Bayesian Model Assessment Using Pivotal Quantities

By Valen E. Johnson. 2007

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Abstract. Suppose that S(Y;) is a function of data Yand a model parameter ,and suppose that the sampling distribution of S(Y;) is invariant when evaluatedat  0 , the \true" (i.e., data-generating) value of . Then S(Y;) is a pivotalquantity, and it follows from simple probability calculus that the distribution ofS(Y; 0 )isidenticaltothedistributionofS(Y; Y ),where Y isavalueof drawnfrom the posterior distribution given Y. This fact makes it possible to de ne alarge numberof Bayesian model diagnostics havinga knownsampling distribution.It also facilitates the calibration of the joint sampling of model diagnostics basedon pivotal quantities.Keywords: prior-predictive density, posterior-predictive density, Bayesian modeldiagnostics, Bayesian chi-squared test. 1 Introduction Within the Bayesian paradigm, a number of general approaches for model evaluationhave been proposed. Although a number of informal measures have been proposed toassess model adequacy, many model assessment strategies have relied on the calculationof Bayesian analogs of frequentist p values. For example, Box (1980) proposed thecalculation of Bayesian p values based on the prior-predictive distribution. In thisapproach, Bayesian p-values are calculated according toPr[p(g(y)jA) < p(g(y

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fa5d3b286cf959e2ad25dcdb43f5d9af3d01d53c

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In Artificial Intelligence

  1. Bruno Sansó
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