2015/06/18 by Mathieu Gerber, Gerber, Mathieu, Florian Pelgrin +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1506.05757
openalex publication_date 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The multivariate extended skew-normal distribution allows for accommodating raw data which are skewed and heavy tailed, and has at least three appealing statistical properties, namely closure under conditioning, affine transformations, and marginalization. In this paper we propose a Bayesian computational approach based on a sequential Monte Carlo (SMC) sampler to estimate such distributions. The practical implementation of each step of the algorithm is discussed and the elicitation of prior distributions takes into consideration some unusual behaviour of the likelihood function and the corresponding Fisher information matrix. Using Monte Carlo simulations, we provide strong evidence regarding the performances of the SMC sampler as well as some new insights regarding the parametrizations of the extended skew-normal distribution. A generalization to the extended skew-normal sample selection model is also presented. Finally we proceed with the analysis of two real datasets.