Results 1  10
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22
A Bayesian semiparametric model for random effects metaanalysis
 Journal of the American Statistical Association
"... In metaanalysis there is an increasing trend to explicitly acknowledge the presence of study variability through random effects models. That is, one assumes that for each study, there is a studyspecific effect and one is observing an estimate of this latent variable. In a random effects model, one ..."
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Cited by 17 (1 self)
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In metaanalysis there is an increasing trend to explicitly acknowledge the presence of study variability through random effects models. That is, one assumes that for each study, there is a studyspecific effect and one is observing an estimate of this latent variable. In a random effects model, one assumes that these studyspecific effects come from some distribution, and one can estimate the parameters of this distribution, as well as the studyspecific effects themselves. This distribution is most often modelled through a parametric family, usually a family of normal distributions. The advantage of using a normal distribution is that the mean parameter plays an important role, and much of the focus is on determining whether or not this mean is 0. For example, it may be easier to justify funding further studies if it is determined that this mean is not 0. Typically, this normality assumption is made for the sake of convenience, rather than from some theoretical justification, and may not actually hold. We present a Bayesian model in which the distribution of the studyspecific effects is modelled through a certain class of nonparametric priors. These priors can be designed to concentrate most of their mass around the family of normal
A Bayesian Approach to Robust Binary Nonparametric Regression
, 1997
"... This paper presents a Bayesian approach to binary nonparametric regression which assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The paper makes the following contributions. First, a comprehensive approach is presented ..."
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Cited by 14 (1 self)
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This paper presents a Bayesian approach to binary nonparametric regression which assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The paper makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out, and the estimates made robust to outliers. Second, the approach can handle a wide rage of link functions. Third, efficient state space based algorithms are used to carry out the computations. Fourth, an extensive set of simulations is carried out which show that the Bayesian estimator works well and compares favorably to two estimators which are widely used in practice.
Bayesian Semiparametric Inference for the Accelerated Failure Time Model
, 1997
"... Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regressio ..."
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Cited by 14 (0 self)
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Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixtureofDirichletprocesses prior on the unknown error distribution. A Markov chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data. Key words and phrases: Censored data; Log linear model; Markov chain Monte Carlo algorithm; Metropolis algori...
Likelihood based inference for monotone response models
 Annals of Statistics
, 2007
"... The behavior of maximum likelihood estimates (MLE’s) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the usual parametric or semiparametric situations in that the ..."
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Cited by 11 (6 self)
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The behavior of maximum likelihood estimates (MLE’s) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the usual parametric or semiparametric situations in that the MLE of the monotone function at a point converges to the truth at rate n 1/3 (slower than the usual √ n rate) with a nonGaussian limit distribution. A framework for likelihood based estimation of monotone functions is developed and limit theorems describing the behavior of the MLE’s and the likelihood ratio statistic are established. In particular, the likelihood ratio statistic is found to be asymptotically pivotal with a limit distribution that is no longer χ 2 but can be explicitly characterized in terms of a functional of Brownian motion. 1
Nonparametric Bayesian Analysis for Assessing Homogeneity in k×l Contingency TABLES WITH FIXED RIGHT MARGIN TOTALS
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... In this work we postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. We assume cell count ..."
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Cited by 10 (1 self)
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In this work we postulate a nonparametric Bayesian model for data that can be accommodated in a contingency table with fixed right margin totals. This data structure usually arises when comparing different groups regarding classification probabilities for a number of categories. We assume cell count vectors for each group to be conditionally independent, and with multinomial distribution given vectors of classification probabilities. In turn, these vectors of probabilities are assumed to be a sample from a distribution F , and the prior distribution of F is assumed to be a Dirichlet process, centered on a probability measure ff and with weight c. We also assume a prior distribution for c, as a way of obtaining a better control on the clustering structure induced by the Dirichlet process. We use this setting to assess homogeneity of classification probabilities, and a "Bayes factor" is proposed. We derive exact expressions for the relevant quantities. These can be directly computed wh...
Nonparametric Bayesian modeling for multivariate ordinal data
 Journal of Computational and Graphical Statistics
, 2005
"... We propose a probability model for kdimensional ordinal outcomes, i.e., we consider inference for data recorded in kdimensional contingency tables with ordinal factors. The proposed approach is based on full posterior inference, assuming a flexible underlying prior probability model for the contin ..."
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Cited by 5 (1 self)
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We propose a probability model for kdimensional ordinal outcomes, i.e., we consider inference for data recorded in kdimensional contingency tables with ordinal factors. The proposed approach is based on full posterior inference, assuming a flexible underlying prior probability model for the contingency table cell probabilities. We use a variation of the traditional multivariate probit model, with latent scores that determine the observed data. In our model, a mixture of normals prior replaces the usual single multivariate normal model for the latent variables. By augmenting the prior model to a mixture of normals we generalize inference in two important ways. First, we allow for different polychoric correlation coefficients across the contingency table. Second, inference in ordinal multivariate probit models is plagued by problems related to the choice and resampling of cutoffs defined for these latent variables. We show how the proposed mixture model approach entirely removes these problems. We illustrate the methodology with two examples, one simulated data set and one data set of interrater agreement.
Approaches for Semiparametric Bayesian Regression
 Computational Approach for Full Nonparametric Bayesian Inference under Dirichlet Process Mixture Models," Journal of Computational and Graphical Statistics
, 1997
"... Developing regression relationships is a primary inferential activity. We consider such relationships in the context of hierarchical models incorporating linear structure at each stage. Modern statistical work encourages less presumptive, i.e., nonparametric specifications for at least a portion of ..."
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Cited by 4 (2 self)
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Developing regression relationships is a primary inferential activity. We consider such relationships in the context of hierarchical models incorporating linear structure at each stage. Modern statistical work encourages less presumptive, i.e., nonparametric specifications for at least a portion of the modeling. That is, we seek to enrich the class of standard parametric hierarchical models by wandering nonparametrically near (in some sense) the standard class but retaining the linear structure. This enterprise falls within what is referred to as semiparametric modeling. We focus here on nonparametric modeling of monotone functions associated with the model. Such monotone functions arise, for example, as the stochastic mechanism itself using the cumulative distribution function, as the link function in a generalized linear model, as the cumulative hazard function in survival analysis models, and as the calibration function in errorsinvariables models. Nonparametric approaches for mod...
Parametric Links for Binary Choice Models: A FisherianBayesian Colloquy
 Journal of Econometrics
, 2009
"... Abstract. The familiar logit and probit models provide convenient settings for many binary response applications, but a larger class of link functions may be occasionally desirable. Two parametric families of link functions are investigated: the Gosset link based on the Student t latent variable mod ..."
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Cited by 3 (0 self)
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Abstract. The familiar logit and probit models provide convenient settings for many binary response applications, but a larger class of link functions may be occasionally desirable. Two parametric families of link functions are investigated: the Gosset link based on the Student t latent variable model with the degrees of freedom parameter controlling the tail behavior, and the Pregibon link based on the (generalized) Tukey λ family with two shape parameters controlling skewness and tail behavior. Both Bayesian and maximum likelihood methods for estimation and inference are explored, compared and contrasted. In applications, like the propensity score matching problem discussed in Section 4, where it is critical to have accurate estimates of the conditional probabilities, we find that misspecification of the link function can create serious bias. Bayesian point estimation via MCMC performs quite competitively with MLE methods; however nominal coverage of Bayes credible regions is somewhat more problematic. 1.
Bayesian Analysis Of A Random Link Function In Binary Response Regression
 Journal of the American Statistical Association Management
, 1994
"... Binary response regression is a useful technique for analyzing categorical data. Popular binary models use special link functions such as the logit or the probit link. We assume that the inverse link function H is a random member of the class of normal scale mixture cdfs. We propose three different ..."
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Cited by 2 (0 self)
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Binary response regression is a useful technique for analyzing categorical data. Popular binary models use special link functions such as the logit or the probit link. We assume that the inverse link function H is a random member of the class of normal scale mixture cdfs. We propose three different models for this random H : (i) H is a finite scale mixture with a Dirichlet distribution prior on the mixing distribution; (ii) H is a general scale mixture, the mixing distribution has a Dirichlet process prior; and (iii) H is a scale mixture of truncated normal distributions with the mixing distribution having a Dirichlet prior. We describe Bayesian analyses of these models using data augmentation and Gibbs sampling. Model diagnostics by cross validation of the conditional predictive distributions are proposed. These analyses are illustrated in two examples. Our proposed models match the performances of Bayesian probit and t link models in the first example whereas they outperform probit and t link models in the second example.