Bayesian autoregressive adaptive refined descriptive sampling algorithm in the Monte Carlo simulation

Abstract

This paper deals with the Monte Carlo Simulation in a Bayesian framework. It shows the importance of the use of Monte Carlo experiments through refined descriptive sampling within the autoregressive model $ X_{t}=\rho X_{t-1}+Y_{t} $ , where $ 0 \lt \rho \lt 1 $ and the errors $ Y_{t} $ are independent random variables following an exponential distribution of parameter θ. To achieve this, a Bayesian Autoregressive Adaptive Refined Descriptive Sampling (B2ARDS) algorithm is proposed to estimate the parameters ρ and θ of such a model by a Bayesian method. We have used the same prior as the one already used by some authors, and computed their properties when the Normality error assumption is released to an exponential distribution. The results show that B2ARDS algorithm provides accurate and efficient point estimates.

Keywords

• monte carlo simulation
• refined descriptive sampling methods
• variance reduction
• autoregressive process
• bayesian estimation