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Graphical models and complex stochastic systems
Lecturer: Peter Green, Statistics group
Test
Here it is!
 Winbugs code for bonus question
 Solutions and comments
Syllabus
 Introduction and motivation: complex stochastic systems in science and technology
 Basic ideas of statistical inference. Probability, statistics and data analysis. Models and data. Estimation, confidence intervals and hypothesis testing.
Maximum likelihood. Bayesian analysis.
 Conditional independence: axioms, graphical representations, directed acyclic graphs.
 Exchangeability and hierarchical models: Bayesian formulations.
 Bayes nets and expert systems; exact computation by probability propagation.
 Hidden Markov models and statespace models.
 Undirected and chain graph models. Markov random fields and Gibbs distributions. HammersleyClifford theorem, spatial models.
 Equilibrium simulation: Markov chain Monte Carlo.
 Model selection and criticism.
 (Learning structure.)
 (Graphical models and causal reasoning.)
 (Role of graphical modelling in computation: specification, visualisation, algorithms.)
Complexity Science graduate programme:
course materials page for this module
Related unit: M6002 Graphical modelling (weeks 1318, in Mathematics)
Lectures:
1 (pdf/ppt)
 2
 34
 5
(& extra figs)
 6 (pdf/ppt)
 7
 8 (pdf/ppt)
 9
 10
Demo code
Brief instructions
Lecture 2:
binomial likelihood 
normal likelihood 
comparing estimators
Lecture 3:
likelihood for mixture of two normals
 betabinomial
Lecture 6:
'Asia' expert system
 biased coins
 hierarchical binomial model
 paternity query
 mixed trace forensic problem
Lecture 7:
2 state Markov chain
 simple hidden Markov model
Lecture 9:
3 Winbugs demos
Exercises 1:
random walk 
percolation
Software
R 
gR 
Grappa 
Hugin (expensive) 
Hugin 5.7 (free) 
WinBugs
Tutorial on R
To run R (version 2.6.0), Hugin (version 5.7) or WinBugs (version 1.4.3) on the BCCS PC's, look under
Start  All Programs  Engineering Apps
Exercises
Sheet: 1
 2
 3
 4
 5
Some relevant work of mine
 BarndorffNielsen, Cox and Klüppelberg (eds.) Complex Stochastic Systems, Chapman and Hall, London, 2001.
 Cappé, Moulines and Rydén. Inference in Hidden Markov Models. Springer, 2005.
 Cowell, Dawid, Lauritzen and Spiegelhalter. Probabilistic Networks and Expert Systems. SpringerVerlag, 1999.
 Gelman, Carlin, Stern and Rubin. Bayesian Data Analysis, Chapman & Hall/CRC, 2003.
 Green, Hjort and Richardson. Highly Structured Stochastic Systems, OUP, 2003.
 Gilks, Richardson and Spiegelhalter. Markov Chain Monte Carlo in Practice, Chapman & Hall, 1996.
 Lauritzen. Graphical Models, OUP, 1996.
 Pearl. Causality: Models, Reasoning and Inference, CUP, 2000.
 Titterington (ed.) Complex Stochastic Systems and Engineering, IMA Conference Series No. 54. OUP, 1995.
 Whittaker. Graphical Models in Applied Multivariate Statistics, Wiley, 1990.
