Estimation of multinomial distribution parameters using the Bayesian sequential approach: a simulation study

This work investigates, through simulation studies, the behavior of the Bayesian sequential approach for estimating the parameters of the multinomial distribution under different prior distributions, decision penalty costs and parameter configurations, with emphasis on estimation accuracy and required sample size. The proposed approach extends Bayesian sequential estimation for the multinomial case to the use of any conjugate Dirichlet prior. The stopping criterion for sequential sampling is established using decision theory. The results show that more informative priors generally provide greater estimation accuracy, while the decision penalty cost has a substantial effect on the required sample size. For scenarios aimed at reducing the required sample size, costs of 10−4, combined with more informative priors, resulted in smaller sample sizes while maintaining satisfactory estimation accuracy. These results indicate that the proposed Bayesian sequential approach can reduce the number of observations required for multinomial parameter estimation, with the choice of the decision penalty cost and prior specification playing an important role in the resulting sample size.