$$
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\newcommand{\gauss}[1]{\mathcal{N}\left(#1\right)}
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\newcommand{\cov}[1]{\mathrm{Cov}\left(#1\right)}
\newcommand{\sumn}{\sum_{n=1}^N}
\newcommand{\meann}{\frac{1}{N} \sumn}
\newcommand{\cltn}{\frac{1}{\sqrt{N}} \sumn}
\newcommand{\trace}[1]{\mathrm{trace}\left(#1\right)}
\newcommand{\diag}[1]{\mathrm{Diag}\left(#1\right)}
\newcommand{\grad}[2]{\nabla_{#1} \left. #2 \right.}
\newcommand{\gradat}[3]{\nabla_{#1} \left. #2 \right|_{#3}}
\newcommand{\fracat}[3]{\left. \frac{#1}{#2} \right|_{#3}}
\newcommand{\W}{\mybold{W}}
\newcommand{\w}{w}
\newcommand{\wbar}{\bar{w}}
\newcommand{\wv}{\mybold{w}}
\newcommand{\X}{\mybold{X}}
\newcommand{\x}{x}
\newcommand{\xbar}{\bar{x}}
\newcommand{\xv}{\mybold{x}}
\newcommand{\Xcov}{\Sigmam_{\X}}
\newcommand{\Xcovhat}{\hat{\Sigmam}_{\X}}
\newcommand{\Covsand}{\Sigmam_{\mathrm{sand}}}
\newcommand{\Covsandhat}{\hat{\Sigmam}_{\mathrm{sand}}}
\newcommand{\Z}{\mybold{Z}}
\newcommand{\z}{z}
\newcommand{\zv}{\mybold{z}}
\newcommand{\zbar}{\bar{z}}
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\newcommand{\yv}{\mybold{y}}
\newcommand{\yhat}{\hat{\y}}
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\newcommand{\res}{\varepsilon}
\newcommand{\resv}{\mybold{\res}}
\newcommand{\resvhat}{\hat{\mybold{\res}}}
\newcommand{\reshat}{\hat{\res}}
\newcommand{\betav}{\mybold{\beta}}
\newcommand{\betavhat}{\hat{\betav}}
\newcommand{\betahat}{\hat{\beta}}
\newcommand{\betastar}{{\beta^{*}}}
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\newcommand{\alphavhat}{\hat{\av}}
\newcommand{\alphahat}{\hat{\alpha}}
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\def\A{\mybold{A}}
\def\av{\mybold{a}}
\def\a{a}
\def\B{\mybold{B}}
\def\S{\mybold{S}}
\def\sv{\mybold{s}}
\def\s{s}
\def\R{\mybold{R}}
\def\rv{\mybold{r}}
\def\r{r}
\def\V{\mybold{V}}
\def\vv{\mybold{v}}
\def\v{v}
\def\U{\mybold{U}}
\def\uv{\mybold{u}}
\def\u{u}
\def\W{\mybold{W}}
\def\wv{\mybold{w}}
\def\w{w}
\def\tv{\mybold{t}}
\def\t{t}
\def\Sc{\mathcal{S}}
\def\ev{\mybold{e}}
\def\Lammat{\mybold{\Lambda}}
$$
\(\,\)
The reading for this section will be sections 10.1 – 10.4 of “Regression and Other Stories” by Gelman, Hill, and Vehtari. The book is freely available here as a pdf, which can also be accessed, along with other materials, at the book webpage.
The book takes a Baysian perspective, and our class is taking a frequentist perspective, but that will not matter for the purposes of this discussion. (I am happy to talk about the differences and commonalities between the two approaches, but I don’t plan to make Bayesian statistics a central part of the course content.)