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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 conditionaldoi:10.1007/s42081-018-0007-5 fatcat:ok4m2jlnojhu5alupicfc6ptcm