Stopping rules based on a posteriori probability for every pattern and every stage

The algorithms for pattern recognition systems considering the observation cost from the viewpoint of the system, can be re duced to the problems of stopping rule in which we must determine when the observation should be stopped. As the stopping rule in the Bayesian pattern recognition, methods based on DP search first given by K. S. Fu et al. is known to be the optimum in the sense of the minimum risk. A problem in those methods is that an exponential amount of data must be stored in memory for each observation stage, which is hard to realize. This paper discusses the new class of stopping rules, where the optimum thresholds based on a posteriori probability are chosen for each pattern and for each stage. the proposed method is not applicable to the problem where the patterns have strong correlations in the observed values along each dimension, but it can realize almost the same performance from the viewpoint of the minimum risk, while eliminating the number of parameters to be stored. the method also provides a model for the conventional method to set the border for the likelihood ratio when the a priori probabilities of the patterns are distributed uniformly.