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Posterior convergence for Bayesian functional linear regression

journal contribution
posted on 05.11.2021, 10:55 by Heng Lian, Taeryon Choi, Jie MengJie Meng, Seongil Jo
We consider the asymptotic properties of Bayesian functional linear regression models where the response is a scalar and the predictor is a random function. Functional linear regression models have been routinely applied to many functional data analytic tasks in practice, and recent developments have been made in theory and methods. However, few works have investigated the frequentist convergence property of the posterior distribution of the Bayesian functional linear regression model. In this paper, we attempt to conduct a theoretical study to understand the posterior contraction rate in the Bayesian functional linear regression. It is shown that an appropriately chosen prior leads to the minimax rate in prediction risk.

Funding

Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No. 2013R1A1A2074463)

History

School

  • Loughborough University London

Published in

Journal of Multivariate Analysis

Volume

150

Pages

27 - 41

Publisher

Elsevier BV

Version

VoR (Version of Record)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Journal of Multivariate Analysis and the definitive published version is available at https://doi.org/10.1016/j.jmva.2016.04.008.

Publication date

2016-05-18

Copyright date

2016

ISSN

0047-259X

eISSN

1095-7243

Language

en

Depositor

Dr Jie Meng. Deposit date: 4 November 2021