Fast numerical computation for multivariate distributions with combinatorial structure and its application to spatial epidemiology

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In spatial epidemiology, it is important to evaluate the multiplicity-adjusted p-value of scan statistics by taking their spatial correlations into account. However, it is difficult to conduct exact numerical calculation because high-dimensional integrations are required. On the other hand, Monte Carlo simulations cannot yield precise results. In our proposed method, we represent the spatial correlations of scan statistics as a graph, and by extracting its Markov structure, rewrite the high-dimensional integration as a successive numerical integration. Although, the proposed method reduces computational time of integration drastically, it is not powerful enough for the real datasets. More research is needed for practical use.