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Introduction to MCMC and BUGS

Introduction to MCMC and BUGS. Computational problems. More parameters -> even more parameter combinations Exact computation and grid approximation become infeasible The posterior distribution can be approximated faster by simulation techniques

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Introduction to MCMC and BUGS

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  1. Introduction to MCMC and BUGS

  2. Computational problems • More parameters -> even more parameter combinations • Exact computation and grid approximation become infeasible • The posterior distribution can be approximated faster by simulation techniques • Simulation: drawing random numbers from a distribution

  3. Simulation

  4. Markov chain Monte Carlo • Draw random numbers from the posterior distribution • Each number depends on the previous one • Start from arbitrary value • Simulation “finds” the posterior distribution and provides random numbers from it • Advantage: very complex models can be analysed • Disadvantage: length of the searching phase is difficult to identify

  5. Remarks • MCMC is only one way to approximate the posterior distribution. It is not a modeling approach itself! • There are other methods as well: • Importance sampling • Sampling- Importance –Resampling • Sequential Monte Carlo (particle filter) • etc. • MCMC usually easier to set up

  6. BUGS • Bayesian Inference Using Gibbs Sampling • Gibbs sampling is one form of MCMC • User specifies the model structure • User inputs the data • Software uses Bayes’ theorem and constructs an MCMC algorithm to sample from the posterior • User assesses the convergence of MCMC • Use software to calculate descriptive statistics and produce figures

  7. Using BUGS • Lots of pointing and clicking • Some time is needed to learn the procedure • Also a scripting language is available • Routine points and clicks can be automated • Useful once you know how to point and click • R interface • BUGS can be used from R by the same scripting language • Results are exported to R for further analysis

  8. How to point and click • Follow these steps to specify a simple model and simulate the posterior distribution • Start BUGS : winbugs.exe • Create new document: File ->New • Write a model specification to the blank document: model{ x~dnorm(10,0.25) }

  9. Running the simulation: • Model ->Specification… • Specification Tool: check model • [Activate the document or area that contains data] • [Specification tool: load data] • Specification tool: compile • [Activate the document or area that contains the set of initial values] • [Specification tool: load inits] • Specification tool: gen inits • Inference -> Samples… • Sample monitor tool: node : “x” • Sample monitor tool: set • Model -> Update… • Update tool: refresh: “1” • Update tool: update • Sample monitor tool: node: “x” • Sample monitor tool: history • Sample monitor tool: stats • Sample monitor tool: density

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