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Seminar on Probability and Statistics
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Organizer(s) | Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike |
|---|
2021/10/13
14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)
Li Cheng (National University of Singapore (NUS))
Bayesian Fixed-domain Asymptotics for Covariance Parameters in Gaussian Random Field Models
https://docs.google.com/forms/d/e/1FAIpQLSfEWrpkVavWEELx93dPxd0g2thhkC8NtA_8We4cDeiCKI6mZg/viewform
Li Cheng (National University of Singapore (NUS))
Bayesian Fixed-domain Asymptotics for Covariance Parameters in Gaussian Random Field Models
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Gaussian random field models are commonly used for modeling spatial processes. In this work we focus on the Gaussian process with isotropic Matern covariance functions. Under fixed-domain asymptotics,it is well known that when the dimension of data is less than or equal to three, the microergodic parameter can be consistently estimated with asymptotic normality while the range (or length-scale) parameter cannot. Motivated by this frequentist result, we prove that under a Bayesian fixed-domain framework, the posterior distribution of the microergodic parameter converges in total variation norm to a normal distribution with shrinking variance, while the posterior of the range parameter does not necessarily converge. Built on this new theory, we further show that the Bayesian kriging predictor satisfies the posterior asymptotic efficiency in linear prediction. We illustrate these asymptotic results in numerical examples.
[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home
Gaussian random field models are commonly used for modeling spatial processes. In this work we focus on the Gaussian process with isotropic Matern covariance functions. Under fixed-domain asymptotics,it is well known that when the dimension of data is less than or equal to three, the microergodic parameter can be consistently estimated with asymptotic normality while the range (or length-scale) parameter cannot. Motivated by this frequentist result, we prove that under a Bayesian fixed-domain framework, the posterior distribution of the microergodic parameter converges in total variation norm to a normal distribution with shrinking variance, while the posterior of the range parameter does not necessarily converge. Built on this new theory, we further show that the Bayesian kriging predictor satisfies the posterior asymptotic efficiency in linear prediction. We illustrate these asymptotic results in numerical examples.
https://docs.google.com/forms/d/e/1FAIpQLSfEWrpkVavWEELx93dPxd0g2thhkC8NtA_8We4cDeiCKI6mZg/viewform
