ALMOST CONSISTENCY AND BAYES CONSISTENCY

This paper Consists of two parts. First we prove a theorem asserting that under the sole condition, that different parameter Values correspond to different distributiona, an "almost consistent" estimate of the para meter must exist. Further based on this result, we show, under very general conditions, that as the sample size tends to infinity, a Bayesian strategy must be "Bayesian Consistent" If we denote by R_n the Baysian risk of the Bayesian strategy with sample size n, then R_n \rightarrow \inf _\theta L\left(\theta_0 a\right), where L is the loss function, a runs over the action space and θ₀ is the true parameter.