1 research outputs found
Recursive computation for evaluating the exact -values of temporal and spatial scan statistics
Let be a finite set of indices, and let , , be subsets
of such that . Let , , be independent
random variables, and let . In this paper, we propose
a recursive computation method to calculate the conditional expectation
with
given, where is an arbitrary function. Our method is based on the
recursive summation/integration technique using the Markov property in
statistics. To extract the Markov property, we define an undirected graph whose
cliques are , and obtain its chordal extension, from which we present the
expressions of the recursive formula. This methodology works for a class of
distributions including the Poisson distribution (that is, the conditional
distribution is the multinomial). This problem is motivated from the evaluation
of the multiplicity-adjusted -value of scan statistics in spatial
epidemiology. As an illustration of the approach, we present the real data
analyses to detect temporal and spatial clustering.Comment: 23 pages, 7 figures, 3 table