lt3L9avX49ff/0Vrq6u2Lt3L7p06fJ0lRMREdVyIjcHeWFrUXh0b5nH\nVA1dcH/8XCTYNCt33fpqW5g7WSMvMwcplZzMKF1OCaXbqmy50mXMrJxgXsUfRzVZe22lr9enOrnX\nNCV16TsHpWqydn1nX1VdSihqpAOAv78//P39n2on169fxyuvvIL09HSoVCpMnToVs2bNQkZGBkaP\nHo2kpCR4eHhg27ZtcHR0fKp9UM1i/1w5mLs8zF6O2noWvSgpHrlrl0KkXC/zmGmX52H16lu4k28K\nGOgx096va5mv4B9X2qWRalZtPd7rAkPM3kTJQrm5uViwYAGaN28Oe3t7AMDevXuxdu1aRTsxNzfH\n6tWrceHCBURHR+Nf//oXLl26hNDQUAQGBiIuLg4BAQEIDQ19+mdCRET0F4miIuTv/gk5779RtoFu\nbgHLSW/CatZiqGzrySmwhpReUF3RT2XXxhCRfihqpM+ZMwfnz5/Hd999BxOTklW8vLzw+eefK9qJ\ni4sLfHx8AJQM3di2bVvcvHkT4eHhCAkJAQCEhIRgx44dT/McSAdORUfKLqFOYu7yMHs5jh07JrsE\nAIAQAoUnjyF7/hTkb1oHFGiPu6xq4gbrJWth3mcgVCqVpCprDo93OWrL8V4XGWL2ir7P+u9//4tr\n166hXr16mg+npk2b4ubNm9XeYWJiIs6cOYOuXbsiLS0NarUaAKBWqysc0nHmzJlwc3MDANjb28Pb\n21vztcWxY8eQ9iBPc8HXpZjfAQBtfbtqpnOdrODeP0CzPACt9R+fPhUdiYTMXK31H9/eqehIXLez\nrHD9J6fLqwcA2vfvo2h9WdOlqqq/osdLp5Xuz9XLT0pete31uXLxAixq8PhTMl3Z+6d0f7JeH10/\nvyc/H6p6frsjDuFRfhE6d+uhyQco6SrjYGWG86d/l/58DW06NjZWej3dG9gjb8uXOH7iZMn0/x+q\nLeruAwDA88NHwfLl6Th+6jSQdFPx7wtZv58qe78qOd4f315N/j6sqen2fl1xP7dQ6/1XWg8ABPTu\nCUdr8xr/fPirr4+s472mjoea3p++fz/FxsbqJe/Kjoekq5eQ/fABjtmaI+t2CiZPnozKqIQQotIl\nALi7u+OPP/6Ao6MjnJyckJmZidu3b6Nbt26Ij4+vanWNhw8folevXli8eDGGDh2q2VYpZ2dnZGRk\naK0TEREBX1/fSreblJlT5Sgj7govVNDXtqqzHRmU5ABUPbqLjNyVqo2vT23NQUZdNUVp7X81h9qc\nAZWv6HoC8r9fj6Kzv5e/gJUNLCe9CfMefcp9WN/vHX0dy6XLATX3GV+T+Du/emrTcVrdHAz595OS\n2mNiYrSGN3+SojPpI0eOxIQJE/Dxxx8DAFJSUjB79mz87W9/U1xsQUEBhg8fjvHjx2Po0KEASs6e\np6amwsXFBSkpKWjUqJHi7RERET2N4jvpyP8xDIXH9gHlnadSmcCsVz9YBL8CE+eywysSEemDokb6\n0qVLMX/+fHTo0AHZ2dlo0aIFpkyZgnfffVfRToQQmDx5Mtq1a4fZs2dr5g8ePBhhYWF45513EBYW\npmm8k3yGPGa0vm8IVJP7M+TcZags++q+zsxeDn2Mky4eZqE49SaKU26gOP4yCg7vKtPnvJSp37PI\nGzIed53+/122yxkBxRhuKlaTx3tNvg+NnSHcF8BYGWL2ihrplpaWWL16NT7++GPcuXMHDRo0qNaF\nM8ePH8emTZvQoUMHdOrUCQCwfPlyzJ8/H6NGjcL69es1QzAS/VVKbwNvqPuj/6kse+Zu/IQQQEE+\nkJsDkZcLkf0QIu1WSWM89SaKU2+gOOUG8DCrym2ZtPKC5d+mwLSVF9IVfH3OY+t/+D4k0g3FA6HG\nxcVh27ZtSElJQZMmTTBy5Ei0atVK0brPPfcciouLy31s//79Va6fEzq/0sftCovgnVdU4eP1LE2R\nY2Za5X70ua3qbEeGFwqL8DDy1wofr2dZUruh5f74tmrq9anJ2pXkXtPHjZIcavI51qSarL2y7Gv6\nmDF8VV7KpJifEMg5Gv7E5stuXxQVAXm5ELk5QF5Oyb+5uYAo/3eLUiZN3WExejJMO3UzilFblOJ9\nAeQwtDO5xsQQs1fUSN+8eTOmTp2KAQMGwN3dHefOncPy5cvxxRdfYNy4cbquEUXnT1f6uAUA56q2\noXBf+tyW0u3IoCQHKFimNuZeuq2aen1q6/GnlJI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} ], - "prompt_number": 12 + "prompt_number": 23 }, { "cell_type": "markdown", @@ -776,7 +785,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Exercises\n", + "##### Exercises\n", "\n", "1\\. Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the positior distributions of $\\lambda_1$ and $\\lambda_2$?" ] @@ -874,8 +883,7 @@ " margin-right:auto;\n", " }\n", " h1 {\n", - " text-align:center;\n", - " font-family:\"Charis SIL\", serif;\n", + " font-family: \"Charis SIL\", Palatino, serif;\n", " }\n", " div.text_cell_render{\n", " font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n", @@ -886,21 +894,38 @@ " margin-right:auto;\n", " }\n", " .CodeMirror{\n", - " font-family: Consolas, monospace;\n", + " font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n", " }\n", " .prompt{\n", " display: None;\n", " }\n", + " .text_cell_render h5 {\n", + " font-weight: 300;\n", + " font-size: 16pt;\n", + " color: #4057A1;\n", + " font-style: italic;\n", + " margin-bottom: .5em;\n", + " margin-top: 0.5em;\n", + " display: block;\n", + " }\n", "" ], "output_type": "pyout", - "prompt_number": 1, + "prompt_number": 22, "text": [ - "" + "" ] } ], - "prompt_number": 1 + "prompt_number": 22 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] } ], "metadata": {} diff --git a/Chapter2_MorePyMC/MorePyMC.ipynb b/Chapter2_MorePyMC/MorePyMC.ipynb index 686a616d..9e564b7b 100644 --- a/Chapter2_MorePyMC/MorePyMC.ipynb +++ b/Chapter2_MorePyMC/MorePyMC.ipynb @@ -18,7 +18,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 8 + "prompt_number": 3 }, { "cell_type": "markdown", @@ -293,6 +293,28 @@ "The call to `random` stores a new value into the variables `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Warning: *Don't update stochastic variables' values in-place.*\n", + "\n", + "\n", + "Straight from the PyMC docs, we quote [4]:\n", + "\n", + "> 'Stochastic' objects' values should be values should not be updated in-place. This confuses PyMC\u2019s caching scheme... The only way a stochastic variable\u2019s value should be updated is using statements of the following form:\n", + "\n", + " A.value = new_value\n", + "\n", + "> The following are in-place updates and should **never** be used:\n", + "\n", + " \n", + " A.value += 3\n", + " A.value[2,1] = 5\n", + " A.value.attribute = new_attribute_value\n", + " " + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -589,9 +611,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "-----------\n", - "### Example: Cheating amoung students\n", + "##### Example: Cheating amoung students\n", "\n", + "------\n", "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed either in person or anonymously (answering without consequence), we will recieve $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, a prior on $p$, and observed data $X$. \n", "\n", "This is a completely absurd model. No student, even with a free pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preseving privacy. The following proposed algorithm is a solution I greatly admire for its enginuity and effectivness:\n", @@ -615,7 +637,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 47 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -645,7 +667,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 48 + "prompt_number": 7 }, { "cell_type": "markdown", @@ -662,12 +684,13 @@ "cell_type": "code", "collapsed": false, "input": [ - "yes_responses = mc.Binomial( \"number_cheaters\", 100, p_skewed, value = 30, observed = True )" + "yes_responses = mc.Binomial( \"number_cheaters\", 100, p_skewed, \n", + " value = 30, observed = True )" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 58 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -680,6 +703,7 @@ "cell_type": "code", "collapsed": false, "input": [ + "### To Be Explained in Chapter 3!\n", "model = mc.Model( [yes_responses, p_skewed, p ] )\n", "mcmc = mc.MCMC(model)\n", "mcmc.sample( 20000, 7500 )\n", @@ -750,9 +774,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "_______\n", - "###Example: Challenger Space Shuttle Disaster\n", "\n", + "#####Example: Challenger Space Shuttle Disaster\n", + "_______\n", "\n", "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle pro-gram ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", "\n", @@ -983,12 +1007,12 @@ "output_type": "pyout", "prompt_number": 5, "text": [ - "" + "" ] }, { "output_type": "display_data", - "png": 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6H5s6dSrs7OwA1BSQISEh2LRpk3KhASQkJCA4OBj3799HdHQ0pkyZovA6TExM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\nO1Y8+uijWofTreeee04oiiJOnDihdSjd+sUvfiHS0tLE+PHjxfXXXy9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9fVlv+zr5cj+97auutLQ07Nq1q8HH/fz8MGnSJK32NXbsWPz4448AAMYYsrKy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\nFZZ4iCKDjczTecsP5dY0aFXMqy58nTN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//jr8/f1RUVGBDRs2AAB+++23eu0xTXFyckJ6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\nrxYsg+ifbOfs/on0T7ZLAt/LAjv34nngIfSqGkiIw3zTDNScLKPDOml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} ], "prompt_number": 5 @@ -1279,7 +1303,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "figsize(12.5, 2.5)\n", + "figsize(8, 2.5)\n", "prob_31 = logistic( 31, beta_samples, alpha_samples )\n", "\n", "\n", @@ -1311,7 +1335,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Is there really a relationship between failure and temperature?\n", + "### More PyMC tricks: \n", + "\n", + "\n", + "##TO DO\n", + "- lambda function\n", + "- potential functions\n", + "- containers?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Returning to the Challenger data\n", + "#####Is there really a relationship between failure and temperature?\n", "\n", "An critism of our above analysis is that *assumed* that the relationship followed a logistic model, this we implictly assumed that the probabilities change over temperature. Let's look at the data again. (Top figure)\n", "\n", @@ -1645,7 +1683,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Exercises\n", + "##### Exercises\n", "\n", "1\\. How would add a prior belief that smoking causes more deaths in first example?" ] @@ -1676,12 +1714,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## References\n", + "### References\n", "\n", "- [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", "- [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from http://data.princeton.edu/wws509/datasets/#smoking.\n", "- [3] Reference bayes book by Dr. Cyntha\n", - "- [4] Newport, Frank, Jeffery M. Jones, and Lydia Saad . \"Final Presidential Estimate.\" Gallup.com. N.p., 02 Nov 2008. Web. 17 Feb 2013. [http://www.gallup.com/poll/111703/Final-Presidential-Estimate-Obama-55-McCain-44.asp&xgt](http://www.gallup.com/poll/111703/Final-Presidential-Estimate-Obama-55-McCain-44.asp&xgt);. " + "- [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. ." ] }, { @@ -1710,8 +1748,7 @@ " margin-right:auto;\n", " }\n", " h1 {\n", - " text-align:center;\n", - " font-family:\"Charis SIL\", serif;\n", + " font-family: \"Charis SIL\", Palatino, serif;\n", " }\n", " div.text_cell_render{\n", " font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n", @@ -1722,21 +1759,34 @@ " margin-right:auto;\n", " }\n", " .CodeMirror{\n", - " font-family: Consolas, monospace;\n", + " font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n", " }\n", " .prompt{\n", " display: None;\n", " }\n", + " .text_cell_render h5 {\n", + " font-weight: 300;\n", + " font-size: 16pt;\n", + " color: #4057A1;\n", + " font-style: italic;\n", + " margin-bottom: .5em;\n", + " margin-top: 0.5em;\n", + " display: block;\n", + " }\n", + " \n", + " .warning{\n", + " color: rgb( 240, 20, 20 )\n", + " }\n", "" ], "output_type": "pyout", - "prompt_number": 1, + "prompt_number": 9, "text": [ - "" + "" ] } ], - "prompt_number": 1 + "prompt_number": 9 }, { "cell_type": "code", diff --git a/Chapter3_MCMC/IntroMCMC.ipynb b/Chapter3_MCMC/IntroMCMC.ipynb index d3b506e0..9e2087a3 100644 --- a/Chapter3_MCMC/IntroMCMC.ipynb +++ b/Chapter3_MCMC/IntroMCMC.ipynb @@ -241,7 +241,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Example: Unsupervised Clustering using Mixture Model\n", + "##### Example: Unsupervised Clustering using Mixture Model\n", "\n", "------------\n", "\n", @@ -642,8 +642,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "_____\n", - "### Example: Poisson Regression [Needs work]\n", + "\n", + "##### Example: Poisson Regression [Needs work]\n", + "\n", + "---\n", "\n", "Perhaps the most important result from medical research was the *now obvious* link between *smoking and cancer*. We'll try to establish a link using Bayesian methods. We have a decision here: should we include a prior that biases us towards there existing a significant link between smoking and cancer? I think we should act like scientists at the turn of the century, and assume there's is no *a priori* reason to assume a link. \n", "\n", @@ -1035,8 +1037,7 @@ " margin-right:auto;\n", " }\n", " h1 {\n", - " text-align:center;\n", - " font-family:\"Charis SIL\", serif;\n", + " font-family: \"Charis SIL\", Palatino, serif;\n", " }\n", " div.text_cell_render{\n", " font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n", @@ -1047,21 +1048,34 @@ " margin-right:auto;\n", " }\n", " .CodeMirror{\n", - " font-family: Consolas, monospace;\n", + " font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n", " }\n", " .prompt{\n", " display: None;\n", " }\n", + " .text_cell_render h5 {\n", + " font-weight: 300;\n", + " font-size: 16pt;\n", + " color: #4057A1;\n", + " font-style: italic;\n", + " margin-bottom: .5em;\n", + " margin-top: 0.5em;\n", + " display: block;\n", + " }\n", + " \n", + " .warning{\n", + " color: rgb( 240, 20, 20 )\n", + " }\n", "" ], "output_type": "pyout", - "prompt_number": 15, + "prompt_number": 1, "text": [ - "" + "" ] } ], - "prompt_number": 15 + "prompt_number": 1 }, { "cell_type": "code", diff --git a/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb b/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb index 75993ca0..4e9b2bb2 100644 --- a/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb +++ b/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb @@ -24,21 +24,20 @@ "metadata": {}, "source": [ "#Chapter 4\n", + "______\n", "\n", "##The greatest theorem never told\n", "\n", "\n", "\n", - "> This relatively short chapter focuses on an idea that is always bouncing around our heads, but is rarely made explicit outside books devoted to statistics or Monte Carlo. In fact, we've been used this idea in every example so far. \n", - "\n", - "______" + "> This relatively short chapter focuses on an idea that is always bouncing around our heads, but is rarely made explicit outside books devoted to statistics or Monte Carlo. In fact, we've been used this idea in every example so far. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "##The Law of Large Numbers\n", + "###The Law of Large Numbers\n", "\n", "Let $Z_i$ be samples from some probability distribution. According to *the Law of Large numbers*, so long as $E[Z]$ is finite, the following holds,\n", "\n", @@ -55,7 +54,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Intution \n", + "### Intuition \n", "\n", "If the above Law is somewhat surprising, it can be made more clear be examining a simple example. \n", "\n", @@ -80,8 +79,9 @@ "\n", "Equality holds in the limit, but we can get closer and closer by using more and more samples in the average. This Law holds for *any distribution*, minus some pathological examples that only mathematicians have fun with. \n", "\n", + "##### Example\n", "____\n", - "### Example\n", + "\n", "\n", "Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n", "\n", @@ -258,8 +258,11 @@ "\n", "The Law of Large Numbers is only valid as $N$ gets *infinitely* large: the law is treasure at the end of an infinite rainbow. While the law is a powerful tool, it is foolhardy to apply it liberally. Our next example illustrates this.\n", "\n", + "\n", + "\n", + "##### Example: Aggregated geographic data\n", + "\n", "--------\n", - "### Example\n", "\n", "Often data comes in aggregated form. For instance, data may be grouped by state, county, or city level. Of course, the population numbers vary per geographic area. If included in the data is an average of some characteristic of each the geographic area, we must be concious of the Law of Large Numbers and how it can *fail* for areas with small populations.\n", "\n", @@ -483,7 +486,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Exercises\n", + "##### Exercises\n", "\n", "1\\. How would you estimate the quantity $E\\left[ \\cos{X} \\right]$, where $X \\sim \\text{Exp}(4)$? What about $E\\left[ \\cos{X} | X \\lt 1\\right]$, i.e. the expected value *given* we know $X$ is less than 1? Would you need more samples than the original samples size to be equally as accurate?" ] @@ -507,7 +510,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "2. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. What mistake have the researchers made?\n", + "2. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. The table ranks football field-goal kickers by there percent of non-misses. What mistake have the researchers made?\n", "\n", "-----\n", "\n", @@ -551,8 +554,7 @@ " margin-right:auto;\n", " }\n", " h1 {\n", - " text-align:center;\n", - " font-family:\"Charis SIL\", serif;\n", + " font-family: \"Charis SIL\", Palatino, serif;\n", " }\n", " div.text_cell_render{\n", " font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n", @@ -563,17 +565,30 @@ " margin-right:auto;\n", " }\n", " .CodeMirror{\n", - " font-family: Consolas, monospace;\n", + " font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n", " }\n", " .prompt{\n", " display: None;\n", " }\n", + " .text_cell_render h5 {\n", + " font-weight: 300;\n", + " font-size: 16pt;\n", + " color: #4057A1;\n", + " font-style: italic;\n", + " margin-bottom: .5em;\n", + " margin-top: 0.5em;\n", + " display: block;\n", + " }\n", + " \n", + " .warning{\n", + " color: rgb( 240, 20, 20 )\n", + " }\n", "" ], "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], diff --git a/Chapter5_LossFunctions/LossFunctions.ipynb b/Chapter5_LossFunctions/LossFunctions.ipynb index 543ce9f9..e3c4cc96 100644 --- a/Chapter5_LossFunctions/LossFunctions.ipynb +++ b/Chapter5_LossFunctions/LossFunctions.ipynb @@ -131,8 +131,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "\n", + "##### Example: Optimizing for the *Showcase* on *The Price is Right*\n", + "\n", "______________________________________\n", - "### Example: Optimizing for the *Showcase* on *The Price is Right*\n", "\n", "Bless you if you are ever choosen as a contestant on the Price is Right, for here we will show you how to optimize your final price on the *Showcase*. For those who forget the rules:\n", "\n", @@ -234,7 +236,8 @@ "input": [ "_hist = plt.hist( price_trace, bins = 50, normed= True, histtype= \"stepfilled\")\n", "plt.title( \"Posterior of the true price estimate\" )\n", - "plt.vlines( mu_prior, 0, 1.1*np.max(_hist[0] ), label = \"prior's mean\", linestyles=\"--\" )\n", + "plt.vlines( mu_prior, 0, 1.1*np.max(_hist[0] ), label = \"prior's mean\",\n", + " linestyles=\"--\" )\n", "plt.vlines( price_trace.mean(), 0, 1.1*np.max(_hist[0] ), \\\n", " label = \"posterior's mean\")\n", "plt.legend()" @@ -518,8 +521,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "\n", + "##### Example: Financial prediction\n", + "\n", "____\n", - "### Example: Financial prediction\n", "\n", "Suppose the future return of a stock price is very small, say 0.01 (or 1%). We have a model that predicts the stock's future price, and our profit and loss is directly tied to us acting on the prediction. How should be measure the loss associated with the model's predictions, and subsequent future predictions? A squared-error loss is agnogstic to the signage and would penalize a prediction of -0.01 equally as bad a prediction of 0.03:\n", "\n", @@ -805,17 +810,16 @@ "\n", "A good sanity check that our model is still reasonable: as the signal becomes more and more extreme, and we feel more and more confident about the positive/negativeness of returns, our position converges with that of the least-squares line. \n", "\n", - "The sparse-prediction model is not trying to *fit* the data the best (according to a *squared-error loss* definition of *fit*). That honour would go to the least-squares model. The sparse-prediction model is trying to find the best prediction *with respect to our `stock_loss`-defined loss*. We can turn this reasoning around: the least-squares model is not try to *predict* the best (according to a *`stock-loss`* definition of *predict*). That honour would go the *sparse prediction* model. The least-squares model is trying to find the best fit of the data *with respect to the squared-error loss*.\n", - "\n", - "\n", - "-------\n" + "The sparse-prediction model is not trying to *fit* the data the best (according to a *squared-error loss* definition of *fit*). That honour would go to the least-squares model. The sparse-prediction model is trying to find the best prediction *with respect to our `stock_loss`-defined loss*. We can turn this reasoning around: the least-squares model is not try to *predict* the best (according to a *`stock-loss`* definition of *predict*). That honour would go the *sparse prediction* model. The least-squares model is trying to find the best fit of the data *with respect to the squared-error loss*.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Example: Kaggle contest on *Observing Dark World*\n", + "##### Example: Kaggle contest on *Observing Dark World*\n", + "\n", + "----\n", "\n", "A personal motivation for learning Bayesian methods was trying to piece together the winning solution to Kaggle's [*Observing Dark Worlds*](http://www.kaggle.com/c/DarkWorlds) contest. From the contest's website:\n", "\n", @@ -1539,8 +1543,7 @@ " margin-right:auto;\n", " }\n", " h1 {\n", - " text-align:center;\n", - " font-family:\"Charis SIL\", serif;\n", + " font-family: \"Charis SIL\", Palatino, serif;\n", " }\n", " div.text_cell_render{\n", " font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n", @@ -1551,17 +1554,30 @@ " margin-right:auto;\n", " }\n", " .CodeMirror{\n", - " font-family: Consolas, monospace;\n", + " font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n", " }\n", " .prompt{\n", " display: None;\n", " }\n", + " .text_cell_render h5 {\n", + " font-weight: 300;\n", + " font-size: 16pt;\n", + " color: #4057A1;\n", + " font-style: italic;\n", + " margin-bottom: .5em;\n", + " margin-top: 0.5em;\n", + " display: block;\n", + " }\n", + " \n", + " .warning{\n", + " color: rgb( 240, 20, 20 )\n", + " }\n", "" ], "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], diff --git a/styles/custom.css b/styles/custom.css index 1fe6dee8..4b5bee0b 100644 --- a/styles/custom.css +++ b/styles/custom.css @@ -9,8 +9,7 @@ margin-right:auto; } h1 { - text-align:center; - font-family:"Charis SIL", serif; + font-family: "Charis SIL", Palatino, serif; } div.text_cell_render{ font-family: Computer Modern, "Helvetica Neue", Arial, Helvetica, Geneva, sans-serif; @@ -21,9 +20,22 @@ margin-right:auto; } .CodeMirror{ - font-family: Consolas, monospace; + font-family: "Source Code Pro", source-code-pro,Consolas, monospace; } .prompt{ display: None; } + .text_cell_render h5 { + font-weight: 300; + font-size: 16pt; + color: #4057A1; + font-style: italic; + margin-bottom: .5em; + margin-top: 0.5em; + display: block; + } + + .warning{ + color: rgb( 240, 20, 20 ) + } \ No newline at end of file