Using Bayesian method to estimate the parameters of Exponential Growth Model with Autocorrelation problem and different values of parameter of correlation-using simulation

Abstract

We have studied Bayesian method in this paper by using the modified exponential growth model, where this model is more using to represent the growth phenomena. We focus on three of prior functions (Informative, Natural Conjugate, and the function that depends on previous experiments) to use it in the Bayesian method. Where almost of observations for the growth phenomena are depended on one another, which in turn leads to a correlation between those observations, which calls to treat such this problem, called Autocorrelation, and to verified this has been used Bayesian method.

The goal of this study is to knowledge the effect of Autocorrelation on the estimation by using Bayesian method. For verifying the goal has been used the simulation technique where has been generated random samples with known parameters and different values of correlation. It has been shown from the computational results that all result has been affected by the values of correlation coefficients used to generate the data, and there is a clear proof and regularity of the sensitivity for Bayesian estimators by Autocorrelation with increase the size of sample.