Bayesian Analysis

Bayesian Functional Linear Regression with Sparse Step Functions

Paul-Marie Grollemund, Christophe Abraham, Meïli Baragatti, and Pierre Pudlo

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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.

Article information

Bayesian Anal., Volume 14, Number 1 (2019), 111-135.

First available in Project Euclid: 19 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 62J05: Linear regression

Bayesian regression functional data support estimate parsimony

Creative Commons Attribution 4.0 International License.


Grollemund, Paul-Marie; Abraham, Christophe; Baragatti, Meïli; Pudlo, Pierre. Bayesian Functional Linear Regression with Sparse Step Functions. Bayesian Anal. 14 (2019), no. 1, 111--135. doi:10.1214/18-BA1095.

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Supplemental materials

  • Supplementary Materials: Bayesian Functional Linear Regression with Sparse Step Functions. The code of the method is available as an R package at