Adaptive Mixture of Student-t distributions as a Flexible Candidate Distribution for Efficient Simulation

This paper presents the R package AdMit which provides functions to approximate and sample from a certain target distribution given only a kernel of the target density function. The core algorithm consists in the function AdMit which fits an adaptive mixture of Student-t distributions to the density of interest via its kernel function. Then, importance sampling or the independence chain Metropolis- Hastings algorithm are used to obtain quantities of interest for the target density, using the fitted mixture as the importance or candidate density. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The relevance of the package is shown in two examples. The first aims at illustrating in detail the use of the functions provided by the package in a bivariate bimodal distribution. The second shows the relevance of the adaptive mixture procedure through the Bayesian estimation of a mixture of ARCH model fitted to foreign exchange log-returns data. The methodology is compared to standard cases of importance sampling and the Metropolis-Hastings algorithm using a naive candidate and with the Griddy-Gibbs approach.