Search

This paper presents a Bayesian analysis of partially linear additive models for quantile regression. We develop a semiparametric Bayesian approach to quantile regression models using a spectral representation of the nonparametric regression functions and the Dirichlet process (DP) mixture for error distribution. We also consider Bayesian variable selection procedures for both parametric and nonparametric components in a partially linear additive model structure based on the Bayesian shrinkage priors via a stochastic search algorithm. Based on the proposed Bayesian semiparametric additive quantile regression model referred to as BSAQ, the Bayesian inference is considered for estimation and model selection. For the posterior computation, we design a simple and efficient Gibbs sampler based on a location-scale mixture of exponential and normal distributions for an asymmetric Laplace distribution, which facilitates the commonly used collapsed Gibbs sampling algorithms for the DP mixture models. Additionally, we discuss the asymptotic property of the sempiparametric quantile regression model in terms of consistency of posterior distribution. Simulation studies and real data application examples illustrate the proposed method and compare it with Bayesian quantile regression methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Bayesian Analysis for the Block and Basu bivariate exponential distribution using Markov Chain Monte Carlo (MCMC) methods and considering lifetimes in presence of covariates and censored data. Posterior summaries of interest are obtained using the popular WinBUGS software. Numerical illustrations are introduced considering a medical data set related to the recurrence times of infection for kidney patients and a medical data set related to bone marrow transplantation for leukemia. [ABSTRACT FROM AUTHOR]

An important problem in statistics is the study of longitudinal data taking into account the effect of other explanatory variables such as treatments and time. In this paper, a new Bayesian approach for analysing longitudinal data is proposed. This innovative approach takes into account the possibility of having nonlinear regression structures on the mean and linear regression structures on the variance-covariance matrix of normal observations, and it is based on the modelling strategy suggested by Pourahmadi [M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterizations, Biometrika, 87 (1999), pp. 667-690.]. We initially extend the classical methodology to accommodate the fitting of nonlinear mean models then we propose our Bayesian approach based on a generalization of the Metropolis-Hastings algorithm of Cepeda [E.C. Cepeda, Variability modeling in generalized linear models, Unpublished Ph.D. Thesis, Mathematics Institute, Universidade Federal do Rio de Janeiro, 2001]. Finally, we illustrate the proposed methodology by analysing one example, the cattle data set, that is used to study cattle growth. [ABSTRACT FROM AUTHOR]

Mixture models provide a method of modelling a complex probability distribution in terms of simpler structures. In particular, the method of mixture of regressions has received considerable attention due to its modelling flexibility and availability of convenient computational algorithms. This paper aims to contribute to theoretical justification for the mixtures of regression model from the Bayesian perspective. In particular, we establish consistency of posterior distribution and determine how fast posterior distribution converges to the true value of the parameter in the context of mixture of binary, Poisson, and Gaussian regressions. [ABSTRACT FROM AUTHOR]

Accelerated life testing (ALT) is commonly used to predict the lifetime of a product at its use stress by subjecting test units to elevated stress conditions that accelerate the occurrence of failures. For new products, the selection of an acceleration model for planning optimal ALT plans is challenging due to the absence of historical lifetime data. The misspecification of an ALT model can lead to considerable errors when it is used to predict the product's life quantiles. This article proposes a two-stage Bayesian approach to constructing ALT plans and predicting lifetime quantiles. At the first stage, the ALT plan is optimized based on the prior information of candidate models under a modified V-optimality criterion that incorporates both asymptotic prediction variance and squared bias. A Bayesian model averaging (BMA) framework is used to derive the posterior model and the posterior distribution for the life quantile of interest under use stress. If the obtained test data cannot provide satisfactory model selection results, an adaptive second-stage test is conducted based on the posterior information from the first stage. A revisited numerical example demonstrates the efficiency and robustness of the resulting Bayesian ALT plans by comparing with the plans derived from previous methods. [ABSTRACT FROM AUTHOR]

We propose a new iterative algorithm, called model walking algorithm, to the Bayesian model averaging method on the longitudinal regression models with AR(1) random errors within subjects. The Markov chain Monte Carlo method together with the model walking algorithm are employed. The proposed method is successfully applied to predict the progression rates on a myopia intervention trial in children. [ABSTRACT FROM PUBLISHER]

In this article, we present a generalization of the Bayesian methodology introduced by Cepeda and Gamerman (2001) for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm. [ABSTRACT FROM AUTHOR]

This article presents a Bayesian approach to the regression analysis of truncated data, with a focus on zero-truncated counts from the Poisson distribution. The approach provides inference not only on the regression coefficients but also on the total sample size and the parameters of the covariate distribution. The theory is applied to some illegal immigrant data from The Netherlands. Several models are fitted with the aid of Markov chain Monte Carlo methods and assessed via posterior predictive p-values. Inferences are compared with those obtained elsewhere using other approaches. [ABSTRACT FROM AUTHOR]