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In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.
Common Distance Measures. Learning Objectives. To consider a range of distance measures used with ecological data, and the types of data for which they are appropriate. To consider whether shared absences matter and how to deal with empty sample units. To continue using R.
We review the statistical properties of distances that are often used in scientific work, present their properties, and show how they compare to each other. We discuss an approximation framework for model-based inference using statistical distances.
1 The Fundamental Statistical Distances There are four notions of distance that have an elevated status in statistical theory. Let P;Q be two probability measures with densities pand q. 1. Total Variation: The TV distance between two distributions is: TV(P;Q) = sup A jP(A) Q(A)j= sup A j Z (p(x) q(x))dxj;
statistical divergence D[p : q] is a measure of dissimilarity between two densities p and q (i.e., a 2-point distance) such that D[p : q] 0 with equality if and only if p(x) = q(x) -almost everywhere. A statistical diversity index D(P) is a measure of variation of the weighted densities in.
Given a p-Wasserstein metric or an f-divergence, which is defined between two probability measures of the same dimension, we show that it naturally defines two different distances for probability measures μ and on spaces of different dimensions — we call these the embedding distance and projection distance respectively.
18 sty 2018 · We will say that ρ(τ, m) is a statistical distance between two probability distributions with densities τ, m if ρ(τ, m) ≥ 0, with equality if and only if τ and m are the same for all statistical purposes. Note that we do not require symmetry or the triangle inequality, so that ρ(τ, m) is not formally a metric. This is not a drawback ...
