2012/03/12 by Sourabh Bhattacharya, Bhattacharya, Sourabh
Computer Science · Engineering · Environmental Science · #FOS: Computer and information sciences #Geochemistry and Geologic Mapping #Methodology (stat.ME) #Reservoir Engineering and Simulation Methods #Soil Geostatistics and Mapping
paper · pdf · doi:10.48550/arxiv.1203.2403
openalex publication_date 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of assessing goodness of fit of a single Bayesian\nmodel to the observed data in the inverse problem context. A novel procedure of\ngoodness of fit test is proposed, based on construction of reference\ndistributions using the `inverse' part of the given model. This is motivated by\nan example from palaeoclimatology in which it is of interest to reconstruct\npast climates using information obtained from fossils deposited in lake\nsediment.\n Technically, given a model f(Y\| X,\θ), where Y is the observed\ndata and X is a set of (non-random) covariates, we obtain reference\ndistributions based on the posterior \π( X\| Y), where X\nmust be interpreted as the it unobserved random vector corresponding to the\n it observed covariates X. Put simply, if the posterior distribution\n\π( X\| Y) gives high density to the observed covariates X, or\nequivalently, if the posterior distribution of T( X) gives high density\nto T(X), where T is any appropriate statistic, then we say that the model\nfits the data. Otherwise the model in question is not adequate. We provide\ndecision-theoretic justification of our proposed approach and discuss other\ntheoretical and computational advantages. We demonstrate our methodology with\nmany simulated examples and three complex, high-dimensional, realistic\npalaeoclimate problems, including the motivating palaeoclimate problem.\n