Seminar on Probability and Statistics

Seminar information archive ~04/30Next seminarFuture seminars 05/01~

Organizer(s) Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike

2025/05/02

13:30-14:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Shunsuke Imai (Kyoto University)
General Bayesian Semiparametric Inference with Hyvärinen Score (Japanese)
[ Abstract ]
This paper proposes a novel framework for semiparametric Bayesian inference on finite-dimensional parameters under existence of nuisance functions. Based on a pseudo-model defined by (profiled) loss functions for the finite dimensional parameters and the Hyv\"arinen score, we propose a general posterior distribution, named semiparametric Hyv\"arinen (SH) posterior. The SH posterior enables us to make inference on the parameters of interest with taking account of uncertainty in the estimation/selection of tuning parameters in estimating the unknown nuisance functions. We establish its theoretical justification of the SH posterior under large samples, and provide posterior computation algorithm. As concrete examples, we provide the posterior inference of partial linear models and single index models, and demonstrate the performance through simulation.
[ Reference URL ]
https://us06web.zoom.us/meeting/register/3XxtsHwaQVSN7BuINu6E8g