Multiplicity adjustment for temporal and spatial scan statistics using Markov property

We discuss computation of the conditional expectation in a multinomial distribution. The problem is motivated by the evaluation of the multiplicity-adjusted p-value of scan statistics in spatial epidemiology. We propose a recursive summation/integration technique using the Markov property, which is extracted from a chordal graph defined by temporal and spatial structures. This methodology can be applied to a class of distributions, including the Poisson distribution (that is, the conditional distribution is the multinomial). To illustrate the approach, we present the real data analyses for detecting temporal and spatial clustering.

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