Bayesian Inference for the Geometric Skew Normal Distribution

Srinivasan, Narayan (2021) Bayesian Inference for the Geometric Skew Normal Distribution. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Narayan Srinivasan (16MS153)) 16MS153_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (478kB)

Abstract

The need to model skewed data has given rise to several skewed probability distributions. However, one of the most commonly used distributions the Skew Normal Distribution proposed by Azzalini(1985)[1] has several problems with Maximum Likelihood Estimation of the parameters. Kundu(2014)[6] has proposed an alternate distribution,the Geometric Skew Normal distribution for modelling skewed data. In This masters project , we first discuss the Skew Normal distribution proposed by Azzalini(1985). Furthermore, we briefly discuss the problem of MLE estimation of the parameters of the Skew Normal distribution and the advantages of a Bayesian scheme of inference. Second, we present a overwiev of Bayesian inference and discuss MCMC based inference and Va riational Inference. Finally, we propose two Bayesian schemes for inference of the parameters of the Geometric Skew Normal distribution. The first, is a MCMC based approach using the Metropolis Hastings algorithm and the second, is a approximate inference method using Variational Bayes. Simulation studies were performed on generated to verify the convergence of the Bayesian scheme of the proposed MCMC algorihtms.

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