A study on the effect of the loss function on Bayesian estimation and posterior risk of binomial distribution

Abstract

The effect of different loss functions on Bayesian estimation and its posterior risk is studied in this paper. The definition of quasi-modified squared error loss function is proposed based on the modified squared error loss function, and the formulas of Bayesian estimation and its posterior risk under the quasi-modified squared error loss function are developed, respectively. Moreover, the Bayesian estimations and its posterior risks of binomial distribution parameter under different loss functions are introduced. Monte Carlo simulation and application examples are provided for illustrative purpose, and the results are compared on the basis of posterior risk and mean square error (MSE). Finally, the Bayesian estimations and the Bayesian credible intervals are obtained, respectively, by MCMC method (also using OpenBUGS).