last updated: October 24, 2024

Bayesian Statistics

\(\newcommand{\footnotename}{footnote}\) \(\def \LWRfootnote {1}\) \(\newcommand {\footnote }[2][\LWRfootnote ]{{}^{\mathrm {#1}}}\) \(\newcommand {\footnotemark }[1][\LWRfootnote ]{{}^{\mathrm {#1}}}\) \(\let \LWRorighspace \hspace \) \(\renewcommand {\hspace }{\ifstar \LWRorighspace \LWRorighspace }\) \(\newcommand {\mathnormal }[1]{{#1}}\) \(\newcommand \ensuremath [1]{#1}\) \(\newcommand {\LWRframebox }[2][]{\fbox {#2}} \newcommand {\framebox }[1][]{\LWRframebox } \) \(\newcommand {\setlength }[2]{}\) \(\newcommand {\addtolength }[2]{}\) \(\newcommand {\setcounter }[2]{}\) \(\newcommand {\addtocounter }[2]{}\) \(\newcommand {\arabic }[1]{}\) \(\newcommand {\number }[1]{}\) \(\newcommand {\noalign }[1]{\text {#1}\notag \\}\) \(\newcommand {\cline }[1]{}\) \(\newcommand {\directlua }[1]{\text {(directlua)}}\) \(\newcommand {\luatexdirectlua }[1]{\text {(directlua)}}\) \(\newcommand {\protect }{}\) \(\def \LWRabsorbnumber #1 {}\) \(\def \LWRabsorbquotenumber "#1 {}\) \(\newcommand {\LWRabsorboption }[1][]{}\) \(\newcommand {\LWRabsorbtwooptions }[1][]{\LWRabsorboption }\) \(\def \mathchar {\ifnextchar "\LWRabsorbquotenumber \LWRabsorbnumber }\) \(\def \mathcode #1={\mathchar }\) \(\let \delcode \mathcode \) \(\let \delimiter \mathchar \) \(\def \oe {\unicode {x0153}}\) \(\def \OE {\unicode {x0152}}\) \(\def \ae {\unicode {x00E6}}\) \(\def \AE {\unicode {x00C6}}\) \(\def \aa {\unicode {x00E5}}\) \(\def \AA {\unicode {x00C5}}\) \(\def \o {\unicode {x00F8}}\) \(\def \O {\unicode {x00D8}}\) \(\def \l {\unicode {x0142}}\) \(\def \L {\unicode {x0141}}\) \(\def \ss {\unicode {x00DF}}\) \(\def \SS {\unicode {x1E9E}}\) \(\def \dag {\unicode {x2020}}\) \(\def \ddag {\unicode {x2021}}\) \(\def \P {\unicode {x00B6}}\) \(\def \copyright {\unicode {x00A9}}\) \(\def \pounds {\unicode {x00A3}}\) \(\let \LWRref \ref \) \(\renewcommand {\ref }{\ifstar \LWRref \LWRref }\) \( \newcommand {\multicolumn }[3]{#3}\) \(\require {textcomp}\) \(\newcommand {\intertext }[1]{\text {#1}\notag \\}\) \(\let \Hat \hat \) \(\let \Check \check \) \(\let \Tilde \tilde \) \(\let \Acute \acute \) \(\let \Grave \grave \) \(\let \Dot \dot \) \(\let \Ddot \ddot \) \(\let \Breve \breve \) \(\let \Bar \bar \) \(\let \Vec \vec \) \(\require {colortbl}\) \(\let \LWRorigcolumncolor \columncolor \) \(\renewcommand {\columncolor }[2][named]{\LWRorigcolumncolor [#1]{#2}\LWRabsorbtwooptions }\) \(\let \LWRorigrowcolor \rowcolor \) \(\renewcommand {\rowcolor }[2][named]{\LWRorigrowcolor [#1]{#2}\LWRabsorbtwooptions }\) \(\let \LWRorigcellcolor \cellcolor \) \(\renewcommand {\cellcolor }[2][named]{\LWRorigcellcolor [#1]{#2}\LWRabsorbtwooptions }\) \(\require {mathtools}\) \(\newenvironment {crampedsubarray}[1]{}{}\) \(\newcommand {\smashoperator }[2][]{#2\limits }\) \(\newcommand {\SwapAboveDisplaySkip }{}\) \(\newcommand {\LaTeXunderbrace }[1]{\underbrace {#1}}\) \(\newcommand {\LaTeXoverbrace }[1]{\overbrace {#1}}\) \(\newcommand {\LWRmultlined }[1][]{\begin {multline*}}\) \(\newenvironment {multlined}[1][]{\LWRmultlined }{\end {multline*}}\) \(\let \LWRorigshoveleft \shoveleft \) \(\renewcommand {\shoveleft }[1][]{\LWRorigshoveleft }\) \(\let \LWRorigshoveright \shoveright \) \(\renewcommand {\shoveright }[1][]{\LWRorigshoveright }\) \(\newcommand {\shortintertext }[1]{\text {#1}\notag \\}\) \(\newcommand {\vcentcolon }{\mathrel {\unicode {x2236}}}\) \(\renewcommand {\intertext }[2][]{\text {#2}\notag \\}\) \(\newenvironment {fleqn}[1][]{}{}\) \(\newenvironment {ceqn}{}{}\) \(\newenvironment {darray}[2][c]{\begin {array}[#1]{#2}}{\end {array}}\) \(\newcommand {\dmulticolumn }[3]{#3}\) \(\newcommand {\LWRnrnostar }[1][0.5ex]{\\[#1]}\) \(\newcommand {\nr }{\ifstar \LWRnrnostar \LWRnrnostar }\) \(\newcommand {\mrel }[1]{\begin {aligned}#1\end {aligned}}\) \(\newcommand {\underrel }[2]{\underset {#2}{#1}}\) \(\newcommand {\medmath }[1]{#1}\) \(\newcommand {\medop }[1]{#1}\) \(\newcommand {\medint }[1]{#1}\) \(\newcommand {\medintcorr }[1]{#1}\) \(\newcommand {\mfrac }[2]{\frac {#1}{#2}}\) \(\newcommand {\mbinom }[2]{\binom {#1}{#2}}\) \(\newenvironment {mmatrix}{\begin {matrix}}{\end {matrix}}\) \(\newcommand {\displaybreak }[1][]{}\) \( \def \offsyl {(\oslash )} \def \msconly {(\Delta )} \) \( \DeclareMathOperator {\var }{var} \DeclareMathOperator {\cov }{cov} \DeclareMathOperator {\Bin }{Bin} \DeclareMathOperator {\Geo }{Geometric} \DeclareMathOperator {\Beta }{Beta} \DeclareMathOperator {\Unif }{Uniform} \DeclareMathOperator {\Gam }{Gamma} \DeclareMathOperator {\Normal }{N} \DeclareMathOperator {\Exp }{Exp} \DeclareMathOperator {\Cauchy }{Cauchy} \DeclareMathOperator {\Bern }{Bernoulli} \DeclareMathOperator {\Poisson }{Poisson} \DeclareMathOperator {\Weibull }{Weibull} \DeclareMathOperator {\IGam }{IGamma} \DeclareMathOperator {\NGam }{NGamma} \DeclareMathOperator {\ChiSquared }{ChiSquared} \DeclareMathOperator {\Pareto }{Pareto} \DeclareMathOperator {\NBin }{NegBin} \DeclareMathOperator {\Studentt }{Student-t} \DeclareMathOperator *{\argmax }{arg\,max} \DeclareMathOperator *{\argmin }{arg\,min} \) \( \def \to {\rightarrow } \def \iff {\Leftrightarrow } \def \ra {\Rightarrow } \def \sw {\subseteq } \def \mc {\mathcal } \def \mb {\mathbb } \def \sc {\setminus } \def \wt {\widetilde } \def \v {\textbf } \def \E {\mb {E}} \def \P {\mb {P}} \def \R {\mb {R}} \def \C {\mb {C}} \def \N {\mb {N}} \def \Q {\mb {Q}} \def \Z {\mb {Z}} \def \B {\mb {B}} \def \~{\sim } \def \-{\,;\,} \def \qed {$\blacksquare $} \CustomizeMathJax {\def \1{\unicode {x1D7D9}}} \def \cadlag {c\`{a}dl\`{a}g} \def \p {\partial } \def \l {\left } \def \r {\right } \def \Om {\Omega } \def \om {\omega } \def \eps {\epsilon } \def \de {\delta } \def \ov {\overline } \def \sr {\stackrel } \def \Lp {\mc {L}^p} \def \Lq {\mc {L}^p} \def \Lone {\mc {L}^1} \def \Ltwo {\mc {L}^2} \def \toae {\sr {\rm a.e.}{\to }} \def \toas {\sr {\rm a.s.}{\to }} \def \top {\sr {\mb {\P }}{\to }} \def \tod {\sr {\rm d}{\to }} \def \toLp {\sr {\Lp }{\to }} \def \toLq {\sr {\Lq }{\to }} \def \eqae {\sr {\rm a.e.}{=}} \def \eqas {\sr {\rm a.s.}{=}} \def \eqd {\sr {\rm d}{=}} \def \approxd {\sr {\rm d}{\approx }} \def \Sa {(S1)\xspace } \def \Sb {(S2)\xspace } \def \Sc {(S3)\xspace } \)

Chapter A Reference Sheets

The reference sheets displayed on the following pages will be provided in the exam. Full size copies will also be given out alongside these lecture notes, at the start of the course.

(Part 1 of the reference sheet)

(Part 1 of the reference sheet)

(Part 2 of the reference sheet)

(Part 3 of the reference sheet)

(Part 5 of the reference sheet)

(Part 6 of the reference sheet)