Results 11  20
of
42
MCMC Methods for Computing Bayes Factors: A Comparative Review
 Journal of the American Statistical Association
, 2000
"... this paper we review several of these methods, and subsequently compare them in the context of two examples, the first a simple regression example, and the second a much more challenging hierarchical longitudinal model of the kind often encountered in biostatistical practice. We find that the joint ..."
Abstract

Cited by 30 (1 self)
 Add to MetaCart
this paper we review several of these methods, and subsequently compare them in the context of two examples, the first a simple regression example, and the second a much more challenging hierarchical longitudinal model of the kind often encountered in biostatistical practice. We find that the joint modelparameter space search methods perform adequately but can be difficult to program and tune, while the marginal likelihood methods are often less troublesome and require less in the way of additional coding. Our results suggest that the latter methods may be most appropriate for practitioners working in many standard model choice settings, while the former remain important for comparing large numbers of models, or models whose parameters cannot be easily updated in relatively few blocks. We caution however that all of the methods we compare require significant human and computer effort, suggesting that less formal Bayesian model choice methods may offer a more realistic alternative in many cases.
Bayesian wavelet regression on curves with application to a spectroscopic calibration problem
 Journal of the American Statistical Association
, 2001
"... Motivated by calibration problems in nearinfrared (N IR) spectroscopy, we consider the linear regression setting in which the many predictor variables arise from sampling an essentially continuous curve at equally spaced points and there may be multiple predictands. We tackle this regression proble ..."
Abstract

Cited by 27 (4 self)
 Add to MetaCart
Motivated by calibration problems in nearinfrared (N IR) spectroscopy, we consider the linear regression setting in which the many predictor variables arise from sampling an essentially continuous curve at equally spaced points and there may be multiple predictands. We tackle this regression problem by calculating the wavelet transforms of the discretized curves, then applying a Bayesian variable selection method using mixture priors to the multivariate regression of predictands on wavelet coef � cients. For prediction purposes, we average over a set of likely models. Applied to a particular problem in N IR spectroscopy, this approach was able to � nd subsets of the wavelet coef � cients with overall better predictive performance than the more usual approaches. In the application, the available predictors are measurements of the N IR re � ectance spectrum of biscuit dough pieces at 256 equally spaced wavelengths. The aim is to predict the composition (i.e., the fat, � our, sugar, and water content) of the dough pieces using the spectral variables. Thus we have a multivariate regression of four predictands on 256 predictors with quite high intercorrelation among the predictors. A training set of 39 samples is available to � t this regression. Applying a wavelet transform replaces the 256 measurements on each spectrum with 256 wavelet coef � cients that carry the same information. The variable selection method could use subsets of these coef � cients that gave good predictions for all four compositional variables on a separate test set of samples. Selecting in the wavelet domain rather than from the original spectral variables is appealing in this application, because a single wavelet coef � cient can carry information from a band of wavelengths in the original spectrum. This band can be narrow or wide, depending on the scale of the wavelet selected.
A method for simultaneous variable selection and outlier identification in linear regression
 COMPUTATIONAL STATISTICS & DATA ANALYSIS
, 1996
"... ..."
An empirical comparison of methods for forecasting using many predictors
, 2005
"... research assistance, and the referees for helpful suggestions. An earlier version of the theoretical results in this paper was circulated earlier under the title “An Empirical ..."
Abstract

Cited by 24 (0 self)
 Add to MetaCart
research assistance, and the referees for helpful suggestions. An earlier version of the theoretical results in this paper was circulated earlier under the title “An Empirical
Objective Bayesian variable selection
 Journal of the American Statistical Association 2006
, 2002
"... 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 ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
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 MetropolisHastings algorithm with a stationary distribution proportional to the model posterior probabilities. The procedure is illustrated on both simulated and real examples.
WaveletBased Nonparametric Bayes Methods
, 1998
"... In this chapter, we will provide an overview of the current status of research involving Bayesian inference in wavelet nonparametric problems. In many statistical applications, there is a need for procedures to (i) adapt to data and (ii) use prior information. The interface of wavelets and the Bayes ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
In this chapter, we will provide an overview of the current status of research involving Bayesian inference in wavelet nonparametric problems. In many statistical applications, there is a need for procedures to (i) adapt to data and (ii) use prior information. The interface of wavelets and the Bayesian paradigm provide a natural terrain for both of these goals.
Bayesian Adaptive Sampling for Variable Selection and Model Averaging
"... For the problem of model choice in linear regression, we introduce a Bayesian adaptive sampling algorithm (BAS), that samples models without replacement from the space of models. For problems that permit enumeration of all models BAS is guaranteed to enumerate the model space in 2 p iterations where ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
For the problem of model choice in linear regression, we introduce a Bayesian adaptive sampling algorithm (BAS), that samples models without replacement from the space of models. For problems that permit enumeration of all models BAS is guaranteed to enumerate the model space in 2 p iterations where p is the number of potential variables under consideration. For larger problems where sampling is required, we provide conditions under which BAS provides perfect samples without replacement. When the sampling probabilities in the algorithm are the marginal variable inclusion probabilities, BAS may be viewed as sampling models “near ” the median probability model of Barbieri and Berger. As marginal inclusion probabilities are not known in advance we discuss several strategies to estimate adaptively the marginal inclusion probabilities within BAS. We illustrate the performance of the algorithm using simulated and real data and show that BAS can outperform Markov chain Monte Carlo methods. The algorithm is implemented in the R package BAS available at CRAN.
Gibbs Variable Selection using BUGS
 Artificial Intelligence
, 1999
"... In this paper we discuss and present in detail the implementation of Gibbs variable selection as defined by Dellaportas et al. (2000, 2002) using the BUGS software (Spiegelhalter et al., 1996a,b,c). The specification of the likelihood, prior and pseudoprior distributions of the parameters as well a ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
In this paper we discuss and present in detail the implementation of Gibbs variable selection as defined by Dellaportas et al. (2000, 2002) using the BUGS software (Spiegelhalter et al., 1996a,b,c). The specification of the likelihood, prior and pseudoprior distributions of the parameters as well as the prior term and model probabilities are described in detail. Guidance is also provided for the calculation of the posterior probabilities within BUGS environment when the number of models is limited. We illustrate the application of this methodology in a variety of problems including linear regression, loglinear and binomial response models.