Bootstrap and permutation tests of independence for point processes

Albert, Mélisande; Bouret, Yann; Fromont, Magalie; Reynaud-Bouret, Patricia

doi:10.1214/15-aos1351

Cited by 22 publications

(36 citation statements)

References 70 publications

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“…In particular, notice that considering such rank statistics is equivalent to considering uniformly permuted statistics. In [ABFRB15], the previous combinatorial central limit theorems is generalized to permuted sums of non-i.i.d. random variables n i=1 Y i,Πn(i) , for particular forms of random variables Y i,j .The main difference with the previous results comes from the fact that the random variables Y i,j are not necessarily exchangeable.…”

Section: Introductionmentioning

confidence: 99%

“…random variables n i=1 Y i,Πn(i) , for particular forms of random variables Y i,j .The main difference with the previous results comes from the fact that the random variables Y i,j are not necessarily exchangeable. Hence, the asymptotic behavior of permuted sums have been vastly investigated in the literature, allowing to deduce good properties for permutation tests based on such statistics, like the asymptotic size, or the power (see for instance [Rom89] or [ABFRB15]). Yet, such results are purely asymptotic, while, in many application fields, such as neurosciences for instance as described in [ABFRB15], few exploitable data are available.…”

Section: Introductionmentioning

confidence: 99%

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Concentration Inequalities for Randomly Permuted Sums

Albert

2019

Progress in Probability

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Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et al. proved a new Bernstein-type concentration inequality based on martingale theory. This work presents a new proof of this inequality based on the fundamental inequalities for random permutations of Talagrand. The idea is to first obtain a rough inequality for the square root of the permuted sum, and then, iterate the previous analysis and plug this first inequality to obtain a general concentration of permuted sums around their median. Then, concentration inequalities around the mean are deduced. This method allows us to obtain the Bernstein-type inequality up to constants, and, in particular, to recovers the Gaussian behavior of such permuted sums under classical conditions encountered in the literature. Then, an application to the study of the second kind error rate of permutation tests of independence is presented.Mathematics Subject Classification: 60E15, 60C05.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Concentration Inequalities for Randomly Permuted Sums

Albert

2019

Progress in Probability

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“…Even if our test remains empirically reliable under a non‐Poissonian framework, it could be therefore of interest to explore surrogate data method such as trial‐shuffling (Pipa et al., ). A very recent work based on permutation approach for delayed coincidence count with

n = 2

neurons (Albert et al., ) is a first step in this direction but needs to be generalized to more than two neurons.…”

Section: Resultsmentioning

confidence: 99%

“…Note that the dependence with respect to the parameter δ has been fully discussed in Albert et al. ().…”

Section: Illustration Study: Poissonian Frameworkmentioning

confidence: 97%

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Detection of dependence patterns with delay

Chevallier

Laloë

2015

Biometrical J

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The Unitary Events (UE) method is a popular and efficient method used this last decade to detect dependence patterns of joint spike activity among simultaneously recorded neurons. The first introduced method is based on binned coincidence count (Grün, 1996) and can be applied on two or more simultaneously recorded neurons. Among the improvements of the methods, a transposition to the continuous framework has recently been proposed in (Muiño and Borgelt, 2014) and fully investigated in for two neurons. The goal of the present paper is to extend this study to more than two neurons. The main result is the determination of the limit distribution of the coincidence count. This leads to the construction of an independence test between L ≥ 2 neurons. Finally we propose a multiple test procedure via a Benjamini and Hochberg approach (Benjamini and Hochberg, 1995). All the theoretical results are illustrated by a simulation study, and compared to the UE method proposed in (Grün et al., 2002). Furthermore our method is applied on real data.Mathematical Subject Classification. 62M07, 62F03, 62H15, 62P10.

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Using the multivariate Hawkes process to study interactions between multiple species from camera trap data

Nicvert,

Donnet,

Keith

et al. 2024

Ecology

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Interspecific interactions can influence species' activity and movement patterns. In particular, species may avoid or attract each other through reactive responses in space and/or time. However, data and methods to study such reactive interactions have remained scarce and were generally limited to two interacting species. At this time, the deployment of camera traps opens new opportunities but adapted statistical techniques are still required to analyze interaction patterns with such data. We present the multivariate Hawkes process (MHP) and show how it can be used to analyze interactions between several species using camera trap data. Hawkes processes use flexible pairwise interaction functions, allowing us to consider asymmetries and variations over time when depicting reactive temporal interactions. After describing the theoretical foundations of the MHP, we outline how its framework can be used to study interspecific interactions with camera trap data. We design a simulation study to evaluate the performance of the MHP and of another existing method to infer interactions from camera trap‐like data. We also use the MHP to infer reactive interactions from real camera trap data for five species from South African savannas (impala Aepyceros melampus, greater kudu Tragelaphus strepsiceros, lion Panthera leo, blue wildebeest Connochaetes taurinus and Burchell's zebra Equus quagga burchelli). The simulation study shows that the MHP can be used as a tool to benchmark other methods of interspecific interaction inference and that this model can reliably infer interactions when enough data are considered. The analysis of real data highlights evidence of predator avoidance by prey and herbivore–herbivore attraction. Lastly, we present the advantages and limits of the MHP and discuss how it can be improved to infer attraction/avoidance patterns more reliably. As camera traps are increasingly used, the multivariate Hawkes process provides a promising framework to decipher the complexity of interactions structuring ecological communities.

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Bootstrap and permutation tests of independence for point processes

Cited by 22 publications

References 70 publications

Concentration Inequalities for Randomly Permuted Sums

Concentration Inequalities for Randomly Permuted Sums

Detection of dependence patterns with delay

Using the multivariate Hawkes process to study interactions between multiple species from camera trap data

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