Chapter

Finite Mixture Examples; MAPIS Details

Russell Cheng

in Non-Standard Parametric Statistical Inference

Published in print June 2017 | ISBN: 9780198505044
Published online September 2017 | e-ISBN: 9780191746390 | DOI: https://dx.doi.org/10.1093/oso/9780198505044.003.0018
Finite Mixture Examples; MAPIS Details

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Two detailed numerical examples are given in this chapter illustrating and comparing mainly the reversible jump Markov chain Monte Carlo (RJMCMC) and the maximum a posteriori/importance sampling (MAPIS) methods. The numerical examples are the well-known galaxy data set with sample size 82, and the Hidalgo stamp issues thickness data with sample size 485. A comparison is made of the estimates obtained by the RJMCMC and MAPIS methods for (i) the posterior k-distribution of the number of components, k, (ii) the predictive finite mixture distribution itself, and (iii) the posterior distributions of the component parameters and weights. The estimates obtained by MAPIS are shown to be more satisfactory and meaningful. Details are given of the practical implementation of MAPIS for five non-normal mixture models, namely: the extreme value, gamma, inverse Gaussian, lognormal, and Weibull. Mathematical details are also given of the acceptance-rejection importance sampling used in MAPIS.

Keywords: galaxy data set; Hidalgo stamp issues data set; MAPIS method; non-normal mixture models; posterior k-distribution; predictive finite mixture distribution; reversible jump MCMC

Chapter.  10557 words.  Illustrated.

Subjects: Probability and Statistics

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