Oswaldo Gressani : Laplace-P-splines for approximate Bayesian inference

Philippe Lambert
Université Catholique de Louvain

Date(s) : 07/12/2020   iCal
14 h 00 min - 16 h 00 min

In Bayesian statistics, a general and widely used approach to extract information from (complex) posterior distributions relies on Markov chain Monte Carlo (MCMC) methods. Although MCMC samplers provide powerful tools for Bayesian inference in various applications, they are often computationally intensive due to their iterative nature. We propose a much faster alternative for approximate Bayesian inference called ‘‘Laplace-P-splines’’ (LPS) that combines Laplace approximations to selected posterior distributions and P-splines for flexible modeling of smooth model terms. After presenting the main ideas underlying the LPS methodology, we show how it can be used for sampling-free approximate Bayesian inference in models for survival data. Moreover, we also motivate the use of LPS in the class of generalized additive models where the response has a distribution belonging to the one-parameter exponential family. The proposed methodology is endowed with closed form expressions for the gradient and Hessian of the (log) posterior penalty vector. This permits a fast and efficient selection of the penalty parameters tuning the smoothness of the functionals modeled with B-splines. Finally, the associated blapsr software package (https://www.blapsr-project.org) is presented to illustrate the use of LPS for inference in latent Gaussian models.


[1] Gressani, O. and Lambert, P. (2018). Fast Bayesian inference using Laplace approximations in a flexible promotion time cure model based on P-splines. Computational Statistics and Data Analysis, 124, 151-167. https://doi.org/10.1016/j.csda.2018.02.007

[2] Gressani, O. and Lambert, P. (2020). The Laplace-P-spline methodology for fast approximate Bayesian inference in additive partial linear models. ISBA Discussion papers. http://hdl.handle.net/2078.1/230728

[3] Gressani, O. and Lambert, P. (2021). Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines. Computational Statistics and Data Analysis, 154. https://doi.org/10.1016/j.csda.2020.107088


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