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Conflict diagnostic in directed acyclic graphs, with applications in Bayesian evidence synthesis
 Statistical Science
, 2013
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Elicitation of Weibull priors
"... Summary − Based on expert opinions, informative prior elicitation for the common Weibull lifetime distribution usually presents some difficulties since it requires to elicit a twodimensional joint prior. We consider here a reliability framework where the available expert information states directly ..."
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Summary − Based on expert opinions, informative prior elicitation for the common Weibull lifetime distribution usually presents some difficulties since it requires to elicit a twodimensional joint prior. We consider here a reliability framework where the available expert information states directly in terms of prior predictive values (lifetimes) and not parameter values, which are less intuitive. The novelty of our procedure is to weigh the expert information by the size m of a virtual sample yielding a similar information, the prior being seen as a reference posterior. Thus, the prior calibration by the Bayesian analyst, who has to moderate the subjective information with respect to the data information, is made simple. A main result is the full tractability of the prior under mild conditions, despite the conjugation issues encountered with the Weibull distribution. Besides, m is a practical focus point for discussion between analysts and experts, and a helpful parameter for leading sensitivity studies and reducing the potential imbalance in posterior selection between Bayesian Weibull models, which can be due to favoring arbitrarily a prior. The calibration of m is discussed and a real example is treated along the paper. Key Words − subjective prior elicitation, Weibull distribution, expert opinion, virtual data, posterior prior. 1
Bayesian Linear Regression — Different Conjugate Models and Their (In)Sensitivity to PriorData Conflict
"... The paper is concerned with Bayesian analysis under priordata conflict, i.e. the situation when observed data are rather unexpected under the prior (and the sample size is not large enough to eliminate the influence of the prior). Two approaches for Bayesian linear regression modeling based on conj ..."
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The paper is concerned with Bayesian analysis under priordata conflict, i.e. the situation when observed data are rather unexpected under the prior (and the sample size is not large enough to eliminate the influence of the prior). Two approaches for Bayesian linear regression modeling based on conjugate priors are considered in detail, namely the standard approach also described in Fahrmeir, Kneib & Lang (2007) and an alternative adoption of the general construction procedure for exponential family sampling models. We recognize that – in contrast to some standard i.i.d. models like the scaled normal model and the BetaBinomial / DirichletMultinomial model, where priordata conflict is completely ignored – the models may show some reaction to priordata conflict, however in a rather unspecific way. Finally we briefly sketch the extension to a corresponding imprecise probability model, where, by considering sets of prior distributions instead of a single prior, priordata conflict can be handled in a very appealing and intuitive way. Key words: Linear regression; conjugate analysis; priordata conflict; imprecise probability 1
unknown title
, 2012
"... Bayesian inference for inverse problems occurring in uncertainty analysis ..."
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Bayesian inference for inverse problems occurring in uncertainty analysis