Bayesian inference for simple and generalized linear models: Comparing INLA and McMC

Abstract

Markov chain Monte Carlo (McMC) is a traditional technique in Bayesian inference. Lately, Integrated Nested Laplace Approximations (INLA) has gained popularity as another technique for Bayesian inference. This paper compares the performance of these techniques in terms of accuracy, execution time, and computational burden in simple and generalized linear models. At the end of the simulation study, INLA produced estimates similar to those of the McMC technique. This observation was evident in the estimates of the fixed parameters of the models. Though random effects of the generalized linear model were not considered in this paper, those of the simple linear model were considered and the estimates by the two techniques were found to be closely identical, leading to the conclusion that INLA is as computationally efficient as McMC. Furthermore, INLA took a shorter time in approximating parameters than McMC. Finally, McMC was found to be more computationally intensive than INLA.