Applied Bayesian Statistics



 

Applied Bayesian Statistics - (L11+5) D.J. Spiegelhalter

This course will count as a 2-unit (16 lecture) course. There will be 11 lectures and five practical classes.

  • Bayes theorem; principles of Bayesian reasoning; probability as a subjective construct
  • Exact conjugate analysis; exponential family; mixture priors
  • Likelihood principle; alternative theories of inference
  • Assessment of prior distributions; imaginary observations
  • Monte Carlo analysis;
  • Conditional independence; graphical models
  • Markov chain Monte Carlo methods; convergence
  • Regression analysis (linear, GLM, nonlinear)
  • Model criticism and comparison; Bayesian P-values; information criteria
  • Hierarchical models (GLMMs)

The practical classes will use WinBUGS.

Pre-requisite Mathematics
This course assumes that students have a working knowledge of non-Bayesian applied statistics, such as the Applied Statistics course. It will be helpful but not essential to attend the Monte Carlo Inference course. Full familiarity with properties and manipulations of probability distributions will be assumed, including marginalisation, change of variable, Fisher information, iterated expectation, conditional independence, and so on.
Literature
1. Lunn, D., Jackson, C., Best, N.G., Thomas, A. and Spiegelhalter, D.J. (2012) The BUGS Book: A Practical Introduction to Bayesian Analysis. Chapman and Hall.
2. Gelman A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2003) Bayesian Data Analysis. 2nd Edition. Chapman and Hall

 

 


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