Bayesian variable selection Research Papers (original) (raw)

Bayesian variable selection in quantile regression models is often a difficult task due to the computational challenges and non-availability of conjugate prior distributions. These challenges are rarely addressed via either penalized... more

Bayesian variable selection in quantile regression models is often a difficult task due to the computational challenges and non-availability of conjugate prior distributions. These challenges are rarely addressed via either penalized likelihood function or stochastic search variable selection. These methods typically use symmetric prior distributions such as a normal distribution or a Laplace distribution for regression coefficients, which may be suitable for median regression. However, an extreme quantile regression should have different regression coefficients from the median regression, and thus the priors for quantile regression should depend on the quantile. In this article an extension of the Zellners prior which allows for a conditional conjugate prior and quantile dependent prior on Bayesian quantile regression is proposed. Secondly, a novel prior based on percentage bend correlation for model selection is also used in Bayesian regression for the first time. Thirdly, a new variable selection method based on a Gibbs sampler is developed to facilitate the computation of the posterior probabilities. The proposed methods are justified mathematically and illustrated with both simulation and real data.

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism, environmental noise, serial correlation and dependence on time-varying factors. This paper... more

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism, environmental noise, serial correlation and dependence on time-varying factors. This paper addresses these issues via suitable Bayesian modelling. In doing so, we utilize a general class of stochastic regression models appropriate for spatio-temporal count data with an excess number of zeros. The developed regression framework does incorporate serial correlation and time-varying covariates through an Ornstein-Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and variations of mixtures of g-priors. The effect of different distance kernels for the epidemic model component is investigated. We proceed by developing branching process-based methods for testing scenarios for disease control, thus linking traditional epidemiological models with stochastic epidemic processes, useful in polic...

A novel fully automatic Bayesian procedure for variable selection in normal regression model is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed... more

A novel fully automatic Bayesian procedure for variable selection in normal regression model is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors for model selection problems. That is, they are derived from the model structure and are free from tuning parameters. Thus, they can be seen as objective priors for variable selection. The stochastic search is based on a Metropolis-Hastings algorithm with a stationary distribution proportional to the model posterior probabilities. The procedure is illustrated on both simulated and real examples.

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism , environmental noise, serial correlation and dependence on time varying factors. This paper... more

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism , environmental noise, serial correlation and dependence on time varying factors. This paper addresses these issues via suitable Bayesian modelling. In doing so we utilise a general class of stochastic regression models appropriate for spatio-temporal count data with an excess number of zeros. The developed regression framework does incorporate serial correlation and time varying covariates through an Ornstein Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and variations of mixtures of g-priors. The effect of different distance kernels for the epidemic model component is investigated. We proceed by developing branching process-based methods for testing scenarios for disease control, thus linking traditional epidemiological models with stochastic epidemic processes, useful in policy-focused decision making. The approach is illustrated with an application to a sheep pox dataset from the Evros region, Greece.

In this study, Bayesian approaches, such as Zellner, Occam's Window and Gibbs sampling, have been compared in terms of selecting the correct subset for the variable selection in a linear regression model. The aim of this comparison is... more

In this study, Bayesian approaches, such as Zellner, Occam's Window and Gibbs sampling, have been compared in terms of selecting the correct subset for the variable selection in a linear regression model. The aim of this comparison is to analyze Bayesian variable selection and the behavior of classical criteria by taking into consideration the different values of beta\betabeta and sigma\sigmasigma and prior expected levels.

In this study, Gibbs sampling has been applied to the variable selection in the linear regression model with outlier values. Gibbs sampling has been compared with classical variable selection criteria by using dummy data with different β... more

In this study, Gibbs sampling has been applied to the variable selection in the linear regression model with outlier values. Gibbs sampling has been compared with classical variable selection criteria by using dummy data with different β and priors.

Speci cation of the linear predictor for a generalised linear model requires determining which variables to include. We consider Bayesian strategies for performing this variable selection. In particular we focus on approaches based on the... more

Speci cation of the linear predictor for a generalised linear model requires determining which variables to include. We consider Bayesian strategies for performing this variable selection. In particular we focus on approaches based on the Gibbs sampler. Such approaches may be implemented using the publically available software BUGS. We illustrate the methods using a simple example. BUGS code is provided in an appendix.

The authors consider the problem of Bayesian variable selection for proportional hazards regression models with right censored data. They propose a semi-parametric approach in which a nonparametric prior is specified for the baseline... more

The authors consider the problem of Bayesian variable selection for proportional hazards regression models with right censored data. They propose a semi-parametric approach in which a nonparametric prior is specified for the baseline hazard rate and a fully parametric prior is specified for the regression coefficients. For the baseline hazard, they use a discrete gamma process prior, and for the regression coefficients and the model space, they propose a semi-automatic parametric informative prior specification that focuses on the observables rather than the parameters. To implement the methodology, they propose a Markov chain Monte Carlo method to compute the posterior model probabilities. Examples using simulated and real data are given to demonstrate the methodology. RÉSUMÉ Les auteurs abordent d'un point de vue bayésien le problème de la sélection de variables dans les modèles de régression des risques proportionnels en présence de censureà droite. Ils proposent une approche semi-paramétrique dans laquelle la loi a priori du taux de base est non paramétrique, mais celle des coefficients de régression est complètement paramétrique. L'information concernant le taux de base est représentée par la loi a priori issue d'un processus gamma discret ; quantà la loi a priori des paramètres du modèle de régression, elle est choisie dans une classe de lois paramétriques au moyen d'une procédure semi-automatique centrée sur les données plutôt que sur les paramètres. La miseà jour de l'information se fait au moyen d'un algorithme de Monte-Carloà chaîne de Markov. Des données réelles et simulées permettent d'illustrer la méthode.

This article proposes a stochastic version of the matching pursuit algorithm for Bayesian variable selection in linear regression. In the Bayesian formulation, the prior distribution of each regression coefficient is assumed to be a... more

This article proposes a stochastic version of the matching pursuit algorithm for Bayesian variable selection in linear regression. In the Bayesian formulation, the prior distribution of each regression coefficient is assumed to be a mixture of a point mass at 0 and a normal distribution with zero mean and a large variance. The proposed stochastic matching pursuit algorithm is designed for sampling from the posterior distribution of the coefficients for the purpose of variable selection. The proposed algorithm can be considered a modification of the componentwise Gibbs sampler. In the componentwise Gibbs sampler, the variables are visited by a random or a systematic scan. In the stochastic matching pursuit algorithm, the variables that better align with the current residual vector are given higher probabilities of being visited. The proposed algorithm combines the efficiency of the matching pursuit algorithm and the Bayesian formulation with well defined prior distributions on coefficients. Several simulated examples of small n and large p are used to illustrate the algorithm. These examples show that the algorithm is efficient for screening and selecting variables.