Bayesian Inference and Computations

Lecturers

Professor Yanan Fan, CSIRO Data61 and UNSW
Dr Ke Sun, CSIRO Data61 and Australian National University

Synopsis

Introduction to Bayesian inference, the role of priors; pior/posterior computations; Point estimation, interval estimation and predictive distributions; Normal models, asymptotics; Monte Carlo methods/introduction to simulation; Markov chain Monte Carlo; reversible jump MCMC; Hamiltonian MCMC, approximate Bayesian inference , variational inference. Instructions with R/Jupyter notebook

Course overview

Week 1: Introduction to Bayesian inference, the role of priors, pior/posterior computations, setting up R, use of R markdown, introduction to using R, point estimation, interval estimation and predictive distributions, normal models, asymptotics

Week 2: Monte Carlo methods/introduction to simulation, Markov chain Monte Carlo, Gibbs sampler/rates of convergence, convergence assessments

Week 3: Reversible jump MCMC, Hamiltonian Monte Carlo, introduction to approximate Bayesian computation (ABC)

Week 4: ABC continued, variational Bayes, Bayesian NN – VAE

Prerequisites

• second year undergraduate level statistical inference
• some familiarity with R or similar computing software

This is intended as a foundation course.

Assessment

TBA

Attendance requirements

Participation in all lectures and tutorials is expected.

For those completing the subject for their own knowledge/interest, evidence of at least 80% attendance at lectures and tutorials is required to receive a certificate of attendance.

Resources/pre-reading

TBA

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