摘要翻译:
目前文献中使用的有限点度量之间的大多数度量都有一个缺陷,即它们没有以适合应用的方式处理不同的总质量。本文引入了一个新的度量$\bar{d}_1$,它将最接近匹配下的点的位置差与总质量的相对差结合起来,以弥补这一缺陷。本文给出了关于点过程分布的$\bar{d}_1$及其诱导的Wasserstein度量$\bar{d}_2$的理论结果,包括有用的$\bar{d}_1$-Lipschitz连续函数的例子,泊松过程逼近的$\bar{d}_2$上界,以及I.I.d.点过程分布之间的$\bar{d}_2$上界和下界。分。此外,我们给出了一个多点模式数据的统计测试,证明了$\bar{d}_1$在应用中的潜力。
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英文标题:
《A new metric between distributions of point processes》
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作者:
Dominic Schuhmacher and Aihua Xia
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric $\bar{d}_1$ that combines positional differences of points under a closest match with the relative difference in total mass in a way that fixes this flaw. A comprehensive collection of theoretical results about $\bar{d}_1$ and its induced Wasserstein metric $\bar{d}_2$ for point process distributions are given, including examples of useful $\bar{d}_1$-Lipschitz continuous functions, $\bar{d}_2$ upper bounds for Poisson process approximation, and $\bar{d}_2$ upper and lower bounds between distributions of point processes of i.i.d. points. Furthermore, we present a statistical test for multiple point pattern data that demonstrates the potential of $\bar{d}_1$ in applications.
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PDF链接:
https://arxiv.org/pdf/708.2777