文章基本信息

标题：On geometric probability distributions on the torus with applications to molecular biology
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作者：Alessandro Selvitella
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：2717-2763
DOI：10.1214/19-EJS1579
语种：English
出版社：Institute of Mathematical Statistics
摘要：In this paper, we study a family of probability distributions, alternative to the von Mises family, called Inverse Stereographic Normal Distributions. These distributions are counterparts of the Gaussian Distribution on $\mathbb{S}^{1}$ (univariate) and $\mathbb{T}^{n}$ (multivariate). We discuss some key properties of the models, such as unimodality and closure with respect to marginalizing and conditioning. We compare this family of distributions to the von Mises’ family and the Wrapped Normal Distribution. Then, we discuss some inferential problems, introduce a notion of moments which is natural for inverse stereographic distributions and revisit a version of the CLT in this context. We construct point estimators, confidence intervals and hypothesis tests and discuss briefly sampling methods. Finally, we conclude with some applications to molecular biology and some illustrative examples. This study is motivated by the Protein Folding Problem and by the fact that a large number of proteins involved in the DNA-metabolism assume a toroidal shape with some amorphous regions.
关键词：Distributions on manifolds; von Mises distributions; inverse stereographic distributions; molecular biology; protein folding problem; DNA-metabolism