Results 11  20
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430
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 23 (4 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
Semiparametric Regression During 2003–2007
, 2008
"... Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a ..."
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Cited by 17 (5 self)
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Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.
Synthesizing open worlds with constraints using locally annealed reversible jump mcmc
 ACM Transactions on Graphics (TOG
, 2012
"... Figure 1: The tablechair sets, arm chairs, plants, shelves, and floor lamps in this coffee shop were arranged using our locally annealed reversible jump MCMC sampling method. The users don’t need to specify the number of objects beforehand. We present a novel Markov chain Monte Carlo (MCMC) algorit ..."
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Cited by 15 (5 self)
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Figure 1: The tablechair sets, arm chairs, plants, shelves, and floor lamps in this coffee shop were arranged using our locally annealed reversible jump MCMC sampling method. The users don’t need to specify the number of objects beforehand. We present a novel Markov chain Monte Carlo (MCMC) algorithm that generates samples from transdimensional distributions encoding complex constraints. We use factor graphs, a type of graphical model, to encode constraints as factors. Our proposed MCMC method, called locally annealed reversible jump MCMC, exploits knowledge of how dimension changes affect the structure of the factor graph. We employ a sequence of annealed distributions during the sampling process, allowing us to explore the state space across different dimensionalities more freely. This approach is motivated by the application of layout synthesis where relationships between objects are characterized as constraints. In particular, our method addresses the challenge of synthesizing open world layouts where the number of objects are not fixed and optimal configurations for different numbers of objects may be drastically different. We demonstrate the applicability of our approach on two open world layout synthesis problems: coffee shops and golf courses.
Bayesian Inference on Order Constrained Parameters in Generalized Linear Models
 Biometrics
, 2002
"... This article proposes a general Bayesian approach for inibrence on order constrained parameters in generalized linear models. Instead of choosing a prior distribution with support on the constrained space, which can result in major computational difficulties, we propose to map draws from an unconstr ..."
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Cited by 15 (5 self)
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This article proposes a general Bayesian approach for inibrence on order constrained parameters in generalized linear models. Instead of choosing a prior distribution with support on the constrained space, which can result in major computational difficulties, we propose to map draws from an unconstrained posterior density using an isotonic regression transformation. This approach allows flat regions over which increases in the level of a predictor have no ef fect. Bayes factors for assessing ordered trends can be computed based on the output from a Gibbs sampling algorithm. Results from a simulatio' study are prese'ted and the approach is applied to data from a time to pregnancy study
Approximate Bayesian Inference for Survival Models
, 2010
"... Bayesian analysis of timetoevent data, usually called survival analysis, has received increasing attention in the last years. In Coxtype models it allows to use information from the full likelihood instead of from a partial likelihood, so that the baseline hazard function and the model parameters ..."
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Cited by 15 (2 self)
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Bayesian analysis of timetoevent data, usually called survival analysis, has received increasing attention in the last years. In Coxtype models it allows to use information from the full likelihood instead of from a partial likelihood, so that the baseline hazard function and the model parameters can be jointly estimated. In general, Bayesian methods permit a full and exact posterior inference for any parameter or predictive quantity of interest. On the other side, Bayesian inference often relies on Markov Chain Monte Carlo (MCMC) techniques which, from the user point of view, may appear slow at delivering answers. In this paper, we show how a new inferential tool named Integrated Nested Laplace approximations (INLA) can be adapted and applied to many survival models making Bayesian analysis both fast and accurate without having to rely on MCMC based inference.
Structured variational distributions in VIBES
 In Proceedings Artificial Intelligence and Statistics
, 2003
"... Variational methods are becoming increasingly popular for the approximate solution of complex probabilistic models in machine learning, computer vision, information retrieval and many other fields. Unfortunately, for every new application it is necessary first to derive the specific forms of the var ..."
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Cited by 14 (4 self)
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Variational methods are becoming increasingly popular for the approximate solution of complex probabilistic models in machine learning, computer vision, information retrieval and many other fields. Unfortunately, for every new application it is necessary first to derive the specific forms of the variational update equations for the particular probabilistic model being used, and then to implement these equations in applicationspecific software. Each of these steps is both time consuming and error prone. We have therefore recently developed a general purpose inference engine called VIBES [1] (‘Variational Inference for Bayesian Networks’) which allows a wide variety of probabilistic models to be implemented and solved variationally without recourse to coding. New models are specified as a directed acyclic graph using an interface analogous to a drawing package, and VIBES then automatically generates and solves the variational equations. The original version of VIBES assumed a fully factorized variational posterior distribution. In this paper we present an extension of VIBES in which the variational posterior distribution corresponds to a subgraph of the full probabilistic model. Such structured distributions can produce much closer approximations to the true posterior distribution. We illustrate this approach using an example based on Bayesian hidden Markov models. 1
Hierarchical Bayesian parameter estimation for cumulative prospect theory
, 2011
"... a b s t r a c t Cumulative prospect theory (CPT Tversky & Kahneman, 1992) has provided one of the most influential accounts of how people make decisions under risk. CPT is a formal model with parameters that quantify psychological processes such as loss aversion, subjective values of gains and ..."
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a b s t r a c t Cumulative prospect theory (CPT Tversky & Kahneman, 1992) has provided one of the most influential accounts of how people make decisions under risk. CPT is a formal model with parameters that quantify psychological processes such as loss aversion, subjective values of gains and losses, and subjective probabilities. In practical applications of CPT, the model's parameters are usually estimated using a singleparticipant maximum likelihood approach. The present study shows the advantages of an alternative, hierarchical Bayesian parameter estimation procedure. Performance of the procedure is illustrated with a parameter recovery study and application to a real data set. The work reveals that without particular constraints on the parameter space, CPT can produce loss aversion without the parameter that has traditionally been associated with loss aversion. In general, the results illustrate that inferences about people's decision processes can crucially depend on the method used to estimate model parameters.
A Bayesian approach to diffusion process models of decisionmaking
 Cognitive Science Society
, 2008
"... The Wiener diffusion model, and its extension to the Ratcliff diffusion model, are powerful and well developed process accounts of the time course of human decisionmaking in twochoice tasks. Typically these models have been applied using standard frequentist statistical methods for relating mode ..."
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Cited by 14 (6 self)
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The Wiener diffusion model, and its extension to the Ratcliff diffusion model, are powerful and well developed process accounts of the time course of human decisionmaking in twochoice tasks. Typically these models have been applied using standard frequentist statistical methods for relating model parameters to behavioral data. Although this approach has achieved notable successes, we argue that the adoption of Bayesian methods promises to broaden the scope of the psychological problems the models can address. In a Bayesian setting, it is straightforward to include linear, nonlinear, and categorical covariates of the basic model parameters, and so provide a much richer characterization of individual differences, the properties of stimuli, the effects of task instructions, and a range of other important issues. In this paper, we provide an example of the Bayesian possibilities by applying the Ratcliff diffusion model to a benchmark data set involving a brightness discrimination task. We simultaneously use a categorical covariate and nonlinear regression to model the psychophysical function in a theoretically satisfying way. We also use Bayesian inference on latent class assignment variables to identify and accommodate contaminant data at the level of individual trials, categorizing them as ‘diffusion ’ trials, ‘guesses’, and ‘delayed startup ’ trials. Using our application as a concrete example, we discuss the potential benefits of applying the Bayesian framework to process models in the cognitive sciences.
Dimension reduction and alleviation of confounding for spatial generalized linear mixed models
 Journal of the Royal Statistical Society: Series B (Statistical Methodology
, 2013
"... Abstract. Nongaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression ..."
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Abstract. Nongaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model (SGLMM) offers a very popular and flexible approach to modeling such data, but the SGLMM suffers from three major shortcomings: (1) uninterpretability of parameters due to spatial confounding, (2) variance inflation due to spatial confounding, and (3) highdimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the SGLMM that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count, and Gaussian spatial datasets, and to a large infant mortality dataset.
Variational Bayesian inference for parametric and nonparametric regression with missing data
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2011
"... Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging and Monte Carlo methods typically are employed. We develop an alternative approach based on deterministic var ..."
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Cited by 13 (3 self)
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Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging and Monte Carlo methods typically are employed. We develop an alternative approach based on deterministic variational Bayes approximations. Both parametric and nonparametric regression are treated. We demonstrate that variational Bayes can achieve good accuracy, but with considerably less computational overhead. The main ramification is fast approximate Bayesian inference in parametric and nonparametric regression models with missing data.