Bayesian analysis for a class of beta mixe models

The beta mixed effects model parameters can be estimated from the Bayesian approach. Bayesian inference on beta mixed models is not straightforward because the posterior distribution is not analytically available.

Markov Chain Monte Carlo (MCMC) technique is the standard approach to fit these models citep{zuniga:2013}.

In practice, this approach comes with a wide range of problems in terms of convergence and computational time.

Moreover, the implementation itself can be problematic, especially for end users who might not be experts in programming.

There are several software platforms for fitting generic models with random effects via MCMC, including JAGS citep{Plummer03jags:a}, BayesX citep{BayesX} and WinBUGS citep{Lunn2000}, among others.

INLA (Integrated Nested Laplace Approximation) approach is a new tool for Bayesian inference on latent Gaussian models when the focus is on posterior marginal distributions citep{Rue2009}. INLA substitutes MCMC simulations with accurate, and deterministic approximations to posterior marginal distributions. A computational implementat...