The R Package MitISEM: Mixture of Student-t Distributions using Importance Sampling Weighted Expectation Maximization for Efficient and Robust Simulation
This paper presents the R package MitISEM, which provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. The package provides also an extended MitISEM algorithm, â€˜sequential MitISEMâ€™, which substantially decreases the computational time when the target density has to be approximated for increasing data samples. This occurs when the posterior distribution 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 the candidate distribution obtained by MitISEM outperforms those obtained by â€˜naiveâ€™ approximations in terms of numerical efficiency. Further, the MitISEM approach can be used for Bayesian model comparison, using the predictive likelihoods.