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Parameter Estimation of Multivariate Multiple Regression Model using Bayesian with Noninformative Jeffreys Prior

Last modified: 2017-07-05

#### Abstract

The main purpose of classical linear and multivariate multiple regression model is to estimate the parameters. Parameter estimation can be point and interval. Point estimation has two methods, the first method is frequentist (classical method). One of the classical approach techniques is maximum likelihood. The second method called Bayesian. Bayesian method use inference process in sample data taken from population and also considering the initial distribution (prior distribution). Information in prior distribution combine with sample data information through Bayes theorem and the result expressed as posterior distribution. Generally, selection of prior distribution based on information about parameters is available or not. This article discusse about parameter estimation of multivariate multiple regression model with the information about parameters isn’t available, so noninformative Jeffreys prior is used. Solution analytically to estimate the parameter of multivariate multiple Bayesian regression is difficult to determine. Therefore, Markov Chain Monte Carlo (MCMC) algorithm is used to estimate the parameters. Parameter estimation is done by determine prior and posterior distribution, then simulated by Gibbs Sampling algorithm. Jeffreys prior distribution of multivariate multiple regression given by . While posterior distribution for parameter μ is multivariate normal distribution and for parameter Σ is invers Wishart distribution .