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• W2010268487 abstract "We consider the problem of assessing goodness of fit of a single Bayesian model to the observed data in the inverse problem context. A novel procedure of goodness of fit test is proposed, based on construction of reference distributions using the `inverse' part of the given model. This is motivated by an example from palaeoclimatology in which it is of interest to reconstruct past climates using information obtained from fossils deposited in lake sediment. Technically, given a model $f(Ymid X,theta)$, where $Y$ is the observed data and $X$ is a set of (non-random) covariates, we obtain reference distributions based on the posterior $pi(tilde Xmid Y)$, where $tilde X$ must be interpreted as the {it unobserved} random vector corresponding to the {it observed} covariates $X$. Put simply, if the posterior distribution $pi(tilde Xmid Y)$ gives high density to the observed covariates $X$, or equivalently, if the posterior distribution of $T(tilde X)$ gives high density to $T(X)$, where $T$ is any appropriate statistic, then we say that the model fits the data. Otherwise the model in question is not adequate. We provide decision-theoretic justification of our proposed approach and discuss other theoretical and computational advantages. We demonstrate our methodology with many simulated examples and three complex, high-dimensional, realistic palaeoclimate problems, including the motivating palaeoclimate problem." @default.
• W2010268487 created "2016-06-24" @default.
• W2010268487 creator A5021207606 @default.
• W2010268487 date "2012-03-12" @default.
• W2010268487 modified "2023-09-23" @default.
• W2010268487 title "A Fully Bayesian Approach to Assessment of Model Adequacy in Inverse Problems" @default.
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• W2010268487 hasPublicationYear "2012" @default.
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