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23
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 820 (19 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple changepoint analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.
Semiparametric Bayesian Analysis Of Survival Data
 Journal of the American Statistical Association
, 1996
"... this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics. ..."
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Cited by 23 (0 self)
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this paper are motivated and aimed at analyzing some common types of survival data from different medical studies. We will center our attention to the following topics.
A tutorial on Reversible Jump MCMC with a view toward applications in QTLmapping
 ON QTL MAPPING. INTERNATIONAL STATISTICAL REVIEW
, 2006
"... A tutorial derivation of the reversible jump Markov chain Monte Carlo (MCMC) algorithm is given. Various examples illustrate how reversible jump MCMC is a general framework for MetropolisHastings algorithms where the proposal and the target distribution may have densities on spaces of varying dimen ..."
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Cited by 21 (1 self)
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A tutorial derivation of the reversible jump Markov chain Monte Carlo (MCMC) algorithm is given. Various examples illustrate how reversible jump MCMC is a general framework for MetropolisHastings algorithms where the proposal and the target distribution may have densities on spaces of varying dimension. It is nally discussed how reversible jump MCMC can be applied in genetics to compute the posterior distribution of the number, locations, eects, and genotypes of putative quantitative trait loci.
Computational Methods for Multiplicative Intensity Models using Weighted Gamma . . .
 PROCESSES: PROPORTIONAL HAZARDS, MARKED POINT PROCESSES AND PANEL COUNT DATA
, 2004
"... We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share ..."
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Cited by 16 (4 self)
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We develop computational procedures for a class of Bayesian nonparametric and semiparametric multiplicative intensity models incorporating kernel mixtures of spatial weighted gamma measures. A key feature of our approach is that explicit expressions for posterior distributions of these models share many common structural features with the posterior distributions of Bayesian hierarchical models using the Dirichlet process. Using this fact, along with an approximation for the weighted gamma process, we show that with some care, one can adapt efficient algorithms used for the Dirichlet process to this setting. We discuss blocked Gibbs sampling procedures and Pólya urn Gibbs samplers. We illustrate our methods with applications to proportional hazard models, Poisson spatial regression models, recurrent events, and panel count data.
Bayesian smoothing in the estimation of the pair potential function of Gibbs point processes
, 1999
"... This paper introduces a method which can be viewed as the first step towards a truly nonparametric Bayesian estimation of Gibbs processes with pairwise interactions. The pair potential is approximated by a step function having a large number of fixed jump points. The induced high dimension of the pa ..."
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Cited by 14 (4 self)
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This paper introduces a method which can be viewed as the first step towards a truly nonparametric Bayesian estimation of Gibbs processes with pairwise interactions. The pair potential is approximated by a step function having a large number of fixed jump points. The induced high dimension of the parameter space causes two kinds of problems. First, each component of the sufficient statistic is typically a function of a small number of point locations, which causes instability in the estimation. Secondly, the computational complexity increases rapidly with the dimension. To combat the first problem we apply Bayesian smoothing by choosing a Markov chain prior which penalises large differences between nearby values of the pair potential function. This idea originates in Bayesian image analysis; see Besag (1986). As regards the computational complexity, we have found the full posterior analysis to be too demanding with the currently available machinery. Consequently, we have concentrated on the task of locating the posterior mode, which is computationally equivalent to that of ønding the maximum likelihood estimate (MLE). Starting from the Monte Carlo NewtonRaphson algorithm of Penttinen (1984) and the Monte Carlo likelihood approach of Geyer and Thompson (1992), we arrived at an efficient algorithm by modifying the former into an MCMC approximation of the Marquardt algorithm (Marquardt 1963) and then combining the two: The first approximation to the posterior mode is obtained using the Monte Carlo Marquardt algorithm, where the first two differentials of the logposterior are approximated by MCMC as in Penttinen (1984), and the final estimate is calculated using the Monte Carlo likelihood approximation. (The naming conventions applied here were introduced by Geyer 1998). Our appr...
Likelihood and nonparametric Bayesian MCMC inference for spatial point processes based on perfect simulation and path sampling
 Scand. J. Statist
, 2003
"... We consider the combination of path sampling and perfect simulation in the context of both likelihood inference and nonparametric Bayesian inference for pairwise interaction point processes. Several empirical results based on simulations and analysis of a dataset are presented, and the merits of us ..."
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Cited by 12 (4 self)
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We consider the combination of path sampling and perfect simulation in the context of both likelihood inference and nonparametric Bayesian inference for pairwise interaction point processes. Several empirical results based on simulations and analysis of a dataset are presented, and the merits of using perfect simulation are discussed.
Curve and Surface Estimation using Dynamic Step Functions
 Practical Nonparametric and Semiparametric Bayesian Statistics, no. 133 in Lecture Notes in Statistics, chap. 14
, 1998
"... This chapter describes a nonparametric Bayesian approach to the estimation of curves and surfaces that act as parameters in statistical models. The approach is based on mixing variable dimensional piecewise constant approximations, whose `smoothness' is regulated by a Markov random field prior. Rand ..."
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Cited by 11 (7 self)
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This chapter describes a nonparametric Bayesian approach to the estimation of curves and surfaces that act as parameters in statistical models. The approach is based on mixing variable dimensional piecewise constant approximations, whose `smoothness' is regulated by a Markov random field prior. Random partitions of the domain are defined by Voronoi tessellations of random generating point patterns. Variable dimension Markov chain Monte Carlo methods are proposed for the numerical estimation, and a detailed algorithm is specified for one special case. General applicability of the approach is discussed in the context of density estimation, regression and interpolation problems, and an application to the intensity estimation for a spatial Poisson point process is presented.
Dynamic and Semiparametric Models
 Smoothing and Regression: Approaches, Computation and Application
, 1999
"... Introduction This chapter surveys dynamic or state space models and their relationship to non and semiparametric models that are based on the roughness penalty approach. We focus on recent advances in dynamic modelling of nonGaussian, in particular discretevalued, time series and longitudinal ..."
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Cited by 11 (5 self)
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Introduction This chapter surveys dynamic or state space models and their relationship to non and semiparametric models that are based on the roughness penalty approach. We focus on recent advances in dynamic modelling of nonGaussian, in particular discretevalued, time series and longitudinal data, make the close correspondence to semiparametric smoothing methods evident, and show how ideas from dynamic models can be adopted for Bayesian semiparametric inference in generalized additive and varying coefficient models. Basic tools for corresponding inference techniques are penalized likelihood estimation, Kalman filtering and smoothing and Markov chain Monte Carlo (MCMC) simulation. Similarities, relative merits, advantages and disadvantages of these methods are illustrated through several applications. Section 2 gives a short introductory review of results for the classical situation of Gaussian time series observations. We start with Whittaker's (1923) "method of graduati
Bayesian semiparametric dynamic frailty models for multiple event time data
 Biometrics
, 2006
"... Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for withinsubject dependency in the multiple event times. Motivated ..."
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Cited by 9 (6 self)
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Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for withinsubject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dynamic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subjectspecific frailties to change dynamically with age while also accommodating nonproportional hazards. Parametric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semiparametric model on a conditionallyconjugate dynamic gamma model, we facilitate posterior computation and lack of fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study.
Models beyond the Dirichlet process
 Bayesian Nonparametrics in Practice, CUP
, 2009
"... www.carloalberto.org/working_papers © 2009 by Antonio Lijoi and Igor Prünster. Any opinions expressed here are those of the authors and not those of the Collegio Carlo Alberto. Models beyond the Dirichlet process ..."
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Cited by 3 (1 self)
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www.carloalberto.org/working_papers © 2009 by Antonio Lijoi and Igor Prünster. Any opinions expressed here are those of the authors and not those of the Collegio Carlo Alberto. Models beyond the Dirichlet process