A Class of Selection Problems for which More Sampling is More Informative
研究了一类选择问题，其中从多元波利亚瓮中抽取样本以选出最大面额的子集，证明了增加样本量能提高正确选择的概率。
We study a class of selection problems for which the ‘more sampling-more information’ principle is true, but not obvious. The case examined, which includes sampling from a multinomial distribution and from a hypergeometric distribution as special cases, concerns a one-sample procedure to select an m-subset of the f largest denominations in a multivariate Polya urn. For a given sample size n, the selection procedure takes the m denominations with highest frequencies, where ties are broken by randomization. Let ψ(n) be the probability of making a correct selection when n is the sample size. According to the ‘more sampling-more information’ principle, we expect ψ(n+1)≥ψ(n) for all n > 0. This inequality is proved.