# 15-042/III (2015-03-30; 2017-07-04)

Nalan Basturk, Maastricht University , the Netherlands; Stefano Grassi, University of Kent, United Kingdom; Lennart Hoogerheide, VU University Amsterdam, the Netherlands; Anne Opschoor, VU University Amsterdam, the Netherlands; Herman K. van Dijk, Erasmus University Rotterdam, the Netherlands
finite mixtures, Student-t densities, importance sampling, MCMC, Metropolis-Hastings algorithm, expectation maximization, Bayesian inference, R-software
JEL codes:
C01, C11, C87

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 (EM) 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.