Bayes theorem, information number and behavior of posteior distributions

Summary

According to the sequential decision theory, one is directed to; (i) stop when the posterior distribution, having been successively watched, frist enters the domain in which by stopping he loses less, and then (ii) take that action which gives him the least loss averaged w.r.t. the current posterior distribution (Blackwell-Girshick [1], p. 254).

For some reasons we don't know, however, the successive behavior of posterior distribution never draws the full attention of statisticians and probabilists, though some of them have developed the asymptotic theory. As far as the sequential decision theory is concerned, however, the asymptotic behavior tells us nothing, since the stopping rule is only related to finite time.

Toe compute the posterior distribution time by time is a laborious task. But to site all possible posterior distributions sometimes facilitates our manipulation of the sequential decision problem. This paper proposes some methods.