Searching for a trail of evidence in a maze
Searching for a trail of evidence in a maze
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DOI：
10.1214/07-aos526
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发表时间：
2008-08-01
影响因子：
4.5
通讯作者：
Zeitouni, Ofer
中科院分区：
文献类型：
--
作者：
Arias-Castro, Ery;Candes, Emmanuel J.;Zeitouni, Ofer
考虑一个带有一组顶点的图形和连接顶点对的方向边缘。每个顶点与随机变量相关联，并且假定它们是独立的。在这种情况下，假设我们希望解决以下假设测试问题：在零下，随机变量具有共同的分布n（0，1）而在替代方案下，有一个未知路径，随机变量具有分布n（MU） ，1），MU> 0，分布n（0，1）远离它。对于均值移动的哪个值，MU可以可靠地检测到这是不可能的值，例如，考虑到form {（i，j）的顶点的通常的常规晶格，而它们是root logm，而它们是root logm如果MU（M）不
Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following hypothesis testing problem: under the null, the random variables have common distribution N(0, 1) while under the alternative, there is an unknown path along which random variables have distribution N(mu, 1), mu > 0, and distribution N(0, 1) away from it. For which values of the mean shift mu can one reliably detect and for which values is this impossible?Consider, for example, the usual regular lattice with vertices of the form{(i, j) : 0 1/root logm, while they are not if mu(m)