Lecture 1 (06 Feb 17):  Introduction: working definitions of classical and Bayesian approaches to inference about parameters. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p45 (middle of Example 3). 
Lecture 2 (07 Feb 17):  §1 The Bayesian method: Bayes' theorem, using Bayes' theorem for parametric inference. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p5 (middle of Example 3)7 (prior to equation (1.6)). 
Lecture 3 (13 Feb 17):  Sequential data updates, conjugate Bayesian updates, BetaBinomial example. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p7 (prior to equation (1.6))9 (equation (1.12)). 
Lecture 4 (14 Feb 17):  Definition of conjugate family, role of prior (weak and strong) and likelihood in the posterior. Handout of beta distributions: pdf. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p9 (equation (1.12))10 (Example 5). 
Lecture 5 (20 Feb 17):  Example of weak/strong prior finished, kernel of a density, conjugate Normal example. Handout of weak/strong prior example: pdf. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p10 (Example 5)13 (equation (1.16)). 
Lecture 6 (21 Feb 17):  Using the posterior for inference, credible interval, highest density regions. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p13 (equation (1.16))15 (end of Example 9). 
Lecture 7 (27 Feb 17):  §2 Modelling: predictive distribution, BinomialBeta example. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p15 (end of Example 9)19 (equation (2.4)). 
Lecture 8 (28 Feb 17):  Predictive summaries, finite exchangeability. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p19 (equation (2.4))21 (end of Example 14). 
Lecture 9 (06 Mar 17):  Infinite exchangeability, example of nonextendibility of finitely exchangeable sequence, general representation theorem for infinitely exchangeable events and random quantities. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p21 (end of Example 14)23 (prior to Theorem 2). 
Lecture 10 (07 Mar 17):  Example of exchangeable Normal random quantities, sufficiency. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p23 (prior to Theorem 2)25 (start of Section 2.3). 
Lecture 11 (13 Mar 17):  kparameter exponential family, sufficient statistics, conjugate priors for exchangeable kparameter exponential family random quantities. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p25 (start of Section 2.3)27 (equation (2.23)). 
Lecture 12 (14 Mar 17):  Hyperparameters, usefulness of conjugate priors. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p27 (equation (2.23))29 (start of Section 2.4). 
Lecture 13 (20 Mar 17):  Improper priors, Fisher information matrix, Jeffreys' prior. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p29 (start of Section 2.4)32 (after Example 25). 
Lecture 14 (21 Mar 17):  Invariance property under transformation of the Jeffreys prior, final remarks about noninformative priors, §3 Computation: preliminary issues. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p32 (after Example 25)36 (prior to Section 3.1). 
Lecture 15 (27 Mar 17):  Normal approximation, expansion about the mode, Monte Carlo integration. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p36 (prior to Section 3.1)38 (prior to Section 3.2.2). 
Lecture 16 (28 Mar 17):  Importance sampling. Basic idea of Markov chain Monte Carlo (MCMC): transition kernel. Handout: pdf. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p38 (prior to Section 3.2.2)40 (equation (3.6)). 
Lecture 17 (03 Apr 17):  Basic definitions (irreducible, periodic, recurrent, ergodic, stationary) and theorems (existence/uniqueness, convergence, ergodic) of Markov chains and their consequences for MCMC techniques. The MetropolisHastings algorithm. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p40 (equation (3.6))43 (prior to equation (3.9)). 
Lecture 18 (04 Apr 17):  Example of the MetropolisHastings algorithm. Handout of example: pdf. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p43 (prior to equation (3.9))52 (start of Section 3.3.3). 
Lecture 19 (06 Apr 17):  The Gibbs sampler algorithm and example. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p52 (start of Section 3.3.3)53 (prior to Example 32). 
Lecture 19A (24 Apr 17):  Gibbs sampler example concluded. Handout of example: pdf. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p53 (prior to Example 32)59 (prior to Section 3.3.4). 
Lecture 20 (25 Apr 17):  Overview of why the MetropolisHastings algorithm works, efficiency of MCMC algorithms. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p59 (prior to Section 3.3.4)61 (after bullet point 2). 
Lecture 21 (27 Apr 17):  §4 Decision theory: Statistical decision theory: loss, risk, Bayes risk and Bayes rule. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p61 (after bullet point 2)65 (beginning of Example 36). Note: Section 4.1 Utility was omitted and is not required for the exam. 
Lecture 22 (02 May 17):  Quadratic loss, Bayes risk of the sampling procedure, worked example . 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p65 (beginning of Example 36)67 (after equation (4.7)). 
Lecture 23 (04 May 17):  Worked example finished. 

Lecture overview: pdf. Handwritten notes: pdf. Online notes: p67 (after equation (4.7))69 (end of notes). 