Bayesian Statistics

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)} \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} $ \( \def \to {\rightarrow } \def \iff {\Leftrightarrow } \def \ra {\Rightarrow } \def \sw {\subseteq } \def \mc {\mathcal } \def \mb {\mathbb } 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\)

Chapter 0 Introduction

0.1 Organization

0.1.1 Syllabus

These notes are for two courses: MPS350 and MPS4111. All of the material in these notes is shared between both courses, but only MPS4111 students continue with the course next semester. Students on MPS4111 have some extra computer sessions this semester in preparation for that, and will do their project work next semester (and not this semester), but otherwise the teaching this semester is identical.

Some parts of the notes are marked with a $\offsyl $ symbol, which means they are off-syllabus, for everyone. These cover some tangential material, technical proofs and other optional content that is included purely for interest.

0.1.2 End-of-chapter questions and problem sheets

At the end of chapter of these notes there is a set of problems for you to solve. The questions are marked with stars to indicate their rough level of difficulty:

$\color {blue}\star $ I think (or rather, hope) that many people will find this question easy.
$\color {blue}\star \,\star $ I think this question is within the usual range of difficulty.
$\color {blue}\star \star \star $ This question is meant as a challenge for people who are already feeling on top of the rest of the material. I think many people will find this question difficult!

Most of the questions have two stars.

All of the solutions to the end-of-chapter questions within these notes are provided at the end of the online version of the notes in Appendix C. You should work through these questions as we go through the chapters, and review your own solutions using the typed solutions.

At two points during the semester, a problem sheet of additional exercises will be set. About one week later, we will go through the questions in lectures, and you should self-mark your solutions. These do not count towards your final mark.