Modelagem bayesiana de dados de degradação: um estudo comparativo dos softwares JAGS e Stan

Abstract

Recently is noticed a demand for highly reliable products whose properties are maintained during their lifetime. Degradation tests aims to provide information for the analysis of the lifetime of highly durable materials in a practical way to quantify durability. In addition to that, the usage of Bayesian inference offers advantages such as the possibility of quantifying the uncertainty about the reliability and durability of materials in a simple and direct way. The recent advancement and popularization of computing combined with the increasing use of specialized software, the Bayesian inference has increasingly increased its contribution to statistical modeling. The present work proposes a comparison between JAGS and Stan, two Bayesian statistical modeling software, by using the same model of degradation analysis of a lasers sample. A linear model is chosen with beta and gamma distributions for the random effects. As each software has a different algorithm for Monte Carlo simulations via Markov Chains (MCMC), the results obtained will be compared regarding the convergence of Markov chains, effective chain size, execution time, data auto-correlation and posterior high-density region. As main results, it was observed that for this specific model, the Stan software obtained better results with a smaller auto-correlation of the data, which led to a larger effective chain size.