Estatística sequencial bayesiana dos parâmetros da distribuição multinomial

Abstract

Sampling is an important step in the process of estimating a parameter, which should have reduced cost and time. Thus, the use of sequential sampling, which has a variable sample size, evaluates each element at a time and permits the decision about when to stop sampling and estimate a parameter to be taken in advance, without having all elements evaluated as expected in the classic inference approach. In addition, bayesian decision theory can be incorporated into sequential sampling to perform parameter estimation, as this permits the inclusion of information about the parameter of interest beforehand, which helps take decisions and optimize the procedure. The greatest challenge of carrying out sequential bayesian estimation lies in the difficulty in establishing stopping criteria. Due to the inherent difficulty of the procedure, most of the works developed in this area are on the binomial distribution, and there are few works on the multinomial distribution. Therefore, the objective of this work is to define stopping criteria for the sequential bayesian estimation process of the multinomial distribution parameters. To validate the proposed methodology, a set of real count data was used, from the X-rays test for quality control of corn seed lots. Thus, the influence of two prioris on the stopping criterion was evaluated, a uniform one and another conjugate, with hyperparameters based on reference information from the literature, besides the cost per observation. The results obtained by the proposed methodology were compared with the frequentist and bayesian approach of parameter estimation, concluding that the sequential bayesian estimation had a good performance, and with the advantage of sample size reduction in most of the evaluated lots. Despite the smaller sample, the sequential bayesian estimation produced estimators that were equivalent or as good as the frequentists and bayesians.