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33
Estimating the integrated likelihood via posterior simulation using the harmonic mean identity
 Bayesian Statistics
, 2007
"... The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison a ..."
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Cited by 49 (2 self)
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The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison and Bayesian testing is a ratio of integrated likelihoods, and the model weights in Bayesian model averaging are proportional to the integrated likelihoods. We consider the estimation of the integrated likelihood from posterior simulation output, aiming at a generic method that uses only the likelihoods from the posterior simulation iterations. The key is the harmonic mean identity, which says that the reciprocal of the integrated likelihood is equal to the posterior harmonic mean of the likelihood. The simplest estimator based on the identity is thus the harmonic mean of the likelihoods. While this is an unbiased and simulationconsistent estimator, its reciprocal can have infinite variance and so it is unstable in general. We describe two methods for stabilizing the harmonic mean estimator. In the first one, the parameter space is reduced in such a way that the modified estimator involves a harmonic mean of heaviertailed densities, thus resulting in a finite variance estimator. The resulting
Nonparametric Bayesian models through probit stickbreaking processes
"... Summary. We describe a novel class of Bayesian nonparametric priors based on stickbreaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of ..."
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Cited by 23 (6 self)
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Summary. We describe a novel class of Bayesian nonparametric priors based on stickbreaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of models while preserving computational simplicity. Particular emphasis is placed on the construction of rich temporal and spatial processes, which are applied to two problems in finance and ecology.
Bayesian Multivariate Logistic Regression
 Biometrics
, 2004
"... This article proposes a new multivariate logistic density, derived by transforming variables that follow a multivariate t distribution. The resulting logistic density is closely approximated by a multivariate t distribution, has an unrestricted correlation structure, and has properties that facilita ..."
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Cited by 20 (2 self)
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This article proposes a new multivariate logistic density, derived by transforming variables that follow a multivariate t distribution. The resulting logistic density is closely approximated by a multivariate t distribution, has an unrestricted correlation structure, and has properties that facilitate efficient computation
Posterior consistency in conditional distribution estimation
"... Abstract: A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as weak and strong posterior consistency. Estimation of an uncountable collect ..."
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Cited by 12 (4 self)
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Abstract: A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as weak and strong posterior consistency. Estimation of an uncountable collection of conditional distributions across different regions of the predictor space is a challenging problem, which differs in some important ways from density and mean regression estimation problems. We first introduce new notions of weak and strong neighborhoods that are applicable to conditional distributions. Focusing on a broad class of priors formulated as predictordependent mixtures of Gaussian kernels, we provide sufficient conditions under which weak and strong posterior consistency hold. This theory is illustrated by showing that the conditions are satisfied for a class of generalized stickbreaking process mixtures in which the stickbreaking lengths are constructed through mapping continuous stochastic processes to the unit interval using a monotone differentiable link function. Probit stickbreaking processes provide a computationally convenient special case. We also provide a set of sufficient conditions to ensure strong and weak posterior consistency using fixedπ dependent Dirichlet process mixtures of
Penalized regression with ordinal predictors
, 2008
"... Ordered categorial predictors are a common case in regression modeling. In contrast to the case of ordinal response variables, ordinal predictors have been largely neglected in the literature. In this article penalized regression techniques are proposed. Based on dummy coding two types of penalizati ..."
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Cited by 8 (4 self)
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Ordered categorial predictors are a common case in regression modeling. In contrast to the case of ordinal response variables, ordinal predictors have been largely neglected in the literature. In this article penalized regression techniques are proposed. Based on dummy coding two types of penalization are explicitly developed; the first imposes a difference penalty, the second is a ridge type refitting procedure. A Bayesian motivation as well as alternative ways of derivation are provided. Simulation studies and real world data serve for illustration and to compare the approach to methods often seen in practice, namely linear regression on the group labels and pure dummy coding. The proposed regression techniques turn out to be highly competitive. On the basis of GLMs the concept is generalized to the case of nonnormal outcomes by performing penalized likelihood estimation.
Additive cubic spline regression with Dirichlet process mixture errors
 Journal of Econometrics
, 2010
"... The goal of this paper is to develop a flexible Bayesian analysis of regression models for continuous and categorical outcomes. In the models we study, covariate (or regression) effects are modeled additively by cubic splines, and the error distribution (that of the latent outcomes in the case of ca ..."
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Cited by 7 (1 self)
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The goal of this paper is to develop a flexible Bayesian analysis of regression models for continuous and categorical outcomes. In the models we study, covariate (or regression) effects are modeled additively by cubic splines, and the error distribution (that of the latent outcomes in the case of categorical data) is modeled as a Dirichlet process mixture. We employ a relatively unexplored but attractive basis in which the spline coefficients are the unknown function ordinates at the knots. We exploit this feature to develop a proper prior distribution on the coefficients that involves the first and second differences of the ordinates, quantities about which one may have prior knowledge. We also discuss the problem of comparing models with different numbers of knots or different error distributions through marginal likelihoods and Bayes factors which are computed within the framework of Chib (1995) as extended to DPM models by Basu and Chib (2003). The techniques are illustrated with simulated and real data.
Disease mapping of stagespecific cancer incidence data
 Biometrics
, 2002
"... SUMMARY. We propose two approaches for the spatial analysis of cancer incidence data with additional information on the stage of the disease at time of diagnosis. The two formulations are extensions of commonly used models for multicategorical response data on an ordinal scale. We include spatial an ..."
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Cited by 7 (0 self)
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SUMMARY. We propose two approaches for the spatial analysis of cancer incidence data with additional information on the stage of the disease at time of diagnosis. The two formulations are extensions of commonly used models for multicategorical response data on an ordinal scale. We include spatial and agegroup effects in both formulations, which we estimate in a nonparametric smooth way. More specifically, we adopt a fully Bayesian approach based on Gaussian pairwise difference priors where additional smoothing parameters are treated as unknown as well. We argue that the methods are useful in monitoring the effectiveness of mass cancer screening and illustrate this through an application to data on cervical cancer in the former German Democratic Republic. The results suggest that there are large spatial differences in the stage proportions, which indicate spatial variability with respect to the introduction and effectiveness of Pap smear screening programs.
Exploring the Mind: Integrating Questionnaires and fMRI
"... A new model is developed for joint analysis of ordered, categorical, real and count data. The ordered and categorical data are answers to questionnaires, the (word) count data correspond to the text questions from the questionnaires, and the real data correspond to fMRI responses for each subject. T ..."
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Cited by 3 (1 self)
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A new model is developed for joint analysis of ordered, categorical, real and count data. The ordered and categorical data are answers to questionnaires, the (word) count data correspond to the text questions from the questionnaires, and the real data correspond to fMRI responses for each subject. The Bayesian model employs the von Mises distribution in a novel manner to infer sparse graphical models jointly across people, questions, fMRI stimuli and brain region, with this integrated within a new matrix factorization based on latent binary features. The model is compared with simpler alternatives on two real datasets. We also demonstrate the ability to predict the response of the brain to visual stimuli (as measured by fMRI), based on knowledge of how the associated person answered classical questionnaires. 1.
Sequential decision approach to ordinal preferences in recommender systems
 In Proc. of the 26th AAAI Conference
, 2012
"... We propose a novel sequential decision approach to modeling ordinal ratings in collaborative filtering problems. The rating process is assumed to start from the lowest level, evaluates against the latent utility at the corresponding level and moves up until a suitable ordinal level is found. Cruci ..."
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Cited by 2 (2 self)
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We propose a novel sequential decision approach to modeling ordinal ratings in collaborative filtering problems. The rating process is assumed to start from the lowest level, evaluates against the latent utility at the corresponding level and moves up until a suitable ordinal level is found. Crucial to this generative process is the underlying utility random variables that govern the generation of ratings and their modelling choices. To this end, we make a novel use of the generalised extreme value distributions, which is found to be particularly suitable for our modeling tasks and at the same time, facilitate our inference and learning procedure. The proposed approach is flexible to incorporate features from both the user and the item. We evaluate the proposed framework on three wellknown datasets: MovieLens, Dating Agency and Netflix. In all cases, it is demonstrated that the proposed work is competitive against stateoftheart collaborative filtering methods.
Econometric Analysis of the Sequential Probit Model: Application to Innovation Surveys
, 2002
"... Abstract. We analyze a two stage sequential probit model that can be used to analyze survey in which questions are asked sequentially and unobservable variables of each stage can be correlated. We apply the model to innovation surveys. In the first stage, the survey asks if firms have developed a pr ..."
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Abstract. We analyze a two stage sequential probit model that can be used to analyze survey in which questions are asked sequentially and unobservable variables of each stage can be correlated. We apply the model to innovation surveys. In the first stage, the survey asks if firms have developed a product or a process innovation. In the second stage, the survey inquires about the degree of novelty o the innovation. We estimate parameters of this model in a classical framework in which multiple integrals that arise in the likelihood function are estimated by simulation and in a Bayesian framework in which we use the latent variable structure of the model to implement a Metropolis Gibbs sampler. We determine the role of information sources on the innovation process and show that they significantly influence the nature of the innovation process.