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

Author

Listed:
  • Gressani, Oswaldo

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Lambert, Philippe

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

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.

Suggested Citation

  • Gressani, Oswaldo & Lambert, Philippe, 2021. "Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines," LIDAM Reprints ISBA 2021056, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  • Handle: RePEc:aiz:louvar:2021056
    DOI: https://doi.org/10.1016/j.csda.2020.107088
    Note: In: Computational Statistics & Data Analysis, 2021, vol. 154, 107088
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    Cited by:

    1. Lambert, Philippe, 2021. "Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    2. Lambert, Philippe & Gressani, Oswaldo, 2022. "Penalty parameter selection and asymmetry corrections to Laplace approximations in Bayesian P-splines models," LIDAM Discussion Papers ISBA 2022030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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