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March 2019 Bayesian Functional Linear Regression with Sparse Step Functions
Paul-Marie Grollemund, Christophe Abraham, Meïli Baragatti, Pierre Pudlo
Bayesian Anal. 14(1): 111-135 (March 2019). DOI: 10.1214/18-BA1095

Abstract

The functional linear regression model is a common tool to determine the relationship between a scalar outcome and a functional predictor seen as a function of time. This paper focuses on the Bayesian estimation of the support of the coefficient function. To this aim we propose a parsimonious and adaptive decomposition of the coefficient function as a step function, and a model including a prior distribution that we name Bayesian functional Linear regression with Sparse Step functions (Bliss). The aim of the method is to recover periods of time which influence the most the outcome. A Bayes estimator of the support is built with a specific loss function, as well as two Bayes estimators of the coefficient function, a first one which is smooth and a second one which is a step function. The performance of the proposed methodology is analysed on various synthetic datasets and is illustrated on a black Périgord truffle dataset to study the influence of rainfall on the production.

Citation

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Paul-Marie Grollemund. Christophe Abraham. Meïli Baragatti. Pierre Pudlo. "Bayesian Functional Linear Regression with Sparse Step Functions." Bayesian Anal. 14 (1) 111 - 135, March 2019. https://doi.org/10.1214/18-BA1095

Information

Published: March 2019
First available in Project Euclid: 19 April 2018

zbMATH: 07001977
MathSciNet: MR3910040
Digital Object Identifier: 10.1214/18-BA1095

Subjects:
Primary: 62F15
Secondary: 62J05

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Vol.14 • No. 1 • March 2019
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