For more details, see the readme file.
Working Paper (2021)
Fernández-de-Marcos Alberto and García-Portugués Eduardo
By Storvik Geir and Hubin Aliaksandr
Computational Statistics and Data Analysis (2018)
Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available introducing a variety of hypothetical explanatory variables for these models to be considered. Selection of an optimal combination of these variables is thus becoming crucial. In a Bayesian setting, the posterior distribution of the models, based on the observed data, can be viewed as a relevant measure for the model evidence. The model space increases exponential in the number of candidate variables and has numerous local extrema. To resolve these issues a novel MCMC algorithm for the search through the model space via efficient mode jumping for GLMMs is introduced. The algorithm is based on that marginal likelihoods can be efficiently calculated within each model. It is recommended that either exact expressions or precise approximations of marginal likelihoods are applied. The suggested algorithm is further applied to some simulated data, the famous U.S. crime data, protein activity data and epigenetic data and compared to several existing approaches.
Storvik G. and Hubin A. (2018) Mode jumping MCMC for Bayesian variable selection in GLMM. Computational Statistics and Data Analysis.