REVERSIBLE JUMP MCMC METHOD FOR HIERARCHICAL BAYESIAN MODEL SELECTION IN MOVING AVERAGEMODEL
Keywords:Bayesian, Moving Average, Exponential Noise, Normal Noise, Reversible Jump MCMC
Moving average (MA) is one of the mathematical models that is often used to model data in various fields. Noise in the MA model is often assumed to be normally distributed. In application, it is often found that noise is exponentially distributed. The parameter of the MA model includes order, coefficient, and noise variance. This paper proposes a procedure to estimate the MA model parameter which contains noise with a normal and exponential distribution where the order is unknown. The estimation of parameters of the MA model parameter is carried out in a hierarchical Bayesian framework. Prior distribution for the parameter is selected. The likelihood function for data is combined with prior distribution for the parameter to get posterior distribution for the parameter. The parameter dimension is a combination of several different dimensional spaces so that the posterior distribution for a parameter has a complex form and the Bayes estimator cannot be determined explicitly. The reversible jump Markov Chain Monte Carlo (MCMC) method is proposed to determine the Bayes estimator of the MA model parameter. The performance of the method is tested using a simulation study. The simulation result shows that the reversible jump MCMC method estimates the MA model parameter well. The reversible jump MCMC method can calculate the MA model parameter simultaneously and produce an invertible MA model.