統計数学セミナー

過去の記録 ~04/16次回の予定今後の予定 04/17~

担当者 吉田朋広、荻原哲平、小池祐太
セミナーURL http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/
目的 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

2021年10月13日(水)

14:30-16:00   数理科学研究科棟(駒場) 号室
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Li Cheng 氏 (National University of Singapore (NUS))
Bayesian Fixed-domain Asymptotics for Covariance Parameters in Gaussian Random Field Models
[ 講演概要 ]
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.
[ 参考URL ]
https://docs.google.com/forms/d/e/1FAIpQLSfEWrpkVavWEELx93dPxd0g2thhkC8NtA_8We4cDeiCKI6mZg/viewform