Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

The evolutionary diversification of parrots supports a taxon pulse model with multiple trans-oceanic dispersal events and local radiations

Vicariance is thought to have played a major role in the evolution of modern parrots. However, as the relationships especially of the African taxa remained mostly unresolved, it has been difficult to draw firm conclusions about the roles of dispersal and vicariance. Our analyses using the broadest taxon sampling of old world parrots ever based on 3219 bp of three nuclear genes revealed well-resolved and congruent phylogenetic hypotheses. Agapornis of Africa and Madagascar was found to be the sister group to Loriculus of Australasia and Indo-Malayasia and together they clustered with the Australasian Loriinae, Cyclopsittacini and Melopsittacus. Poicephalus and Psittacus from mainland Africa formed the sister group Of the Neotropical Arini and Coracopsis from Madagascar and adjacent islands may be the closest relative of Psittrichas from New Guinea. These biogeographic relationships are best explained by independent colonization of the African continent via trans-oceanic dispersal from Australasia and Antarctica in the Paleogene following what may have been vicariance events in the late Cretaceous and/or early Paleogene. Our data support a taxon pulse model for the diversification of parrots whereby trans-oceanic dispersal played a more important role than previously thought and was the prerequisite for range expansion into new continents. (C) 2009 Elsevier Inc. All rights reserved