Dependence of Bayesian Model Selection Criteria and Fisher Information Matrix on Sample Size View Full Text


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Article Info

DATE

2011-10-14

AUTHORS

Dan Lu, Ming Ye, Shlomo P. Neuman

ABSTRACT

Geostatistical analyses require an estimation of the covariance structure of a random field and its parameters jointly from noisy data. Whereas in some cases (as in that of a Matérn variogram) a range of structural models can be captured with one or a few parameters, in many other cases it is necessary to consider a discrete set of structural model alternatives, such as drifts and variograms. Ranking these alternatives and identifying the best among them has traditionally been done with the aid of information theoretic or Bayesian model selection criteria. There is an ongoing debate in the literature about the relative merits of these various criteria. We contribute to this discussion by using synthetic data to compare the abilities of two common Bayesian criteria, BIC and KIC, to discriminate between alternative models of drift as a function of sample size when drift and variogram parameters are unknown. Adopting the results of Markov Chain Monte Carlo simulations as reference we confirm that KIC reduces asymptotically to BIC and provides consistently more reliable indications of model quality than does BIC for samples of all sizes. Practical considerations often cause analysts to replace the observed Fisher information matrix entering into KIC with its expected value. Our results show that this causes the performance of KIC to deteriorate with diminishing sample size. These results are equally valid for one and multiple realizations of uncertain data entering into our analysis. Bayesian theory indicates that, in the case of statistically independent and identically distributed data, posterior model probabilities become asymptotically insensitive to prior probabilities as sample size increases. We do not find this to be the case when working with samples taken from an autocorrelated random field. More... »

PAGES

971-993

References to SciGraph publications

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  • 2008-01-01. Bayesian Multilevel Analysis and MCMC in HANDBOOK OF MULTILEVEL ANALYSIS
  • 2002-02. Calculation of Uncertainty in the Variogram in MATHEMATICAL GEOSCIENCES
  • 2004-11. Estimating Variogram Uncertainty in MATHEMATICAL GEOSCIENCES
  • 1999-08. Geostatistical Space–Time Models: A Review in MATHEMATICAL GEOSCIENCES
  • 1986. Spatial Variation in NONE
  • 2009-10-10. Measures of Parameter Uncertainty in Geostatistical Estimation and Geostatistical Optimal Design in MATHEMATICAL GEOSCIENCES
  • 2004-04. Transformation of Residuals to Avoid Artifacts in Geostatistical Modelling with a Trend in MATHEMATICAL GEOSCIENCES
  • 2001-05. Variance–Covariance Matrix of the Experimental Variogram: Assessing Variogram Uncertainty in MATHEMATICAL GEOSCIENCES
  • 1989-10. When do we need a trend model in kriging? in MATHEMATICAL GEOSCIENCES
  • 2010-05-12. Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework in STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
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    http://scigraph.springernature.com/pub.10.1007/s11004-011-9359-0

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    http://dx.doi.org/10.1007/s11004-011-9359-0

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