Search

A bridge-randomized penalization that employs a prior for the shrinkage parameter, as opposed to the conventional bridge penalization with a fixed penalty, often delivers more superior performance compared to many other traditional shrinkage methods. In this paper, we develop an efficient Bayesian computational algorithm via the two-block Markov Chain Monte Carlo method for the bridge-randomized penalization in quantile regression to perform inference in the high-dimensional 'large-p' and 'large-p-small-n' settings. To construct a fully Bayesian formulation, we utilize the asymmetric Laplace distribution as an auxiliary error distribution and the generalized Gaussian distribution prior for the regression coefficients. Simulation studies encompassing a wide range of scenarios indicate that the proposed method performs at least as well as, and often better than, other existing procedures in terms of both parameter estimation and variable selection. Finally, a real-data application is provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

Empirical models that relate multiple quality features to a set of design variables play a vital role in many industrial process optimization methods. Many of the current modeling methods employ a single-response normal model to analyze industrial processes without taking into consideration the high correlations and the non-normality among the response variables. Also, the problem of variable selection has also not yet been fully investigated within this modeling framework. Failure to account for these issues may result in a misleading prediction model, and therefore, poor process design. In this article, we propose a robust Bayesian seemingly unrelated regression model to simultaneously analyze multiple-feature systems while accounting for the high correlation, non-normality, and variable selection issues. Additionally, we propose a Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full joint posterior distribution to obtain the robust Bayesian estimates. Simulation experiments are executed to investigate the performance of the proposed Bayesian method, which is also illustrated by application to a laser cladding repair process. The analysis results show that the proposed modeling technique compares favorably with its classic counterpart in the literature. [ABSTRACT FROM AUTHOR]

In recent years, the continual reassessment method (CRM) has gained considerable popularity in Phase I cancer studies. In this article, we propose a two-parameter probit model with latent variables. Introducing the latent variables enables exact Bayesian inference in the sense that conditional posterior distributions of all the parameters, including the latent variables, are known. Such inference can be more accurate than the maximum likelihood inference and can also alleviate the estimation issue due to small sample size [Albert J, Chib S. Bayesian analysis of binary and polychotomous response data. J Amer Statist Assoc. 1993;88:669–679] in Phase I studies. Simulation studies demonstrated that the proposed method compares favourably to the one-parameter CRM. [ABSTRACT FROM PUBLISHER]