A Class of Adaptive EM-based Importance Sampling Algorithms for Efficient and Robust Posterior and Predictive Simulation

Arbeitspapier

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 problem.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 11-004/4

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Statistical Simulation Methods: General ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Multiple or Simultaneous Equation Models: Instrumental Variables (IV) Estimation
• Subject: mixture of Student-t distributions ; importance sampling ; Kullback-Leibler divergence ; Expectation Maximization ; Metropolis-Hastings algorithm ; predictive likelihoods ; mixture GARCH models ; Value at Risk ; Statistische Verteilung ; Stichprobenverfahren ; Risikomaß ; Algorithmus ; ARCH-Modell ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Hoogerheide, Lennart ; Opschoor, Anne ; van Dijk, Herman K.
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/86717
• Last update: 10.03.2025, 11:44 AM CET