Pesquisa Operacional (2022) 42: e254533 p.1-26 doi: 10.1590/0101-7438.2022.042.00254533 © 2022 Brazilian Operations Research Society Printed version ISSN 0101-7438 / Online version ISSN 1678-5142 www.scielo.br/pope ARTICLES BAYESIAN ESTIMATION FOR THE STABLE DISTRIBUTIONS IN THE PRESENCE OF COVARIATES WITH APPLICATIONS IN CLINICAL ISSUES Jorge Alberto Achcar 1 , Roberto Molina de Souza 2 , Daiane Bussola 3 and Fernando A. Moala 4* Received July 22, 2021 / Accepted March 14, 2022 ABSTRACT. In this paper we explore a Bayesian approach for stable distributions in presence of covari- ates. This class of distribution has great flexibility for fitting asymmetric and heavy-tailed empirical data. These models are commonly used for data sets in finance and insurance. In this paper we show that these distributions can also be used to fit clinical data. Since there is not an analytical form for the density prob- ability function which implies in serious difficulties to obtain the maximum likelihood estimators for the parameters, we use Bayesian methods with data augmentation techniques to get the inferences of interest. In this study we also discuss the choice of different prior distributions for the parameters considering re- gression models for the location and scale parameters of the stable distribution. We use MCMC (Markov Chain Monte Carlo) algorithms to generate samples from the posterior distributions in order to evaluate the point and interval estimators. A great simplification is obtained using the OpenBugs software. Two real data examples illustrate the applicability of the proposed modeling approach. Keywords: table distributions, Bayesian approach, regression models, prior distributions, MCMC methods. 1 INTRODUCTION In many areas of applications, the usual assumption of normality of the data needed in many sta- tistical models is not satisfied in practice, even using data transformations to improve the symme- try of the data. The assumption of normality is essential for the use of traditional techniques such as ANOVA (analysis of variance) models, linear regression models, hypothesis tests for compar- ison of means, medians or variances, especially with small sample sizes. In this situation, usually *Corresponding author 1 University of S˜ ao Paulo, Department of Public Health, Av. Bandeirantes, 3900, Monte Alegre, 14049-900 Ribeir˜ ao Preto, SP, Brazil – E-mail: achcar@fmrp.usp.br – http://orcid.org/0000-0002-9868-9453 2 Federal Technological University of Paran´ a, Department of Mathematics, Av. Alberto Carazzai, 1640, Centro, 86300- 000 Corn´ elio Proc ´ opio, PR, Brazil – E-mail: rmolinasouza@utfpr.edu.br – http://orcid.org/0000-0002-0638-3650 3 University of S˜ ao Paulo, Department of Public Health, Av. Bandeirantes, 3900, Monte Alegre, 14049-900 Ribeir˜ ao Preto, SP, Brazil – E-mail: dpsampaiob@gmail.com – http://orcid.org/0000-0002-0362-2871 4 S˜ ao Paulo State University, Department of Statistics, R. Roberto S´ ımonsen, 305, Centro Educacional, 19060-900 Presidente Prudente, SP, Brazil – E-mail: f.moala@unesp.br – http://orcid.org/0000-0002-2445-0407