Testing statistical hypothesis on random trees
Jorge R. Busch, Pablo A. Ferrari, Georgina Flesia, Ricardo Fraiman, Sebastian P. Grynberg · 2006
Abstract: To distinguish between populations of trees, we consider the hypothesis test proposed recently by Balding, Ferrari, Fraiman and Sued (BFFS–test). A direct approach to calculate effectively the test statistic is quite difficult, since it is based on a supremum defined over the space of all trees, which grows exponentially fast. We show how to transform this problem into a max-flow over a network which can be solved using a Ford Fulkerson algorithm in polynomial time on the maximal number of vertices of the random tree. We also describe conditions that imply the characterization of the measure by the marginal distributions of each node of the random tree, which validate the use of the BFFS– test for measure discrimination. The performance of the test is studied via simulations on Galton-Watson processes. 1