Fitting double hierarchical GLM with INLA and the Importance sampling algorithm

M. Morales Otero, V. Gómez Rubio, V. Núñez Antón

Double hierarchical generalized linear models (DHGLM) are highly structured models which can be rather difficult to fit. A good option for their estimation could be given by the Integrated nested Laplace approximation (INLA). However, due to the specific structure of these models, they cannot be directly implemented in INLA. Therefore, in this work we propose an innovative modelling approach combining INLA and the Adaptive multiple importance sampling (AMIS) algorithm. We have carried out different simulation studies and applications to real data examples, where we have compared the use of Markov chain Monte Carlo (MCMC) and our proposed approach. In all cases, AMIS-INLA provided good estimates, which were very close to those obtained with MCMC. We concluded that our proposed method provides an efficient way of fitting DHGLM, increasing the range of models that can be fitted in INLA and allowing posterior inference processes to be performed following this approach.

Keywords: INLA, MCMC, Importance Sampling

Bayesian methods II
November 10, 2023  12:00 PM
HC2: Canónigos Room 2

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