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Business Analytics

The Bayesian Parallel Computation for Intractable Likelihood

Dr Nuttanan Wichitaksorn, Department of Mathematics and Statistics; University of Canterbury, NZ

18th Oct 2013  11:00 am - Room 498 Merewether Bldg H04

Parallel computation is a fast growing computing environment in many areas including computational Bayesian statistics.  However, most of the Bayesian parallel computing have been implemented through the sequential Monte Carlo method where model parameters are updated sequentially and it is suitable for some large-scale problems.  This talk is the first to revive the use of adaptive griddy Gibbs (AGG) algorithm under the Markov chain Monte Carlo framework and show how to implement the AGG using the parallel computation.  The parallel AGG is suitable for (i) small to medium-scale problems where the dimension of model parameter space is not very high, (ii) some or all model parameters are defined on a specific interval, and (iii) model likelihood is intractable. In addition, the parallel AGG is relatively easy to implement and code.  Since the AGG is a Gibbs algorithm where each of model parameters is directly drawn from the conditional posterior density, the model marginal likelihood can be conveniently computed and immediately provided after the end of posterior simulation.  Three examples including a linear regression model with Student-t error, a nonlinear regression model, and a financial time series model (GARCH), will be illustrated to show the applicability of the AGG to the parallel computing environment.