Bayesian sequential estimation of the proportion of damage in maize seeds

ABSTRACT Sampling is an essential step in estimating a parameter: thus, cost and time associated to this step should be minimized. Sequential sampling is characterized by using samples of variable sizes given as a function of observations, and sequential sampling provides a smaller sample size than a fixed-size sample in most cases. In addition, the Bayesian decision theory can be incorporated into sequential sampling to perform parameter estimation because it allows the inclusion of a priori information about the parameter of interest, which optimizes the procedure. However, the great challenge to performing the Bayesian sequential estimation in establishing the stopping criteria. Most studies in this area investigate binomial distributions, while few analyze multinomial distributions. This study aimed to define the stopping criteria for the Bayesian sequential estimation of the parameters of multinomial distributions with conjugate Dirichlet priors. The proposed methodology was applied to a set of X-ray test data for quality control of maize seed lots. This test uses conventional sampling techniques in which a sample has a fixed size with 200 seeds. The influence of two priors on the stopping criteria was evaluated, one uniform and one conjugate, with hyperparameters based on reference information from the literature. The results indicated a reduction in the sample size in most lots evaluated.