From 486174ed55f3f5f143586d56221e52a781edc76d Mon Sep 17 00:00:00 2001 From: Quarto GHA Workflow Runner Date: Tue, 26 Sep 2023 17:39:04 +0000 Subject: [PATCH] Built site for gh-pages --- .nojekyll | 2 +- schedule/slides/06-information-criteria.html | 8 ++-- search.json | 2 +- sitemap.xml | 50 ++++++++++---------- 4 files changed, 31 insertions(+), 31 deletions(-) diff --git a/.nojekyll b/.nojekyll index e4a8d47..b3b36cd 100644 --- a/.nojekyll +++ b/.nojekyll @@ -1 +1 @@ -1ad63189 \ No newline at end of file +67bfa027 \ No newline at end of file diff --git a/schedule/slides/06-information-criteria.html b/schedule/slides/06-information-criteria.html index c0a1ee0..7f7a405 100644 --- a/schedule/slides/06-information-criteria.html +++ b/schedule/slides/06-information-criteria.html @@ -496,12 +496,12 @@

AIC and BIC

\(\textrm{AIC}/n = -2\textrm{loglikelihood}/n + 2\textrm{df}/n\)

\(\textrm{BIC}/n = -2\textrm{loglikelihood}/n + 2\log(n)\textrm{df}/n\)

-

In the case of a linear model with Gaussian errors,

+

In the case of a linear model with Gaussian errors and \(p\) predictors

\[\begin{aligned} -\textrm{AIC} &= -n + 2n\log(2\pi) - 2 + 2\log(n) - 2\log(RSS) + 2(p+2) \\ -&\propto -2\log(RSS) + 2(p+2) +\textrm{AIC}/n &= \log(2\pi) + \log(RSS/n) + 2(p+1)/n \\ +&\propto \log(RSS) + 2(p+1)/n \end{aligned}\] -

( \(p+2\) because of the intercept and the unknown variance)

+

( \(p+1\) because of the unknown variance, intercept included in \(p\) or not)

diff --git a/search.json b/search.json index 96d002d..3992824 100644 --- a/search.json +++ b/search.json @@ -221,7 +221,7 @@ "href": "schedule/slides/06-information-criteria.html#aic-and-bic", "title": "UBC Stat406 2023W", "section": "AIC and BIC", - "text": "AIC and BIC\nThese have a very similar flavor to \\(C_p\\), but their genesis is different.\nWithout going into too much detail, they look like\n\\(\\textrm{AIC}/n = -2\\textrm{loglikelihood}/n + 2\\textrm{df}/n\\)\n\\(\\textrm{BIC}/n = -2\\textrm{loglikelihood}/n + 2\\log(n)\\textrm{df}/n\\)\n\nIn the case of a linear model with Gaussian errors,\n\\[\\begin{aligned}\n\\textrm{AIC} &= -n + 2n\\log(2\\pi) - 2 + 2\\log(n) - 2\\log(RSS) + 2(p+2) \\\\\n&\\propto -2\\log(RSS) + 2(p+2)\n\\end{aligned}\\]\n( \\(p+2\\) because of the intercept and the unknown variance)\n\n\n\n\n\n\n\n\nImportant\n\n\nUnfortunately, different books/software/notes define these differently. Even different R packages. This is super annoying.\nForms above are in [ESL] eq. (7.29) and (7.35). [ISLR] gives special cases in Section 6.1.3. Remember the generic form here." + "text": "AIC and BIC\nThese have a very similar flavor to \\(C_p\\), but their genesis is different.\nWithout going into too much detail, they look like\n\\(\\textrm{AIC}/n = -2\\textrm{loglikelihood}/n + 2\\textrm{df}/n\\)\n\\(\\textrm{BIC}/n = -2\\textrm{loglikelihood}/n + 2\\log(n)\\textrm{df}/n\\)\n\nIn the case of a linear model with Gaussian errors and \\(p\\) predictors\n\\[\\begin{aligned}\n\\textrm{AIC}/n &= \\log(2\\pi) + \\log(RSS/n) + 2(p+1)/n \\\\\n&\\propto \\log(RSS) + 2(p+1)/n\n\\end{aligned}\\]\n( \\(p+1\\) because of the unknown variance, intercept included in \\(p\\) or not)\n\n\n\n\n\n\n\n\nImportant\n\n\nUnfortunately, different books/software/notes define these differently. Even different R packages. This is super annoying.\nForms above are in [ESL] eq. (7.29) and (7.35). [ISLR] gives special cases in Section 6.1.3. 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