Abstract
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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Acknowledgements
The authors are grateful to Takashi Tsuchiya, Anthony J. Hayter, Nobuki Takayama, and Yi-Ching Yao for their helpful comments. They also thank the Editor and the two referees for their constructive and insightful comments. This work was supported by JSPS KAKENHI Grant nos. 21500288 and 24500356.
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Kuriki, S., Takahashi, K. & Hara, H. Multiplicity adjustment for temporal and spatial scan statistics using Markov property. Jpn J Stat Data Sci 1, 191–213 (2018). https://doi.org/10.1007/s42081-018-0007-5
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DOI: https://doi.org/10.1007/s42081-018-0007-5