A calibration-based method in computing bayesian posterior distributions with applications in stock market

Abstract

Finding effective methods to compute or estimate posterior distributions of model parameters is of paramount importance in Bayesian statistics. In fact, Bayesian inference has only been extraordinarily popular in applications after the births of efficient algorithms like the Monte Carlo Markov Chain. Practicality of posterior distributions depends heavily on the combination of likelihood functions and prior distributions. In certain cases, closed-form formulas for posterior distributions can be attained; in this paper, based on the theory of distortion functions, a calibration-like method to calculate explicitly the posterior distributions for three crucial models, namely the normal, Poisson and Bernoulli is introduced. The paper ends with some applications in stock market.