College of Liberal Arts & Sciences
Cheng Li - Colloquium Speaker
Assistant Professor, Department of Statistics and Applied Probability, National University of Singapore
Date:
Thursday, November 18, 2021 - 3:15pm
Colloquium Title:
Bayesian Fixed-domain Asymptotics for Covariance Parameters in a Gaussian Process Model
Abstract:
Gaussian process models are widely used in spatial statistics. In this work we focus on the Gaussian process with isotropic Matern covariance functions. Under fixed-domain asymptotics, it is known that when the domain has a dimension less than or equal to three, the microergodic parameter can be consistently estimated with asymptotic normality while the range parameter cannot. Motivated by this frequentist result, we show that the posterior of the microergodic parameter is asymptotically close in total variation distance to a normal distribution with shrinking variance, while the posterior distribution of the range parameter does not converge to any point mass distribution in general. We further show that the Bayesian kriging predictor satisfies the posterior asymptotic efficiency in linear prediction. We verify these asymptotic results in numerical experiments.
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Topic: Colloquia: Department of Statistics and Actuarial Science, The University of Iowa
Time: November 18, 2021 03:15 PM Central Time (US and Canada)
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Meeting ID: 989 2869 3758