Testing goodness of fit for point processes via topological data analysis

被引：14

作者：

Biscio, Christophe A. N. ^{[1
]}

Chenavier, Nicolas ^{[2
]}

Hirsch, Christian ^{[3
]}

Svane, Anne Marie ^{[1
]}

机构：

[1] Aalborg Univ, Dept Math Sci, Skjernvej 4, DK-9220 Aalborg O, Denmark

[2] Univ Littoral Cote dOpale, EA 2797, LMPA, 50 Rue Ferdinand Buisson, F-62228 Calais, France

[3] Univ Groningen, Bernoulli Inst, Nijenborgh 9, NL-68161 Groningen, Netherlands

来源：

ELECTRONIC JOURNAL OF STATISTICS | 2020年 / 14卷 / 01期

关键词：

Point processes; goodness-of-fit tests; central limit theorem; topological data analysis; persistent Betti number; GAUSSIAN LIMITS; CONVERGENCE;

D O I：

10.1214/20-EJS1683

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We introduce tests for the goodness of fit of point patterns via methods from topological data analysis. More precisely, the persistent Betti numbers give rise to a bivariate functional summary statistic for observed point patterns that is asymptotically Gaussian in large observation windows. We analyze the power of tests derived from this statistic on simulated point patterns and compare its performance with global envelope tests. Finally, we apply the tests to a point pattern from an application context in neuroscience. As the main methodological contribution, we derive sufficient conditions for a functional central limit theorem on bounded persistent Betti numbers of point processes with exponential decay of correlations.

引用

页码：1024 / 1074

页数：51

共 42 条

[1] Sharpness of the phase transition for continuum percolation in R2 [J].

Ahlberg, Daniel ;

Tassion, Vincent ;

Teixeira, Augusto .

PROBABILITY THEORY AND RELATED FIELDS, 2018, 172 (1-2) :525-581

[2]

[Anonymous], 2004, STAT INFERENCE SIMUL

[3]

[Anonymous], 2014, ARXIV PREPRINT ARXIV

[4] spatstat: An R package for analyzing spatial point patterns [J].

Baddeley, A ;

Turner, R .

JOURNAL OF STATISTICAL SOFTWARE, 2005, 12 (06) :1-42

[5] A CAUTIONARY EXAMPLE ON THE USE OF 2ND-ORDER METHODS FOR ANALYZING POINT PATTERNS [J].

BADDELEY, AJ ;

SILVERMAN, BW .

BIOMETRICS, 1984, 40 (04) :1089-1093

[6] Gaussian limits for random measures in geometric probability [J].

Baryshnikov, Y ;

Yukich, JE .

ANNALS OF APPLIED PROBABILITY, 2005, 15 (1A) :213-253

[7] CONVERGENCE CRITERIA FOR MULTIPARAMETER STOCHASTIC PROCESSES AND SOME APPLICATIONS [J].

BICKEL, PJ ;

WICHURA, MJ .

ANNALS OF MATHEMATICAL STATISTICS, 1971, 42 (05) :1656-&

[8]

Billingsley P., 1968, Convergence of Probability Measures

[9] The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications [J].

Biscio, Christophe A. N. ;

Moller, Jesper .

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, 2019, 28 (03) :671-681

[10] LIMIT THEORY FOR GEOMETRIC STATISTICS OF POINT PROCESSES HAVING FAST DECAY OF CORRELATIONS [J].

Blaszczyszyn, B. ;

Yogeshwaran, D. ;

Yukich, J. E. .

ANNALS OF PROBABILITY, 2019, 47 (02) :835-895

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