Results 1  10
of
407
Bayesian Data Analysis
, 1995
"... I actually own a copy of Harold Jeffreys’s Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jeffreys was not too proud to use a classical chisquared pvalue when he wanted to check the misfit of a model to data (Gelman, Meng and Ste ..."
Abstract

Cited by 2132 (59 self)
 Add to MetaCart
I actually own a copy of Harold Jeffreys’s Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jeffreys was not too proud to use a classical chisquared pvalue when he wanted to check the misfit of a model to data (Gelman, Meng and Stern, 2006). I do, however, feel that it is important to understand where our probability models come from, and I welcome the opportunity to use the present article by Robert, Chopin and Rousseau as a platform for further discussion of foundational issues. 2 In this brief discussion I will argue the following: (1) in thinking about prior distributions, we should go beyond Jeffreys’s principles and move toward weakly informative priors; (2) it is natural for those of us who work in social and computational sciences to favor complex models, contra Jeffreys’s preference for simplicity; and (3) a key generalization of Jeffreys’s ideas is to explicitly include model checking in the process of data analysis.
Mplus: Statistical Analysis with Latent Variables (Version 4.21) [Computer software
, 2007
"... Chapter 3: Regression and path analysis 19 Chapter 4: Exploratory factor analysis 43 ..."
Abstract

Cited by 162 (0 self)
 Add to MetaCart
Chapter 3: Regression and path analysis 19 Chapter 4: Exploratory factor analysis 43
MCMC Methods for Multiresponse Generalized Linear Mixed Models: The MCMCglmm R Package
"... Generalized linear mixed models provide a flexible framework for modeling a range of data, although with nonGaussian response variables the likelihood cannot be obtained in closed form. Markov chain Monte Carlo methods solve this problem by sampling from a series of simpler conditional distribution ..."
Abstract

Cited by 72 (0 self)
 Add to MetaCart
(Show Context)
Generalized linear mixed models provide a flexible framework for modeling a range of data, although with nonGaussian response variables the likelihood cannot be obtained in closed form. Markov chain Monte Carlo methods solve this problem by sampling from a series of simpler conditional distributions that can be evaluated. The R package MCMCglmm, implements such an algorithm for a range of model fitting problems. More than one response variable can be analysed simultaneously, and these variables are allowed to follow Gaussian, Poisson, multi(bi)nominal, exponential, zeroinflated and censored distributions. A range of variance structures are permitted for the random effects, including interactions with categorical or continuous variables (i.e., random regression), and more complicated variance structures that arise through shared ancestry, either through a pedigree or through a phylogeny. Missing values are permitted in the response variable(s) and data can be known up to some level of measurement error as in metaanalysis. All simulation is done in C / C++ using the CSparse library for sparse linear systems. If you use the software please cite this article, as published in the Journal of Statistic Software
Metaanalysis of functional neuroimaging data: Current and future directions
 Social Cognitive and Affective Neuroscience
, 2007
"... ar ..."
Bayesian analysis for penalized spline regression using WinBUGS
 J. Statist. Soft
, 2005
"... Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys t ..."
Abstract

Cited by 54 (6 self)
 Add to MetaCart
(Show Context)
Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. Good mixing properties of the MCMC chains are obtained by using lowrank thinplate splines, while simulation times per iteration are reduced employing WinBUGS specific computational tricks.
Struggles with Survey Weighting and Regression Modeling
 Statistical Science
, 2007
"... Abstract. The general principles of Bayesian data analysis imply that models for survey responses should be constructed conditional on all variables that affect the probability of inclusion and nonresponse, which are also the variables used in survey weighting and clustering. However, such models ca ..."
Abstract

Cited by 53 (3 self)
 Add to MetaCart
(Show Context)
Abstract. The general principles of Bayesian data analysis imply that models for survey responses should be constructed conditional on all variables that affect the probability of inclusion and nonresponse, which are also the variables used in survey weighting and clustering. However, such models can quickly become very complicated, with potentially thousands of poststratification cells. It is then a challenge to develop general families of multilevel probability models that yield reasonable Bayesian inferences. We discuss in the context of several ongoing public health and social surveys. This work is currently openended, and we conclude with thoughts on how research could proceed to solve these problems. Multilevel modeling, poststratification, samKey words and phrases:
Modeling changing dependency structure in multivariate time series
 In International Conference in Machine Learning
, 2007
"... We show how to apply the efficient Bayesian changepoint detection techniques of Fearnhead in the multivariate setting. We model the joint density of vectorvalued observations using undirected Gaussian graphical models, whose structure we estimate. We show how we can exactly compute the MAP segmenta ..."
Abstract

Cited by 48 (0 self)
 Add to MetaCart
(Show Context)
We show how to apply the efficient Bayesian changepoint detection techniques of Fearnhead in the multivariate setting. We model the joint density of vectorvalued observations using undirected Gaussian graphical models, whose structure we estimate. We show how we can exactly compute the MAP segmentation, as well as how to draw perfect samples from the posterior over segmentations, simultaneously accounting for uncertainty about the number and location of changepoints, as well as uncertainty about the covariance structure. We illustrate the technique by applying it to financial data and to bee tracking data. 1.
Handling sparsity via the horseshoe
 Journal of Machine Learning Research, W&CP
"... This paper presents a general, fully Bayesian framework for sparse supervisedlearning problems based on the horseshoe prior. The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used approaches for sparse Bayesian learni ..."
Abstract

Cited by 31 (1 self)
 Add to MetaCart
This paper presents a general, fully Bayesian framework for sparse supervisedlearning problems based on the horseshoe prior. The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used approaches for sparse Bayesian learning, including, among others, Laplacian priors (e.g. the LASSO) and Studentt priors (e.g. the relevance vector machine). The advantages of the horseshoe are its robustness at handling unknown sparsity and large outlying signals. These properties are justified theoretically via a representation theorem and accompanied by comprehensive empirical experiments that compare its performance to benchmark alternatives. 1
Why we (usually) don’t have to worry about multiple comparisons ∗
, 2008
"... The problem of multiple comparisons can disappear when viewed from a Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. These address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low g ..."
Abstract

Cited by 29 (7 self)
 Add to MetaCart
(Show Context)
The problem of multiple comparisons can disappear when viewed from a Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. These address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low grouplevel variation, which is where multiple comparisons are a particular concern. Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the pvalues corresponding to intervals of fixed width). Multilevel estimates make comparisons more conservative, in the sense that intervals for comparisons are less likely to include zero; as a result, those comparisons that are made with confidence are more likely to be valid.
Default prior distributions and efficient posterior computation in Bayesian factor analysis
 Journal of Computational and Graphical Statistics
, 2009
"... Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal prior distributions for factor loadings and inverse gamma prior distributions for residual variances are a popular choice b ..."
Abstract

Cited by 27 (6 self)
 Add to MetaCart
Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal prior distributions for factor loadings and inverse gamma prior distributions for residual variances are a popular choice because of their conditionally conjugate form. However, such prior distributions require elicitation of many hyperparameters and tend to result in poorly behaved Gibbs samplers. In addition, one must choose an informative specification, as high variance prior distributions face problems due to impropriety of the posterior distribution. This article proposes a default, heavy tailed prior distribution specification, which is induced through parameter expansion while facilitating efficient posterior computation. We also develop an approach to allow uncertainty in the number of factors. The methods are illustrated through simulated examples and epidemiology and toxicology applications.