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Assessment and Propagation of Model Uncertainty
, 1995
"... this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the ..."
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Cited by 108 (0 self)
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this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the U.S. Space Shuttle.
BUGS  Bayesian inference Using Gibbs Sampling Version 0.50
, 1995
"... e wrong, which is even worse. Please let us know of any successes or failures. Beware  Gibbs sampling can be dangerous!. BUGS c flcopyright MRC Biostatistics Unit 1995. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully acknowledged. The work was funde ..."
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Cited by 64 (0 self)
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e wrong, which is even worse. Please let us know of any successes or failures. Beware  Gibbs sampling can be dangerous!. BUGS c flcopyright MRC Biostatistics Unit 1995. ALL RIGHTS RESERVED. The support of the Economic and Social Research Council (UK) is gratefully acknowledged. The work was funded in part by ESRC (UK) Award Number H519 25 5023. 1 2 Contents 1 Introduction 5 1.1 What is BUGS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 For what kind of problems is BUGS best suited? . . . . . . . . . . . . . . . . . . . . . 5 1.3 Markov Chain Monte Carlo (MCMC) techniques . . . . . . . . . . . . . . . . . . . . 5 1.4 A simple example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Hardware platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Software . . .
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
Incorporating Variability in Estimates of Heterogeneity in the Random Effects Model in MetaAnalysis
, 1996
"... When combining results from separate investigations in a metaanalysis, random effects methods enable the modeling of differences between studies by incorporating a heterogeneity parameter ø 2 that accounts explicitly for acrossstudy variation. We develop a simple form for the variance of Cochran ..."
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Cited by 14 (3 self)
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When combining results from separate investigations in a metaanalysis, random effects methods enable the modeling of differences between studies by incorporating a heterogeneity parameter ø 2 that accounts explicitly for acrossstudy variation. We develop a simple form for the variance of Cochran's homogeneity statistic Q, leading to interval estimation of ø 2 utilizing an approximating distribution for Q; this enables us to extend the point estimation of DerSimonian and Laird. We also develop asymptotic likelihood methods and compared them with this method. We then use these approximating distributions to give a new method of calculating the weight given to the individual studies' results when estimating the overall mean which takes into account variation in these point estimates of ø 2 . Two examples illustrate the methods presented, where we show that the new weighting scheme is between the standard fixed and random effects models in downweighting the results of large studie...
Publication Bias in MetaAnalysis: A Bayesian DataAugmentation Approach to Account for Issues Exemplified in the Passive Smoking Debate
 Statistical Science
, 1997
"... `Publication bias' is a relatively new statistical phenomenon that only arises when one attempts through a metaanalysis to review all studies, significant or insignificant, in order to provide a total perspective on a particular issue. This has recently received some notoriety as an issue in the ev ..."
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Cited by 11 (5 self)
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`Publication bias' is a relatively new statistical phenomenon that only arises when one attempts through a metaanalysis to review all studies, significant or insignificant, in order to provide a total perspective on a particular issue. This has recently received some notoriety as an issue in the evaluation of the relative risk of lung cancer associated with passive smoking, following legal challenges to a 1992 EPA analysis which concluded that such exposure is associated with significant excess risk of lung cancer. We introduce a Bayesian approach which estimates and adjusts for publication bias. Estimation is based on a data augmentation principle within a hierarchical model, and the number and outcomes of unobserved studies are simulated using Gibbs sampling methods. This technique yields a quantitative adjustment for the passive smoking metaanalysis. We estimate that there may be both negative and positive but insignificant studies omitted, and that failing to allow for these woul...
Nonparametric Modelling of Hierarchically Exchangeable Data
, 2003
"... Hierarchically exchangeable data are characterized by the exchangeability of a population of units and the exchangeability of observations from each individual unit. A flexible model for such data is the hierarchical logisticnormal model, which provides unconstrained sampling distributions at the w ..."
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Cited by 9 (0 self)
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Hierarchically exchangeable data are characterized by the exchangeability of a population of units and the exchangeability of observations from each individual unit. A flexible model for such data is the hierarchical logisticnormal model, which provides unconstrained sampling distributions at the withinunit level and an unconstrained covariance structure at the betweenunit level. Also, the sampling distribution at the betweenunit level is unimodal in a weak sense. Parameter estimation and inference for the hierarchical logisticnormal model is relatively straightforward via Markov chain Monte Carlo or an approximate EM algorithm. These and other features of the hierarchical logistic normal model are explored, and the model is applied to the analysis of tumor locations in a mammalian population. A comparison is made to a similar data analysis based on Dirichlet distributions.
Combining information from related regressions
 Journal of Agricultural, Biological, and Environmental Statistics
, 1997
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 8 (0 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
NonParametric Classes of Weight Functions to Model Publication Bias
, 1995
"... This paper addresses the use of weight functions to model publication bias in metaanalysis. Since this bias is hard to gauge, we introduce a nonparametric "contamination class of weight functions. We then illustrate how to explore sensitivity of conclusions to the specification of the weight func ..."
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Cited by 5 (0 self)
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This paper addresses the use of weight functions to model publication bias in metaanalysis. Since this bias is hard to gauge, we introduce a nonparametric "contamination class of weight functions. We then illustrate how to explore sensitivity of conclusions to the specification of the weight function by examining the range of results for the entire class. We find lower bounds on the coverage of confidence intervals. If no publication bias is present, results are robust even when considered over the entire "contamination class. However, if publication bias is present, then the coverage provided by the usual interval estimator is not robust. In this case, an alternative interval estimator is suggested. We also illustrate how both upper and lower bounds on posterior quantities of interest may be found for the case in which prior information is available. Some key words: Weight functions; Selection bias; Metaanalysis. 1 Introduction This paper addresses the use of weight functions t...
Passive Smoking in the Workplace: Classical and Bayesian Metaanalyses
 Int. Arch. Occupational and Environmental Health
, 1994
"... There are currently several classical and Bayesian methods of metaanalysis available for combining epidemiological results. We describe and compare these in a consistent framework, and apply them to published studies of the relative risk of lung cancer associated with exposure to environmental toba ..."
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Cited by 5 (3 self)
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There are currently several classical and Bayesian methods of metaanalysis available for combining epidemiological results. We describe and compare these in a consistent framework, and apply them to published studies of the relative risk of lung cancer associated with exposure to environmental tobacco smoke in the workplace. We find that although all methods give reasonably similar combined estimates of relative risk of lung cancer associated with this exposure (none of which is significantly raised above unity, in either a frequentist or a Bayesian sense), the approximations arising from classical methods appear to be nonconservative and should be used with caution. The Bayesian methods, which account more explicitly for possible inhomogeneity in studies, give slightly lower estimates again of relative risk and wider posterior credible intervals, indicating that inference from the nonBayesian approaches might be optimistic. Keywords: Passive smoking, metaanalysis, environmental tob...
Bayesian Assessment Of Publication Bias In MetaAnalyses Of Cervical Cancer And Oral Contraceptives
 In Proceedings of the Joint Statistical Meetings
, 1996
"... Metaanalysis is well known to be susceptible to publication bias (PB), caused by lack of publication of all works on the area in question. This paper applies a recently developed Bayesian method for assessing PB to a collection of studies of the possible effects of oral contraceptive use on inciden ..."
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Cited by 4 (3 self)
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Metaanalysis is well known to be susceptible to publication bias (PB), caused by lack of publication of all works on the area in question. This paper applies a recently developed Bayesian method for assessing PB to a collection of studies of the possible effects of oral contraceptive use on incidence of cervical cancer. We build on a metaanalysis developed in DelgadoRodriguez et al. [2]. We apply a more formal approach to evaluating and adjusting for PB than the ad hoc funnel plot procedure used in that paper. We conclude that there is support for the existence of publication bias in the main data set analyzed in [2], and we show it is probably caused by the explicit disregard of `low quality' studies in [2]. Overall we conclude that there is rather weak support for a positive association between oral contraceptive use and incidence of cervical cancer. 1 Introduction Metaanalysis is a widely applied technique for statistically combining analyses from individual studies into a sing...