Discrete Approximation of a Mixture Distribution via Restricted Divergence

Mixture distributions arise in many application areas, for example, as marginal distributions or convolutions of distributions. We present a method of constructing an easily tractable discrete mixture distribution as an approximation to a mixture distribution with a large to infinite number, discrete or continuous, of components. The proposed DIRECT (divergence restricting conditional tesselation) algorithm is set up such that a prespecified precision, defined in terms of Kullback–Leibler divergence between true distribution and approximation, is guaranteed. Application of the algorithm is demonstrated in two examples. Supplementary materials for this article are available online.

混合分布在诸多应用领域中均有出现，例如作为边缘分布或分布的卷积形式。我们提出一种构造易于处理的离散混合分布的方法，用以近似分量数量从大量直至无穷（涵盖离散与连续分量）的混合分布。所提出的散度约束条件细分（DIRECT, divergence restricting conditional tesselation）算法的设计目标为：确保达到基于真实分布与近似分布间的库尔贝克-莱布勒散度（Kullback–Leibler divergence）定义的预设精度。本文通过两个示例演示了该算法的应用。本文的补充材料可在线获取。