Posterior convergence for Bayesian functional linear regression

Heng Lian, Taeryon Choi, Jie Meng, Seongil Jo

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)27-41
Number of pages15
JournalJournal of Multivariate Analysis
Volume150
DOIs
Publication statusPublished - Sep 2016

Keywords

  • functional regression
  • minimax rate
  • posterior contraction rate
  • prediction risk
  • reproducing kernel Hilbert space

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