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Markov chain Monte Carlo is a stochastic simulation technique that is very useful for computing inferential quantities. It is often used in a Bayesian context, but not restricted to a Bayesian setting.
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Markov Chain Monte Carlo and Applied
Bayesian Statistics
Hilary Term 2007
Prof. Gesine Reinert
Markov chain Monte Carlo is a stochastic simulation
technique that is very useful for computing inferential
quantities. It is often used in a Bayesian context, but
not restricted to a Bayesian setting.
1
Outline
1. Review of Bayesian inference
2. Monte Carlo integration
3. Markov chains
4. MCMC in Bayesian inference: ideas
5. MCMC in Bayesian inference: algorithms
6. Output analysis and diagnostics
7. Another example
8. Concluding remarks
2
Reading
1. Gelman, A. et al. (2004). Bayesian Data Analysis.
Chapman & Hall.
2. Gilks, W.R. et al. eds. (1996). Markov Chain Monte
Carlo in Practice. Chapman & Hall.
3. Robert, C.P. and Casella, G. (2004) Monte Carlo
Statistical Methods. 2nd ed. Springer.
4. Norris, J.R. (1997). Markov Chains. Cambridge
University Press.
5. ( Chen, M-H. et al. (2000). Monte Carlo Methods
in Bayesian Computation. Springer. )
3
Lectures will take place Mondays 12-1 and Wednesdays
11-12, Weeks 5-7, in the Department of Statistics. There
will be a practical session, using the software package
WinBUGS, Friday week 5, 1:30 -3 pm, 3 - 4:30 pm, and
4:30 - 6 pm.
Acknowledgement: Chris Holmes for providing his
lecture notes and examples, which are partly due to Nicky
Best.
4
1. Review of Bayesian inference
Data y = y
1
, y
2
, . . . , y
n
, realisations of random vari-
ables Y
1
, Y
2
, . . . , Y
n
, with distribution (model)
f(y
1
, y
2
, . . . , y
n
|θ)
L(θ|y) = f(y|θ) is the likelihood of y if θ is the true
parameter (vector)
Parameter (vector) θ = (θ
1
, . . . , θ
p
) has a prior distribu-
tion π(θ)
5
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