Syllabus (lecture by lecture):25/09/17: Examples to compare Bayesian and frequentist approaches; Bayesian paradigm; A beta-binomial model for proportion estimation.Textbook: Chapter 1 (with the exclusion of 1.2.2, which is a suggested reading).---28/09/17: Belief functions and probability measures; Conditional independence.Textbook: Chapter 2, pag. 13-17 and pag. 26. (read also Section 2.4 and 2.5 if you need to review these topics).---02/10/17: Exchangeability; Comparison of i.i.d. and exchangeability assumption; de Finetti representation theorem (0-1 and general case); Sketch of the proof for the 0-1 case.Textbook: Chapter 2, pag. 27-30.---05/10/17: Binomial model with beta prior; conjugate priors.Textbook: Chapter 3, pag. 31-38.---09/10/17: More on Binomial model; Predictive distribution; Bayesian coverage; Quantile-based posterior credible intervals; Poisson model with gamma prior; Birth rates example (see R script).Textbook: Chapter 3, pag. 38-50.---12/10/17: One-dimensional exponential family; Binomial and Poisson as members of the exponential family; Conjugate prior for the exponential family.Textbook: Chapter 3, pag. 51-52.---19/10/17: Conjugate priors: from the exponential family to Binomial and Poisson;Textbook: Chapter 3, pag. 51-52.Assignment: Problem 3.9 pag. 230; Problem on Normal model with variance fixed=1.---23/10/17: Monte Carlo method (see slides); Normal model with fixed variance; Normal prior. Textbook: Chapter 4, pag. 53-65. Chapter 5, pag. 68-71.---26/10/17: Precision; Normal model with fixed variance: interpretation of the posterior distribution, predictive distribution.Textbook: Chapter 5, pag. 71-73.---02/11/17: Normal model with conjugate priors on mean and variance; Point estimation: Bayesian (posterior mean) vs frequentist (empirical mean); Bias.Textbook: Chapter 5, pag. 73-80 (with the exclusion of "improper priors").---13/11/17: Mean squared error for posterior mean and empirical mean; Gibbs sampler.Textbook: Chapter 5, pag 81-82. Chapter 6, pag. 89-98 (with the exclusion of Section 6.2)---16/11/17: Lab 1 - Monte Carlo methods.---20/11/17: Multivariate normal model: normal prior for the mean vector.---23/11/17: Lab 2 - Normal model: joint inference for mean and variance---27/11/17: Multivariate normal model: inverse-Wishart prior for the covariance matrix.---28/11/17: Multivariate normal model: an illustration.---30/11/17: Lab 3 - Multivariate normal model---11/12/17: Bayesian linear regression.---12/12/17: Bayesian model selection.---14/12/17: Solutions of the mock exam.---

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