A BAYES TEST OF P LESS THAN OR EQUAL TO 1/2 VERSUS P >1/2
Sigeiti Moriguti, Herbert E. Robbins · 1961
Abstract : Consider the following sequential decision problem:--An urn contains white and black balls, the proportion p of black balls being unknown, 0 < p < 1. A single ball is to be drawn at random from the urn tomorrow and we must guess its color; it our guess is correct we are to receive a reward of $ A, and if incorrect we are to receive nothing. In order to obtain some information about p we are allowed to draw as many balls as we like from the urn today, one at a time and with replacement, observing the color of each ball drawn, but for each such ball drawn we must pay $ 1. Problem: how many balls should we observe today and what color should we then predict for the ball to be drawn tomorrow. (Author)