Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines

Oswaldo Gressani and Philippe Lambert
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Oswaldo Gressani: Université catholique de Louvain, LIDAM/ISBA, Belgium
Philippe Lambert: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2021056, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between covariates and a response assumed to have a conditional distribution in the exponential family. To make inference in this model class, a fast and flexible approach is considered based on Bayesian P-splines and the Laplace approximation. The proposed Laplace-P-spline model contributes to the development of a new methodology to explore the posterior penalty space by considering a deterministic grid-based strategy or a Markov chain sampler, depending on the number of smooth additive terms in the predictor. The approach has the merit of relying on a simple Gaussian approximation to the conditional posterior of latent variables with closed form analytical expressions available for the gradient and Hessian of the approximate posterior penalty vector. This enables to construct accurate posterior pointwise and credible set estimators for (functions of) regression and spline parameters at a relatively low computational budget even for a large number of smooth additive components. The performance of the Laplace-P-spline model is confirmed through different simulation scenarios and the method is illustrated on two real datasets.

Keywords: Laplace approximation; Generalized additive models; Fast Bayesian computation; P-splines (search for similar items in EconPapers)
Pages: 26
Date: 2021-01-01
Note: In: Computational Statistics & Data Analysis, 2021, vol. 154, 107088
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2021056

DOI: 10.1016/j.csda.2020.107088

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