Abstract
In a practical testing hypothesis, sample data is often used to construct testing rules for input information. It is empirically known that if we have small samples, we must compress or reduce the input information to obtain satisfactory results.
The paper discusses the above relation from a Bayesian theoretical point of view.
First, we take notice of the structural properties of the information and its compression form the probability theoretical point of view. Consequently, the effect of information compression on Bayesian testing rules and the relation to Bayes risk are presented.
As it is difficult to treat the risk theoretically, we introduce an information theoretical measure closely related to it. The measure enables us to evaluate the effect of information compression in a Bayesian testing hypothesis.
The structural properties of information and the above evaluation determine the rules for optimum information compression.
Finally, the effect of sample size on the optimum compression is made clear.
