A Class of Adaptive EM-Based Importance Sampling Algorithms for Efficient and Robust Posterior and Predictive Simulation
Tinbergen Institute Discussion Paper No. 2011-004/4
53 Pages Posted: 10 Jan 2011
Date Written: January, 10 2011
Abstract
A class of adaptive sampling methods is introduced for efficient posterior and predictive simulation. The proposed methods are robust in the sense that they can handle target distributions that exhibit non-elliptical shapes such as multimodality and skewness. The basic method makes use of sequences of importance weighted Expectation Maximization steps in order to efficiently construct a mixture of Student-t densities that approximates accurately the target distribution - typically a posterior distribution, of which we only require a kernel - in the sense that the Kullback-Leibler divergence between target and mixture is minimized. We label this approach Mixture of t by Importance Sampling and Expectation Maximization (MitISEM). We also introduce three extensions of the basic MitISEM approach. First, we propose a method for applying MitISEM in a sequential manner, so that the candidate distribution for posterior simulation is cleverly updated when new data become available. Our results show that the computational effort reduces enormously. This sequential approach can be combined with a tempering approach, which facilitates the simulation from densities with multiple modes that are far apart. Second, we introduce a permutation-augmented MitISEM approach, for importance sampling from posterior distributions in mixture models without the requirement of imposing identification restrictions on the model's mixture regimes' parameters. Third, we propose a partial MitISEM approach, which aims at approximating the marginal and conditional posterior distributions of subsets of model parameters, rather than the joint. This division can substantially reduce the dimension of the approximation
Keywords: Mixture of Student-T Distributions, Importance Sampling, Kullback-Leibler Divergence, Expectation Maximization, Metropolis-Hastings Algorithm, Predictive Likelihoods, Mixture GARCH Models, Value at Risk
JEL Classification: C11, C15, C22, C36
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
By Lennart F. Hoogerheide, Anne Opschoor, ...
-
By Lukasz T. Gatarek, Lennart F. Hoogerheide, ...