Consistency of the maximum likelihood estimator and Bayesian estimator based on sequential sensitivity experiments

It is often of interest to estimate parameters of a response curve based on sequential sensitivity experiments. However, there is no general method to establish consistency of the maximum likelihood estimators or Bayesian estimators. In this paper, we focus on a general sequential design with a general parametric model. Under mild conditions, we prove the consistency of the estimators. Also we give a higher order approximation for the posterior expectation.