Logistic mixed-effects models are widely used to study the relationship between the binary response and covariates for longitudinal data analysis, where the random effects are typically assumed to have a fully parametric distribution. As this assumption is likely limited or unreasonable in a multitude of practical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of binomial distribution logistic mixed-effects models, a general Bayesian framework is presented in which a semiparametric hierarchical modelling with an approximate truncated Dirichlet process prior distribution is specified for the random effects. The stick-breaking prior and the blocked Gibbs sampler using Pólya-Gamma mixture are employed to efficiently sample in the posterior analysis. Besides, a procedure calculating DIC for Bayesian model comparison is addressed. The methodology is demonstrated through simulation studies and a real example.

In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies.

In the development of simplex mixed-effects models, random effects in these mixed-effects models are generally distributed in normal distribution. The normality assumption may be violated in an analysis of skewed and multimodal longitudinal data. In this paper, we adopt the centered Dirichlet process mixture model (CDPMM) to specify the random effects in the simplex mixed-effects models. Combining the block Gibbs sampler and the Metropolis–Hastings algorithm, we extend a Bayesian Lasso (BLasso) to simultaneously estimate unknown parameters of interest and select important covariates with nonzero effects in semiparametric simplex mixed-effects models. Several simulation studies and a real example are employed to illustrate the proposed methodologies.

We propose a full Bayesian subset selection method for reproductive dispersion linear models, which bases on expanding the usual link function to a function that incorporates all possible subsets of predictors by adding indictors as parameters. The vector of indicator variables dictates which predictors to delete. An efficient MCMC procedure that combining Gibbs sampler and Metropolis-Hastings algorithm is presented to approximate the posterior distribution of the indicator variables. The promising subsets of predictors can be identified as those with higher posterior probability. Several numerical examples are used to illustrate the newly developed methodology.