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Hierarchical Priors and Mixture Models, With Application in Regression and Density Estimation
, 1993
"... ..."
Sequential Importance Sampling for Nonparametric Bayes Models: The Next Generation
 Journal of Statistics
, 1998
"... this paper, we exploit the similarities between the Gibbs sampler and the SIS, bringing over the improvements for Gibbs sampling algorithms to the SIS setting for nonparametric Bayes problems. These improvements result in an improved sampler and help satisfy questions of Diaconis (1995) pertaining t ..."
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Cited by 67 (5 self)
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this paper, we exploit the similarities between the Gibbs sampler and the SIS, bringing over the improvements for Gibbs sampling algorithms to the SIS setting for nonparametric Bayes problems. These improvements result in an improved sampler and help satisfy questions of Diaconis (1995) pertaining to convergence. Such an effort can see wide applications in many other problems related to dynamic systems where the SIS is useful (Berzuini et al. 1996; Liu and Chen 1996). Section 2 describes the specific model that we consider. For illustration we focus discussion on the betabinomial model, although the methods are applicable to other conjugate families. In Section 3, we describe the first generation of the SIS and Gibbs sampler in this context, and present the necessary conditional distributions upon which the techniques rely. Section 4 describes the alterations that create the second generation techniques, and provides specific algorithms for the model we consider. Section 5 presents a comparison of the techniques on a large set of data. Section 6 provides theory that ensures the proposed methods work and that is generally applicable to many other problems using importance sampling approaches. The final section presents discussion. 2 The Model
Bayesian Variable Selection for Proportional Hazards Models
, 1996
"... The authors consider the problem of Bayesian variable selection for proportional hazards regression models with right censored data. They propose a semiparametric approach in which a nonparametric prior is specified for the baseline hazard rate and a fully parametric prior is specified for the regr ..."
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Cited by 15 (1 self)
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The authors consider the problem of Bayesian variable selection for proportional hazards regression models with right censored data. They propose a semiparametric approach in which a nonparametric prior is specified for the baseline hazard rate and a fully parametric prior is specified for the regression coe#cients. For the baseline hazard, they use a discrete gamma process prior, and for the regression coe#cients and the model space, they propose a semiautomatic 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. R ESUM E Les auteurs abordent d'un point de vue bayesien le problemedelaselection de variables dans les modeles de regression des risques proportionnels en presence de censure a droite. Ils proposent une approche semip...
Markov Chain Monte Carlo Methods in Biostatistics
 Statistical Methods in Medical Research 5:339355
, 1996
"... this article, we review some important general methods for Markov chain Monte Carlo ..."
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Cited by 7 (0 self)
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this article, we review some important general methods for Markov chain Monte Carlo
Prediction and Decision Making Using Bayesian Hierarchical Models Statistics in Medicine
, 1995
"... This paper uses Bayesian hierarchical models to analyze multicenter clinical trial data where the outcome variable of interest is continuous, but not normally distributed, and where censoring has occurred. The goal of such an analysis is the same as for any subgroup analysis, to provide survival es ..."
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Cited by 5 (0 self)
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This paper uses Bayesian hierarchical models to analyze multicenter clinical trial data where the outcome variable of interest is continuous, but not normally distributed, and where censoring has occurred. The goal of such an analysis is the same as for any subgroup analysis, to provide survival estimates for specific subgroups as well as for the population and to provide estimates of the degree of heterogeneity between subgroups. An analysis of the Collaborative Study of LongTerm Maintenance Drug Therapy in Recurrent Affective Illness, a multicenter clinical trial funded by the National Institute for Mental Health's Pharmacologic Research Branch, serves to illustrate the proposed methodology. A feature of this data set is that one treatment group was withdrawn from medication at the time of randomization. The paper contains comparison of models, one that accounts for the drug washout period through the use of a changepoint model as well as a comparison of results across several choi...
Discovery Sampling And Selection Models
 In Decision Theory and Related Topics
, 1994
"... Various aspects of Bayesian inference in selection and size biased sampling problems are presented, beginning with discussion of general problems of inference in infinite and finite populations subject to selection sampling. Estimation of the size of finite populations and inference about superpopul ..."
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Cited by 5 (2 self)
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Various aspects of Bayesian inference in selection and size biased sampling problems are presented, beginning with discussion of general problems of inference in infinite and finite populations subject to selection sampling. Estimation of the size of finite populations and inference about superpopulation distributions when sampling is apparently informative is then developed in two specific problems. The first is a simple example of truncated data analysis, and some details of simulation based Bayesian analysis are presented. The second concerns discovery sampling in which units of a finite population are selected with probabilities proportional to some measure of size. A wellknown area of application is in the discovery of oil reserves, and some recently published data from this area is analysed here. Solutions to the computational problems arising are developed using iterative simulation methods. Finally, some comments are made on extensions, including multiparameter superpopulation...
A MixtureModel Approach to the Analysis of Survival Data
"... this paper, we study a mixture model for survival data where covariates may influence both the incidence probabilities and their conditional latency distributions. The data may include the exactly observed, the rightcensored, and the intervalcensored failure times. We apply the EM algorithm to fin ..."
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Cited by 2 (0 self)
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this paper, we study a mixture model for survival data where covariates may influence both the incidence probabilities and their conditional latency distributions. The data may include the exactly observed, the rightcensored, and the intervalcensored failure times. We apply the EM algorithm to find the maximum likelihood estimate. We also carry out a Markov chain Monte Carlo algorithm for Bayesian inference. Model selection methods based on the predictive density for crossvalidated data are developed. These methods allow us to assess whether simpler models would suffice as opposed to the mixture models. The potential of the methods is illustrated with flour beetle (Tribolium castaneum) data given by Hewlett (1974).
Monte Carlo Methods for Bayesian Analysis of Survival Data Using Mixtures of Dirichlet Process Priors
, 1998
"... Consider the model in which the data consist of possibly censored lifetimes, and one puts a mixture of Dirichlet process priors on the common survival distribution. The exact computation of the posterior distribution of the survival function is in general impossible to obtain. This paper develops ..."
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Consider the model in which the data consist of possibly censored lifetimes, and one puts a mixture of Dirichlet process priors on the common survival distribution. The exact computation of the posterior distribution of the survival function is in general impossible to obtain. This paper develops and compares the performance of several simulation techniques, based on Markov chain Monte Carlo and sequential importance sampling, for approximating this posterior distribution. One scheme, whose derivation is based on sequential importance sampling, gives an exactly iid sample from the posterior for the case of right censored data. A second contribution of this paper is a battery of programs that implement the various schemes discussed in this paper. The programs and methods are illustrated on a data set of intervalcensored times arising from two treatments for breast cancer.
Inference in Successive Sampling Discovery Models
, 1996
"... A variety of practical problems of finite population inference can be addressed in the framework of successive sampling discovery models  population units are assumed drawn from a superpopulation distribution and then successively sampled according to a specified `sizebiased' selection mechanism. ..."
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Cited by 1 (1 self)
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A variety of practical problems of finite population inference can be addressed in the framework of successive sampling discovery models  population units are assumed drawn from a superpopulation distribution and then successively sampled according to a specified `sizebiased' selection mechanism. Formal statistical analysis of discovery data under such models is technically challenging, as exemplified by the likelihood analyses of Nair and Wang (1989). Assessment of uncertainties about superpopulation parameters and, more critically, appropriate forms of predictive inference for the unsampled units in the finite population, are open issues that are addressed here from a Bayesian perspective. Motivated by the likelihood analysis of Nair and Wang (1989), we develop a formal Bayesian approach to analysis in the same class of models; we show how simulation methods provide for the computation of required posterior and predictive distributions of relevance. We further develop model extens...
On Bayesian Statistics in Astronomical Investigation  Source Detection with Low Particle Counts
, 1991
"... This paper is largely concerned with cameo examples designed to communicate this precept to astronomers interested and involved in statistical work in their investigations. I like the paper, and have a great deal of respect for the entrepreneurial efforts of the author and his coauthors to shift th ..."
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This paper is largely concerned with cameo examples designed to communicate this precept to astronomers interested and involved in statistical work in their investigations. I like the paper, and have a great deal of respect for the entrepreneurial efforts of the author and his coauthors to shift the focus of statistical analysis in the field toward the Bayesian paradigm. That these efforts have been rewarded is clear from browsing some of the referenced articles, notably the works of Loredo and Lamb (referenced in text). Here we find advanced physical and statistical models subjected to formal and rigorous Bayesian analysis, some requiring high dimensional numerical integrations performed via Monte Carlo, that yield inferences in terms of posterior distributions for parameters of interest that clearly and unambiguously address detailed and substantive scientific issues. A reading of these works provides a clear picture of investigators led to adherence to the Bayesian paradigm on pragmatic and empirical grounds  the Bayesian approach gets the (right) job done where all others fail. The current paper, by comparison, focuses on elementary examples to clearly identify difficulties and inconsistencies, both conceptual and technical, inherent in traditional inferential paradigms, and zealously argues for the Bayesian approach as the preferred alternative. I agree with much of what Loredo has written here. The Scientific Organising Committee exhorted invited discussants to