Multiple Monte Carlo testing, with applications in spatial point processes

Mrkvička, Tomáš; Myllymäki, Mari; Hahn, Ute

doi:10.1007/s11222-016-9683-9

Cited by 31 publications

(31 citation statements)

References 41 publications

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“…(The combined test function is simply a concatenation ofK 1 andK 2 . Mrkvička et al (2017) recommended using such a combination rather thanK 1 orK 2 as a test function.) Specifically, we consider a homogeneous LGCP X driven by a random field Λ(y, u) = ρ exp{Z(y, u)}, where ρ > 0 and…”

Section: Simulation Studymentioning

confidence: 99%

“…For one-dimensional test functions, Myllymäki et al (2017) recommend using 2499 simulations to perform a global rank envelope test, and Mrkvička et al (2017) discuss the appropriate number of simulations when using a multivariate test function (as the empirical space-sphere K-function). In Section 6.2, we used 49999 simulations for the global rank envelope test based onK, sinceK had steep jumps.…”

Section: Simulation Studymentioning

confidence: 99%

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Structured Space-Sphere Point Processes and K-Functions

Møller

Christensen

Cuevas-Pacheco

et al. 2019

Methodol Comput Appl Probab

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This paper concerns space-sphere point processes, that is, point processes on the product space of R d (the d-dimensional Euclidean space) and S k (the kdimensional sphere). We consider specific classes of models for space-sphere point processes, which are adaptations of existing models for either spherical or spatial point processes. For model checking or fitting, we present the space-sphere K-function which is a natural extension of the inhomogeneous K-function for point processes on R d to the case of space-sphere point processes. Under the assumption that the intensity and pair correlation function both have a certain separable structure, the space-sphere K-function is shown to be proportional to the product of the inhomogeneous spatial and spherical K-functions. For the presented space-sphere point process models, we discuss cases where such a separable structure can be obtained. The usefulness of the space-sphere K-function is illustrated for real and simulated datasets with varying dimensions d and k.

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Section: Simulation Studymentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

Structured Space-Sphere Point Processes and K-Functions

Møller

Christensen

Cuevas-Pacheco

et al. 2019

Methodol Comput Appl Probab

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“…We remark that the sample cross K-function is estimated for a given number of arguments (50 in our study), which results in the same number of simultaneous Monte Carlo tests. The multiple correction was resolved in our study by the global envelope test Mrkvička et al, 2017). Due to this multiple testing correction and the fact that the cross K-function summarizes the information from some neighborhood of the observed points (which was not the case for the sample covariance of two random fields) the variance correction tests are conservative and less powerful than the torus correction approach, as shown in the simulation study below.…”

Section: Point Process Casementioning

confidence: 99%

Revisiting the random shift approach for testing in spatial statistics

Mrkvička¹,

Dvořák²,

González³

et al. 2021

Spatial Statistics

Self Cite

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We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality caused by breaking the marginal spatial correlation structure due to the toroidal correction. This indeed causes that the assumption of exchangability, which is essential for the Monte Carlo test to be exact, is not fulfilled.We present a number of permutation strategies and show that the random shift with the variance correction brings a suitable improvement compared to the torus correction in the random field case. It reduces the liberality and achieves the largest power from all investigated variants. To obtain the variance for the variance correction method, several approaches were studied. The best results were achieved, for the sample covariance as the test statistics, with the correction factor 1/n. This corresponds to the asymptotic order of the variance of the test statistics.In the point process case, the problem of deviations from exchangeability is far more complex and we propose an alternative strategy based on the mean cross nearest-neighbor distance and torus correction. It reduces the liberality but achieves slightly lower power than the usual cross K-function. Therefore we recommend it, when the point patterns are clustered, where the cross Kfunction achieves liberality.

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“…In this section, we introduce a tool (test) used for testing equality of distributions of random geometrical objects recently developed by Myllymäki et al (2016) and Mrkvička et al (2015). Also, we describe the customization of the test to fit our needs.…”

Section: Envelope Testsmentioning

confidence: 99%

“…Thus we do not explicitly have only one characteristic T 1 (ϕ) to be compared to T k (ϕ), k = 2, ..., s + 1. Therefore we decided to use a permutation version of the above-mentioned test to attain functional ANOVA procedure (Mrkvička et al, 2015). It works as follows.…”

Section: The Width Of the Interval Between P + And P − Ismentioning

confidence: 99%

Assessing Dissimilarity of Random Sets Through Convex Compact Approximations, Support Functions and Envelope Tests

2016

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In recent years random sets were recognized as a valuable tool in modelling different processes from fields like biology, biomedicine or material sciences. Nevertheless, the full potential of applications has not still been reached and one of the main problems in advancement is the usual inability to correctly differentiate between underlying processes generating real world realisations. This paper presents a measure of dissimilarity of stationary and isotropic random sets through a heuristic based on convex compact approximations, support functions and envelope tests. The choice is justified through simulation studies of common random models like Boolean and Quermass-interaction processes.

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Multiple Monte Carlo testing, with applications in spatial point processes

Abstract: The rank envelope test (Myllymäki et al., Global

Cited by 31 publications

References 41 publications

Structured Space-Sphere Point Processes and K-Functions

Structured Space-Sphere Point Processes and K-Functions

Revisiting the random shift approach for testing in spatial statistics

Assessing Dissimilarity of Random Sets Through Convex Compact Approximations, Support Functions and Envelope Tests

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