实体和物理建模讨论会(SPM)是国际会议系列,每年在实体建模协会(SMA),ACM SIGGRAPH和SIAM几何设计活动组的支持下举办。该会议的重点是几何和物理建模的各个方面,以及它们在设计、分析和制造以及生物医学、地球物理、数字娱乐和其他领域中的应用。该、 官网地址:http://dblp.uni-trier.de/db/conf/sma/

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The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its elements can take value 1 with a certain probability. Those probabilities are different for the $m$ elements across the $n$ random vectors, and form an $n \times m$ matrix with row sum equals to 1. We call this $n\times m$ matrix the success probability matrix (SPM). Each SPM uniquely defines a PMD. The PMD is useful in many areas such as, voting theory, ecological inference, and machine learning. The distribution functions of PMD, however, are usually difficult to compute. In this paper, we develop efficient methods to compute the probability mass function (pmf) for the PMD using multivariate Fourier transform, normal approximation, and simulations. We study the accuracy and efficiency of those methods and give recommendations for which methods to use under various scenarios. We also illustrate the use of the PMD via three applications, namely, in voting probability calculation, aggregated data inference, and uncertainty quantification in classification. We build an R package that implements the proposed methods, and illustrate the package with examples.

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