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33
Statistical Methods for Eliciting Probability Distributions
 Journal of the American Statistical Association
, 2005
"... Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting the experience of statisticia ..."
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Cited by 61 (3 self)
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Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.
A WEAKLY INFORMATIVE DEFAULT PRIOR DISTRIBUTION FOR LOGISTIC AND OTHER REGRESSION MODELS
"... We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Studentt prior distributions on the coefficients. As a default choice, we reco ..."
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Cited by 59 (10 self)
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We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Studentt prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with center 0 and scale 2.5, which in the simplest setting is a longertailed version of the distribution attained by assuming onehalf additional success and onehalf additional failure in a logistic regression. Crossvalidation on a corpus of datasets shows the Cauchy class of prior distributions to outperform existing implementations of Gaussian and Laplace priors. We recommend this prior distribution as a default choice for routine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of predictors is small), and also automatically applying more shrinkage to higherorder interactions. This can
What to do about missing values in time series crosssection data
, 2009
"... Applications of modern methods for analyzing data with missing values, based primarily on multiple imputation, have in the last halfdecade become common in American politics and political behavior. Scholars in this subset of political science have thus increasingly avoided the biases and inefficien ..."
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Cited by 29 (6 self)
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Applications of modern methods for analyzing data with missing values, based primarily on multiple imputation, have in the last halfdecade become common in American politics and political behavior. Scholars in this subset of political science have thus increasingly avoided the biases and inefficiencies caused by ad hoc methods like listwise deletion and best guess imputation. However, researchers in much of comparative politics and international relations, and others with similar data, have been unable to do the same because the best available imputation methods work poorly with the timeseries cross section data structures common in these fields. Weattempttorectify this situation with three related developments. First, we build a multiple imputation model that allows smooth time trends, shifts across crosssectional units, and correlations over time and space, resulting in far more accurate imputations. Second, we enable analysts to incorporate knowledge from area studies experts via priors on individual missing cell values, rather than on difficulttointerpret model parameters. Third, because these tasks could not be accomplished within existing imputation algorithms, in that they cannot handle as many variables as needed even in the simpler crosssectional data for which they were designed, we also develop a new algorithm that substantially expands the range of computationally feasible data types and sizes for which multiple imputation can be used. These developments also make it possible to implement the methods introduced here in freely available open source software that is considerably more reliable than existing algorithms. We develop an approach to analyzing data with
Sequential Ordinal Modeling with Applications to Survival Data
 Biometrics
, 2001
"... This paper considers the class of sequential probit models in relation to other models for ordinal data. Hierarchical and other extensions of the model are proposed for applications involving discrete time (grouped) survival data. Computationally practical Markov chain Monte Carlo algorithms are dev ..."
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Cited by 24 (2 self)
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This paper considers the class of sequential probit models in relation to other models for ordinal data. Hierarchical and other extensions of the model are proposed for applications involving discrete time (grouped) survival data. Computationally practical Markov chain Monte Carlo algorithms are developed for the fitting of these models. The ideas and methods are illustrated in detail with a real data example on the length of hospital stay for patients undergoing heart surgery. A notable aspect of this analysis is the comparison, based on marginal likelihoods and training sample priors, of several nonnested models, such as the sequential model, the cumulative ordinal model and Weibull and loglogistic models. Keywords: Bayes factor; Discrete hazard function; Gibbs sampling; Marginal likelihood; MetropolisHastings algorithm; Nonnested models; Sequential probit; Training sample prior; Model comparison. 1 Introduction Ordinal response data is generally analyzed using the cumulative o...
General design Bayesian generalized linear mixed models.” Statistical Science, 21(1), 35–51. Hadfield 17 A. Appendix A.1. Updating the latent variables l The conditional density of l is given by: P r(liy, θ, R, G) ∝ fi(yili)fN(eiriR −1 /i e /i, ri − ri
 P r(ljy, θ, R, G) ∝ ∏ pi(yili)fN(ej0, Rj
, 2006
"... Abstract. Linear mixed models are able to handle an extraordinary range of complications in regressiontype analyses. Their most common use is to account for withinsubject correlation in longitudinal data analysis. They are also the standard vehicle for smoothing spatial count data. However, when t ..."
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Cited by 10 (1 self)
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Abstract. Linear mixed models are able to handle an extraordinary range of complications in regressiontype analyses. Their most common use is to account for withinsubject correlation in longitudinal data analysis. They are also the standard vehicle for smoothing spatial count data. However, when treated in full generality, mixed models can also handle splinetype smoothing and closely approximate kriging. This allows for nonparametric regression models (e.g., additive models and varying coefficient models) to be handled within the mixed model framework. The key is to allow the random effects design matrix to have general structure; hence our label general design. For continuous response data, particularly when Gaussianity of the response is reasonably assumed, computation is now quite mature and supported by the R, SAS and SPLUS packages. Such is not the case for binary and count responses, where generalized linear mixed models (GLMMs) are required, but are hindered by the presence of intractable multivariate
Bayesian variable selection for time series count data Statistica Sinica
, 2000
"... Abstract: We consider a parametric model for time series of counts by constructing a likelihoodbased generalization of a model considered by Zeger (1988). We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for variable su ..."
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Cited by 6 (0 self)
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Abstract: We consider a parametric model for time series of counts by constructing a likelihoodbased generalization of a model considered by Zeger (1988). We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for variable subset selection. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified in a prior distribution for the current study. We derive theoretical and computational properties of the proposed priors and develop novel methods for computing posterior model probabilities. To compute the posterior model probabilities, we show that only posterior samples from the full model are needed to estimate the posterior probabilities for all of the possible subset models. We demonstrate our methodology with a simulated and a real data set.
Variable selection for multivariate logistic regression models
 Journal of Statistical Planning and Inference
, 2003
"... In this paper, we use multivariate logistic regression models to incorporate correlation among binary response data. Our objective is to develop a variable subset selection procedure to identify important covariates in predicting correlated binary responses using a Bayesian approach. In order to inc ..."
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Cited by 6 (0 self)
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In this paper, we use multivariate logistic regression models to incorporate correlation among binary response data. Our objective is to develop a variable subset selection procedure to identify important covariates in predicting correlated binary responses using a Bayesian approach. In order to incorporate available prior information, we propose a class of informative prior distributions on the model parameters and on the model space. The propriety of the proposed informative prior is investigated in detail. Novel computational algorithms are also developed for sampling from the posterior distribution as well as for computing posterior model probabilities. Finally, a simulated data example and a real data example from a prostate cancer study are used to illustrate the proposed methodology.
The Elicitation of Probabilities A Review of the Statistical Literature
, 2005
"... “We live in an uncertain world, and probability risk assessment deals as directly with that fact as anything we do. Uncertainty arises partly because we are fallible. ..."
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Cited by 3 (0 self)
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“We live in an uncertain world, and probability risk assessment deals as directly with that fact as anything we do. Uncertainty arises partly because we are fallible.
Modelling and eliciting expert knowledge with fictitious data
 in &quot;Proceedings of the Workshop on the use of Expert Judgement for decisionmaking, CEA Cadarache
, 2005
"... ABSTRACT: Considering reliability models In a Bayesian context, we propose an approach where experts opinions are supposed to come from fictitious data. Acting in such a way allows the analyst to weight the importance of the expert opinion in regard to the actual sample size in a sensible and reliab ..."
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Cited by 2 (1 self)
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ABSTRACT: Considering reliability models In a Bayesian context, we propose an approach where experts opinions are supposed to come from fictitious data. Acting in such a way allows the analyst to weight the importance of the expert opinion in regard to the actual sample size in a sensible and reliable way. The control of experts knowledge becomes a control of the Fisher information on the reliability model parameters. Thus, the comparison between Feedback Experience Data (FED) and expert data through the reliability model and the prior distribution is easy and makes simple the calibration of the hyperparameters prior distribution to control the importance of expert contribution compared to the information provided by the observed sample. The presented approach is exemplified with Weibull models. 1
Default Bayesian analysis for multiway tables: a dataaugmentation approach. arXiv:1109.4180v1
, 2011
"... This paper proposes a strategy for regularized estimation in multiway contingency tables, which are common in metaanalyses and multicenter clinical trials. Our approach is based on data augmentation, and appeals heavily to a novel class of Polya–Gamma distributions. Our main contributions are to ..."
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This paper proposes a strategy for regularized estimation in multiway contingency tables, which are common in metaanalyses and multicenter clinical trials. Our approach is based on data augmentation, and appeals heavily to a novel class of Polya–Gamma distributions. Our main contributions are to build up the relevant distributional theory and to demonstrate three useful features of this dataaugmentation scheme. First, it leads to simple EM and Gibbssampling algorithms for posterior inference, circumventing the need for analytic approximations, numerical integration, Metropolis–Hastings, or variational methods. Second, it allows modelers much more flexibility when choosing priors, which have traditionally come from the Dirichlet or logisticnormal family. For example, our approach allows users to incorporate Bayesian analogues of classical penalizedlikelihood techniques (e.g. the lasso or bridge) in computing regularized estimates for logodds ratios. Finally, our dataaugmentation scheme naturally suggests a default strategy for prior selection based on the logisticZ model, which is strongly related to Jeffreys ’ prior for a binomial proportion. To illustrate the method we focus primarily on the particular case of a metaanalysis/multicenter study (or a J ×K ×N table). But the general approach encompasses many other common situations, of which we will provide examples.