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 B Advice for revision/exams

There are two different exam papers, one for MPS350 (sat in January) and one for MPS4111 (sat in the summer). The MPS4111 exam covers additional material taught in semester 2. All questions within the exams are compulsory. Within these notes, material marked with a $\offsyl $ is non-examinable for everyone. You do not need to study these parts during your revision.

• You will be asked to solve problems based on the material in these notes. There will be a broad range of difficulty amongst the questions. Some will be variations of questions in the assignments/notes, others will also try to test your ingenuity.
• Many of the important definitions and results appear on the (six page long!) reference sheets. You should practice using the reference sheets to help you solve problems.
• You will not be expected to reproduce long proofs from memory. Most proofs are marked as off-syllabus anyway, within these notes. You are expected to have followed the techniques within the proofs when they are present, and to be able to use these techniques in your own problem solving (e.g. Lemma 1.5.1).
• There are marks for attempting a suitable method, and for justifying mathematical steps, as well as for reaching a correct conclusion.

Revision activities

You should have done the two homework assignments during the semester and marked your own work using the model solutions. After that, the most important activities:

1. Solve the assignment questions, and end-of-chapter exercises that are at $\star $ and $\star \,\star $ difficulty levels. Check your solutions against the typed solutions.
2. Learn the key definitions, results, and examples.
3. Do the past exam papers and mark your own solutions.

In all cases, you are welcome to come and discuss any questions/comments/typos. Please use office hours or email to arrange a convenient time.