STAT 530

Welcome to Stat 530!

Instructor: Ruben Zamar, LSK 331, ruben at stat dot ubc dot ca, (604) 822-3167

Office hours: Monday and Wednesday, 2:45-3:45

Textbook: Bayesian Data Analysis, Second Edition, by Gelman, Carlin, Stern and Rubin, Chapman & Hall

Expected Background


- Good knowledge of probability (e.g. Math 418)
- Good knowledge of mathematical statistics (e.g. Casella and Berger)
- Confortable with statistical modelling
- Confortable with R


Grading

- reports on assigned problems 50%
- midterm exam  20%
- final project written report 15%
- final project presentation 15%


Outline

Intro to Bayesian Inference

- derivation of posterior densities for several single and multiple parameter models
- constucting point estimates (posterior mode), credible intervals, bayesian prediction
- generating random samples from posterior densities and posterior predictive distributions
- regression models
- some simple hierarchical models

Intro to Markov Chain Monte Carlo  (MCMC)

- Metropolis-Hasting algorithm
- Gibbs sampler
- application to bayesian inference
- other applications

Robustness

- main robustness concepts and tools
- frequentist location/scale/regression robusty estimates
- prior robustness and sensitivity analysis
- likelihood robustness

EM Algorithm

- maximizing the likelihood in the presence of incomplete information
- problems with missign data
- application of EM to compute posterior modes

 

 

 

 

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