We could now define a new cost function to minimize, namely the negative logarithm of the above PDF
$$ -C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}, +C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}, $$which becomes
$$ -C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}. +C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}. $$Taking the derivative of the new cost function with respect to the parameters \( \beta \) we recognize our familiar OLS equation, namely
diff --git a/doc/pub/week37/html/week37-reveal.html b/doc/pub/week37/html/week37-reveal.html index 17b1fe2f1..36362d2c7 100644 --- a/doc/pub/week37/html/week37-reveal.html +++ b/doc/pub/week37/html/week37-reveal.html @@ -319,14 +319,14 @@ is equivalent to the maximization/minimization of the function itself.
$$
-C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
+C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})},
$$
which becomes
$$
-C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}.
$$
diff --git a/doc/pub/week37/html/week37-solarized.html b/doc/pub/week37/html/week37-solarized.html
index 490d110cb..af481406b 100644
--- a/doc/pub/week37/html/week37-solarized.html
+++ b/doc/pub/week37/html/week37-solarized.html
@@ -349,12 +349,12 @@ is equivalent to the maximization/minimization of the function itself.
We could now define a new cost function to minimize, namely the negative logarithm of the above PDF
$$ -C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}, +C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}, $$which becomes
$$ -C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}. +C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}. $$Taking the derivative of the new cost function with respect to the parameters \( \beta \) we recognize our familiar OLS equation, namely
diff --git a/doc/pub/week37/html/week37.html b/doc/pub/week37/html/week37.html index c9f2c36e3..f123bd311 100644 --- a/doc/pub/week37/html/week37.html +++ b/doc/pub/week37/html/week37.html @@ -426,12 +426,12 @@ is equivalent to the maximization/minimization of the function itself.We could now define a new cost function to minimize, namely the negative logarithm of the above PDF
$$ -C(\boldsymbol{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}, +C(\boldsymbol{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\beta})}, $$which becomes
$$ -C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}. +C(\boldsymbol{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}. $$Taking the derivative of the new cost function with respect to the parameters \( \beta \) we recognize our familiar OLS equation, namely
diff --git a/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz b/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz index 2670a3ec3..879198238 100644 Binary files a/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz and b/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz differ diff --git a/doc/pub/week37/ipynb/week37.ipynb b/doc/pub/week37/ipynb/week37.ipynb index e095b7a5e..59a0291e5 100644 --- a/doc/pub/week37/ipynb/week37.ipynb +++ b/doc/pub/week37/ipynb/week37.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c2b9402a", + "id": "a7d5c536", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "a491dc47", + "id": "dbae05db", "metadata": { "editable": true }, @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "e25fb167", + "id": "e675a4f4", "metadata": { "editable": true }, @@ -52,7 +52,7 @@ }, { "cell_type": "markdown", - "id": "0e065ecb", + "id": "72e22eb1", "metadata": { "editable": true }, @@ -62,7 +62,7 @@ }, { "cell_type": "markdown", - "id": "94f9361e", + "id": "aa7455c5", "metadata": { "editable": true }, @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "c45e3846", + "id": "da753a6e", "metadata": { "editable": true }, @@ -97,7 +97,7 @@ }, { "cell_type": "markdown", - "id": "3d064ff7", + "id": "d08f3c99", "metadata": { "editable": true }, @@ -110,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "b3a5f9aa", + "id": "1e593e87", "metadata": { "editable": true }, @@ -122,7 +122,7 @@ }, { "cell_type": "markdown", - "id": "24dfa4b7", + "id": "562fb753", "metadata": { "editable": true }, @@ -134,7 +134,7 @@ }, { "cell_type": "markdown", - "id": "24220329", + "id": "61c57c27", "metadata": { "editable": true }, @@ -146,7 +146,7 @@ }, { "cell_type": "markdown", - "id": "edee6a0e", + "id": "4f994156", "metadata": { "editable": true }, @@ -157,7 +157,7 @@ }, { "cell_type": "markdown", - "id": "961c7491", + "id": "1c88800c", "metadata": { "editable": true }, @@ -169,7 +169,7 @@ }, { "cell_type": "markdown", - "id": "bd873c08", + "id": "dfb6ddc0", "metadata": { "editable": true }, @@ -180,7 +180,7 @@ }, { "cell_type": "markdown", - "id": "fec9c100", + "id": "e00ff2d0", "metadata": { "editable": true }, @@ -192,7 +192,7 @@ }, { "cell_type": "markdown", - "id": "87befb9e", + "id": "0ee92073", "metadata": { "editable": true }, @@ -202,7 +202,7 @@ }, { "cell_type": "markdown", - "id": "1fb68439", + "id": "25b3b019", "metadata": { "editable": true }, @@ -233,7 +233,7 @@ }, { "cell_type": "markdown", - "id": "4cf1063d", + "id": "cbea4097", "metadata": { "editable": true }, @@ -245,19 +245,19 @@ }, { "cell_type": "markdown", - "id": "3bde131d", + "id": "164e9ccc", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\beta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})},\n", + "C(\\boldsymbol{\\beta})=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})},\n", "$$" ] }, { "cell_type": "markdown", - "id": "917edb51", + "id": "baa9c4ea", "metadata": { "editable": true }, @@ -267,19 +267,19 @@ }, { "cell_type": "markdown", - "id": "d2a53e5e", + "id": "c7ee6c55", "metadata": { "editable": true }, "source": [ "$$\n", - "C(\\boldsymbol{\\beta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}.\n", + "C(\\boldsymbol{\\beta})=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}.\n", "$$" ] }, { "cell_type": "markdown", - "id": "639a96b1", + "id": "2e0e6f19", "metadata": { "editable": true }, @@ -289,7 +289,7 @@ }, { "cell_type": "markdown", - "id": "f6db79be", + "id": "51dda28a", "metadata": { "editable": true }, @@ -301,7 +301,7 @@ }, { "cell_type": "markdown", - "id": "4b971cc2", + "id": "badc2cd1", "metadata": { "editable": true }, @@ -311,7 +311,7 @@ }, { "cell_type": "markdown", - "id": "99885fae", + "id": "da8a99d6", "metadata": { "editable": true }, @@ -323,7 +323,7 @@ }, { "cell_type": "markdown", - "id": "d21d7adb", + "id": "df928f1e", "metadata": { "editable": true }, @@ -335,7 +335,7 @@ }, { "cell_type": "markdown", - "id": "940f20cd", + "id": "803020ce", "metadata": { "editable": true }, @@ -347,7 +347,7 @@ }, { "cell_type": "markdown", - "id": "c0c42790", + "id": "1b218c48", "metadata": { "editable": true }, @@ -357,7 +357,7 @@ }, { "cell_type": "markdown", - "id": "052f445f", + "id": "aafbde68", "metadata": { "editable": true }, @@ -369,7 +369,7 @@ }, { "cell_type": "markdown", - "id": "e5f56dd6", + "id": "50487196", "metadata": { "editable": true }, @@ -379,7 +379,7 @@ }, { "cell_type": "markdown", - "id": "b7c4b4df", + "id": "e805b8b9", "metadata": { "editable": true }, @@ -396,7 +396,7 @@ }, { "cell_type": "markdown", - "id": "52444cf8", + "id": "b6f0c1c4", "metadata": { "editable": true }, @@ -415,7 +415,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "05363fd5", + "id": "a89b0a40", "metadata": { "collapsed": false, "editable": true @@ -491,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "faac3a50", + "id": "e7b7b3d7", "metadata": { "editable": true }, @@ -501,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "77424f12", + "id": "04b0edaf", "metadata": { "editable": true }, @@ -531,7 +531,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "34233a4d", + "id": "7ab076c6", "metadata": { "collapsed": false, "editable": true @@ -580,7 +580,7 @@ }, { "cell_type": "markdown", - "id": "96c00ffe", + "id": "187229b0", "metadata": { "editable": true }, @@ -594,7 +594,7 @@ }, { "cell_type": "markdown", - "id": "661f7c05", + "id": "08ac2fe5", "metadata": { "editable": true }, @@ -606,7 +606,7 @@ }, { "cell_type": "markdown", - "id": "e19fba88", + "id": "8211f32a", "metadata": { "editable": true }, @@ -616,7 +616,7 @@ }, { "cell_type": "markdown", - "id": "f805fdff", + "id": "0dc9f7ef", "metadata": { "editable": true }, @@ -628,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "939ed78b", + "id": "fb775663", "metadata": { "editable": true }, @@ -638,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "efcf7649", + "id": "6d681b44", "metadata": { "editable": true }, @@ -650,7 +650,7 @@ }, { "cell_type": "markdown", - "id": "49799788", + "id": "2c171fae", "metadata": { "editable": true }, @@ -660,7 +660,7 @@ }, { "cell_type": "markdown", - "id": "cc834447", + "id": "df685126", "metadata": { "editable": true }, @@ -672,7 +672,7 @@ }, { "cell_type": "markdown", - "id": "8ac5d900", + "id": "4f56735f", "metadata": { "editable": true }, @@ -682,7 +682,7 @@ }, { "cell_type": "markdown", - "id": "cc4ab483", + "id": "253dd4c0", "metadata": { "editable": true }, @@ -698,7 +698,7 @@ }, { "cell_type": "markdown", - "id": "1aa8a7f2", + "id": "8872b434", "metadata": { "editable": true }, @@ -710,7 +710,7 @@ }, { "cell_type": "markdown", - "id": "5b836700", + "id": "e46a853d", "metadata": { "editable": true }, @@ -720,7 +720,7 @@ }, { "cell_type": "markdown", - "id": "9b0ba8f2", + "id": "a0f42b10", "metadata": { "editable": true }, @@ -732,7 +732,7 @@ }, { "cell_type": "markdown", - "id": "4470a1af", + "id": "ee519173", "metadata": { "editable": true }, @@ -745,7 +745,7 @@ }, { "cell_type": "markdown", - "id": "cde5f188", + "id": "5f6b835d", "metadata": { "editable": true }, @@ -757,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "1af738ef", + "id": "74b26056", "metadata": { "editable": true }, @@ -767,7 +767,7 @@ }, { "cell_type": "markdown", - "id": "a8fe63c1", + "id": "2826d888", "metadata": { "editable": true }, @@ -779,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "8a0314c7", + "id": "fb761472", "metadata": { "editable": true }, @@ -789,7 +789,7 @@ }, { "cell_type": "markdown", - "id": "2890ed8c", + "id": "835e0510", "metadata": { "editable": true }, @@ -801,7 +801,7 @@ }, { "cell_type": "markdown", - "id": "39eab4d6", + "id": "5621fa84", "metadata": { "editable": true }, @@ -813,7 +813,7 @@ }, { "cell_type": "markdown", - "id": "ba66c505", + "id": "a2fef1c2", "metadata": { "editable": true }, @@ -823,7 +823,7 @@ }, { "cell_type": "markdown", - "id": "a97c20c7", + "id": "439ca1a7", "metadata": { "editable": true }, @@ -835,7 +835,7 @@ }, { "cell_type": "markdown", - "id": "32fb7195", + "id": "3009c333", "metadata": { "editable": true }, @@ -847,7 +847,7 @@ }, { "cell_type": "markdown", - "id": "9df80b8d", + "id": "c3caa559", "metadata": { "editable": true }, @@ -859,7 +859,7 @@ }, { "cell_type": "markdown", - "id": "700ffb68", + "id": "7afe3a58", "metadata": { "editable": true }, @@ -869,7 +869,7 @@ }, { "cell_type": "markdown", - "id": "c1708480", + "id": "90d58fb5", "metadata": { "editable": true }, @@ -881,7 +881,7 @@ }, { "cell_type": "markdown", - "id": "b2aeabe2", + "id": "ac888160", "metadata": { "editable": true }, @@ -891,7 +891,7 @@ }, { "cell_type": "markdown", - "id": "1c415246", + "id": "dd528a97", "metadata": { "editable": true }, @@ -910,7 +910,7 @@ }, { "cell_type": "markdown", - "id": "2c371dae", + "id": "f4d4a3bd", "metadata": { "editable": true }, @@ -938,7 +938,7 @@ }, { "cell_type": "markdown", - "id": "c38905f3", + "id": "b3bffa08", "metadata": { "editable": true }, @@ -964,7 +964,7 @@ }, { "cell_type": "markdown", - "id": "8582ebdf", + "id": "9ec4aa4e", "metadata": { "editable": true }, @@ -981,7 +981,7 @@ }, { "cell_type": "markdown", - "id": "189ec909", + "id": "b8524d4e", "metadata": { "editable": true }, @@ -1001,7 +1001,7 @@ }, { "cell_type": "markdown", - "id": "212662d2", + "id": "02d95749", "metadata": { "editable": true }, @@ -1030,7 +1030,7 @@ }, { "cell_type": "markdown", - "id": "ab73c7a9", + "id": "9d12e492", "metadata": { "editable": true }, @@ -1055,7 +1055,7 @@ }, { "cell_type": "markdown", - "id": "58e40636", + "id": "90f8467d", "metadata": { "editable": true }, @@ -1069,7 +1069,7 @@ }, { "cell_type": "markdown", - "id": "e165c758", + "id": "da753b8f", "metadata": { "editable": true }, @@ -1081,7 +1081,7 @@ }, { "cell_type": "markdown", - "id": "32c51f40", + "id": "d322a2ad", "metadata": { "editable": true }, @@ -1094,7 +1094,7 @@ }, { "cell_type": "markdown", - "id": "a5bec823", + "id": "aa1ddd91", "metadata": { "editable": true }, @@ -1105,7 +1105,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "57b86cdf", + "id": "3c534b63", "metadata": { "collapsed": false, "editable": true @@ -1144,7 +1144,7 @@ }, { "cell_type": "markdown", - "id": "0d969b98", + "id": "acb1d760", "metadata": { "editable": true }, @@ -1169,7 +1169,7 @@ }, { "cell_type": "markdown", - "id": "b66524c3", + "id": "47024fea", "metadata": { "editable": true }, @@ -1189,7 +1189,7 @@ }, { "cell_type": "markdown", - "id": "4d9476a3", + "id": "5f659cd0", "metadata": { "editable": true }, @@ -1201,7 +1201,7 @@ }, { "cell_type": "markdown", - "id": "7a32056b", + "id": "45f1710f", "metadata": { "editable": true }, @@ -1211,7 +1211,7 @@ }, { "cell_type": "markdown", - "id": "6c8b0666", + "id": "8e9e489f", "metadata": { "editable": true }, @@ -1226,7 +1226,7 @@ }, { "cell_type": "markdown", - "id": "dae9dc94", + "id": "35779aca", "metadata": { "editable": true }, @@ -1239,7 +1239,7 @@ }, { "cell_type": "markdown", - "id": "35438879", + "id": "bbf52fb5", "metadata": { "editable": true }, @@ -1252,7 +1252,7 @@ }, { "cell_type": "markdown", - "id": "21257570", + "id": "a62fed9c", "metadata": { "editable": true }, @@ -1264,7 +1264,7 @@ }, { "cell_type": "markdown", - "id": "1a1fc0ba", + "id": "8fa78ab6", "metadata": { "editable": true }, @@ -1277,7 +1277,7 @@ }, { "cell_type": "markdown", - "id": "e4bed73b", + "id": "d198d513", "metadata": { "editable": true }, @@ -1288,7 +1288,7 @@ }, { "cell_type": "markdown", - "id": "1fa5809c", + "id": "e92b0ef9", "metadata": { "editable": true }, @@ -1302,7 +1302,7 @@ }, { "cell_type": "markdown", - "id": "dc273e52", + "id": "e7cc2d45", "metadata": { "editable": true }, @@ -1312,7 +1312,7 @@ }, { "cell_type": "markdown", - "id": "3b64bbe8", + "id": "8550636d", "metadata": { "editable": true }, @@ -1326,7 +1326,7 @@ }, { "cell_type": "markdown", - "id": "97a2d53c", + "id": "c5111414", "metadata": { "editable": true }, @@ -1339,7 +1339,7 @@ }, { "cell_type": "markdown", - "id": "ed0ae36e", + "id": "d54b09b8", "metadata": { "editable": true }, @@ -1352,7 +1352,7 @@ }, { "cell_type": "markdown", - "id": "54dcd6de", + "id": "dd73e014", "metadata": { "editable": true }, @@ -1362,7 +1362,7 @@ }, { "cell_type": "markdown", - "id": "3defb137", + "id": "62ffc5dc", "metadata": { "editable": true }, @@ -1375,7 +1375,7 @@ }, { "cell_type": "markdown", - "id": "aff3be1f", + "id": "c1d795de", "metadata": { "editable": true }, @@ -1385,7 +1385,7 @@ }, { "cell_type": "markdown", - "id": "2376b5f2", + "id": "7fcf3019", "metadata": { "editable": true }, @@ -1398,7 +1398,7 @@ }, { "cell_type": "markdown", - "id": "00ad7733", + "id": "0552d7bc", "metadata": { "editable": true }, @@ -1410,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "b2221018", + "id": "eb7a91c5", "metadata": { "editable": true }, @@ -1429,7 +1429,7 @@ }, { "cell_type": "markdown", - "id": "6898f3c9", + "id": "ab440229", "metadata": { "editable": true }, @@ -1442,7 +1442,7 @@ }, { "cell_type": "markdown", - "id": "fae20567", + "id": "ee6827e6", "metadata": { "editable": true }, @@ -1454,7 +1454,7 @@ }, { "cell_type": "markdown", - "id": "4280b4ec", + "id": "61f634e3", "metadata": { "editable": true }, @@ -1467,7 +1467,7 @@ }, { "cell_type": "markdown", - "id": "f941ffce", + "id": "577e2d4a", "metadata": { "editable": true }, @@ -1487,7 +1487,7 @@ }, { "cell_type": "markdown", - "id": "35303c06", + "id": "7325e61e", "metadata": { "editable": true }, @@ -1510,7 +1510,7 @@ }, { "cell_type": "markdown", - "id": "22f20c7c", + "id": "cebf0788", "metadata": { "editable": true }, @@ -1525,7 +1525,7 @@ }, { "cell_type": "markdown", - "id": "5691293d", + "id": "00e3df1a", "metadata": { "editable": true }, @@ -1537,7 +1537,7 @@ }, { "cell_type": "markdown", - "id": "0fed50f5", + "id": "3cf522f9", "metadata": { "editable": true }, @@ -1557,7 +1557,7 @@ }, { "cell_type": "markdown", - "id": "74bb8673", + "id": "4a62e5f8", "metadata": { "editable": true }, @@ -1577,7 +1577,7 @@ }, { "cell_type": "markdown", - "id": "5dd984cb", + "id": "40fbcc46", "metadata": { "editable": true }, @@ -1601,7 +1601,7 @@ }, { "cell_type": "markdown", - "id": "ca5cf7b3", + "id": "465f33e4", "metadata": { "editable": true }, @@ -1622,7 +1622,7 @@ }, { "cell_type": "markdown", - "id": "19e99b84", + "id": "a0ea5679", "metadata": { "editable": true }, @@ -1652,7 +1652,7 @@ }, { "cell_type": "markdown", - "id": "061d3721", + "id": "8ec0902e", "metadata": { "editable": true }, @@ -1676,7 +1676,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "272a7bbb", + "id": "c2d74c1e", "metadata": { "collapsed": false, "editable": true @@ -1713,7 +1713,7 @@ }, { "cell_type": "markdown", - "id": "5653c44f", + "id": "74369b44", "metadata": { "editable": true }, @@ -1723,7 +1723,7 @@ }, { "cell_type": "markdown", - "id": "53d0aba3", + "id": "d205b0c2", "metadata": { "editable": true }, @@ -1734,7 +1734,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "68911c84", + "id": "100fc3de", "metadata": { "collapsed": false, "editable": true @@ -1754,7 +1754,7 @@ }, { "cell_type": "markdown", - "id": "5c12d033", + "id": "b253044c", "metadata": { "editable": true }, @@ -1772,7 +1772,7 @@ }, { "cell_type": "markdown", - "id": "d935e99b", + "id": "64c00831", "metadata": { "editable": true }, @@ -1784,7 +1784,7 @@ }, { "cell_type": "markdown", - "id": "d1169087", + "id": "beeb5ea8", "metadata": { "editable": true }, @@ -1801,7 +1801,7 @@ }, { "cell_type": "markdown", - "id": "60c0c1bd", + "id": "38c7666b", "metadata": { "editable": true }, @@ -1813,7 +1813,7 @@ }, { "cell_type": "markdown", - "id": "c4152366", + "id": "61d5e884", "metadata": { "editable": true }, @@ -1823,7 +1823,7 @@ }, { "cell_type": "markdown", - "id": "61bfa7c4", + "id": "eef1bc58", "metadata": { "editable": true }, @@ -1835,7 +1835,7 @@ }, { "cell_type": "markdown", - "id": "4fc282d6", + "id": "8df9ad22", "metadata": { "editable": true }, @@ -1852,7 +1852,7 @@ }, { "cell_type": "markdown", - "id": "bb3717a1", + "id": "a1209aca", "metadata": { "editable": true }, @@ -1864,7 +1864,7 @@ }, { "cell_type": "markdown", - "id": "bfb7bb28", + "id": "60d581e0", "metadata": { "editable": true }, @@ -1874,7 +1874,7 @@ }, { "cell_type": "markdown", - "id": "d3a8c068", + "id": "ae89f86c", "metadata": { "editable": true }, @@ -1886,7 +1886,7 @@ }, { "cell_type": "markdown", - "id": "db157ecf", + "id": "d6d0c413", "metadata": { "editable": true }, @@ -1896,7 +1896,7 @@ }, { "cell_type": "markdown", - "id": "0e04f574", + "id": "b4d2f170", "metadata": { "editable": true }, @@ -1908,7 +1908,7 @@ }, { "cell_type": "markdown", - "id": "293252e2", + "id": "166ba820", "metadata": { "editable": true }, @@ -1918,7 +1918,7 @@ }, { "cell_type": "markdown", - "id": "028e9aab", + "id": "95fa4c33", "metadata": { "editable": true }, @@ -1934,7 +1934,7 @@ }, { "cell_type": "markdown", - "id": "106ac47f", + "id": "2b61652b", "metadata": { "editable": true }, @@ -1945,7 +1945,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "ac981367", + "id": "d20a0717", "metadata": { "collapsed": false, "editable": true @@ -2010,7 +2010,7 @@ }, { "cell_type": "markdown", - "id": "70e63796", + "id": "dc44872d", "metadata": { "editable": true }, @@ -2021,7 +2021,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "12106663", + "id": "272840a7", "metadata": { "collapsed": false, "editable": true @@ -2078,7 +2078,7 @@ }, { "cell_type": "markdown", - "id": "298e77be", + "id": "ab78c9db", "metadata": { "editable": true }, @@ -2116,7 +2116,7 @@ }, { "cell_type": "markdown", - "id": "e75e6b04", + "id": "051948dc", "metadata": { "editable": true }, @@ -2127,7 +2127,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "0d6a4d60", + "id": "bbc4645b", "metadata": { "collapsed": false, "editable": true @@ -2209,7 +2209,7 @@ }, { "cell_type": "markdown", - "id": "a8d85f13", + "id": "a3cbbbdf", "metadata": { "editable": true }, @@ -2234,7 +2234,7 @@ }, { "cell_type": "markdown", - "id": "a1735b39", + "id": "1d2bee06", "metadata": { "editable": true }, @@ -2250,7 +2250,7 @@ }, { "cell_type": "markdown", - "id": "75bd8242", + "id": "0989a27c", "metadata": { "editable": true }, @@ -2266,7 +2266,7 @@ }, { "cell_type": "markdown", - "id": "0b85ab87", + "id": "5742c19e", "metadata": { "editable": true }, @@ -2280,7 +2280,7 @@ }, { "cell_type": "markdown", - "id": "5daaa71c", + "id": "f9f7ee5f", "metadata": { "editable": true }, @@ -2294,7 +2294,7 @@ }, { "cell_type": "markdown", - "id": "54608282", + "id": "1f579900", "metadata": { "editable": true }, @@ -2322,7 +2322,7 @@ }, { "cell_type": "markdown", - "id": "38dbaf67", + "id": "a63d0cd5", "metadata": { "editable": true }, @@ -2335,7 +2335,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "6b9d105a", + "id": "9abd645b", "metadata": { "collapsed": false, "editable": true @@ -2435,7 +2435,7 @@ }, { "cell_type": "markdown", - "id": "4ae36554", + "id": "0bdb9275", "metadata": { "editable": true }, @@ -2446,7 +2446,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "0ed647d1", + "id": "00fdc87e", "metadata": { "collapsed": false, "editable": true @@ -2535,7 +2535,7 @@ }, { "cell_type": "markdown", - "id": "b4bb43b3", + "id": "b067da97", "metadata": { "editable": true }, @@ -2545,7 +2545,7 @@ }, { "cell_type": "markdown", - "id": "cb8c05f3", + "id": "feb9f426", "metadata": { "editable": true }, @@ -2558,7 +2558,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "bebdd3d3", + "id": "f45744d8", "metadata": { "collapsed": false, "editable": true diff --git a/doc/src/week37/week37.do.txt b/doc/src/week37/week37.do.txt index af1132200..4a0726303 100644 --- a/doc/src/week37/week37.do.txt +++ b/doc/src/week37/week37.do.txt @@ -113,13 +113,13 @@ We could now define a new cost function to minimize, namely the negative logarit !bt \[ -C(\bm{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\beta})}, +C(\bm{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\beta})}, \] !et which becomes !bt \[ -C(\bm{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}. +C(\bm{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}. \] !et