The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference

Tinbergen Institute Discussion Paper 15-042/III

43 Pages Posted: 31 Mar 2015 Last revised: 8 Jul 2017

See all articles by Nalan Basturk

Nalan Basturk

Maastricht University - Department of Quantitative Economics

Stefano Grassi

University of Kent - Canterbury Campus

Lennart F. Hoogerheide

VU University Amsterdam

Anne Opschoor

Vrije Universiteit Amsterdam

H. K. van Dijk

Tinbergen Institute; Econometric Institute

Multiple version iconThere are 2 versions of this paper

Date Written: July 7, 2017

Abstract

This paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization) which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel - typically a posterior density kernel - using an adaptive mixture of Student-t densities as approximating density. In the first stage a mixture of Student-t densities is fitted to the target using an expectation maximization algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings (MH) method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bio-informatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of education's effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, `sequential MitISEM', which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler candidate, as well as the Gibbs sampler. The MitISEM approach is also used for Bayesian model comparison using predictive likelihoods.

Keywords: finite mixtures, Student-t densities, importance sampling, MCMC, Metropolis-Hastings algorithm, expectation maximization, Bayesian inference, R-software

JEL Classification: C11, C01, C87

Suggested Citation

Basturk, Nalan and Grassi, Stefano and Hoogerheide, Lennart F. and Opschoor, Anne and van Dijk, Herman K., The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference (July 7, 2017). Tinbergen Institute Discussion Paper 15-042/III, Available at SSRN: https://ssrn.com/abstract=2587011 or http://dx.doi.org/10.2139/ssrn.2587011

Nalan Basturk (Contact Author)

Maastricht University - Department of Quantitative Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

Stefano Grassi

University of Kent - Canterbury Campus ( email )

Keynes College
Canterbury, Kent CT2 7NP
United Kingdom

Lennart F. Hoogerheide

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Anne Opschoor

Vrije Universiteit Amsterdam ( email )

De Boelelaan 1105
Amsterdam, NL 1081 HV
Netherlands

Herman K. Van Dijk

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Burg. Oudlaan 50
Amsterdam/Rotterdam, 1082 MS
Netherlands
+31104088955 (Phone)
+31104089031 (Fax)

HOME PAGE: http://people.few.eur.nl/hkvandijk/

Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 4088955 (Phone)
+31 10 4527746 (Fax)

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