Modeling, Statistical Analyses and Simulations of Random Items and Behavior on Material Surfaces

Helisová, Kateřina

doi:10.1002/9781118889879.ch56

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…From the relations (9) and (10), it follows that the mentioned N-distance can be expressed as a limit of integrals of negative definite kernel L n , n ∈ N defined by (8). Suppose that the measure µ on l 0 takes the form of µ g defined by relation (6) and that A n = ι 1,...,n (R n ), n ∈ N. Let A and B be two realisations of random convex compact sets, and suppose we know the values of their support functions h(A, u 1 ), .…”

Section: Approximation Of N-distance Based On Samplementioning

confidence: 99%

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Testing equality in distribution of random convex compact sets via theory of N-distances and its application to assessing similarity of general random sets

Gotovac,

Helisová

2018

Preprint

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This paper concerns a method of testing equality of distribution of random convex compact sets and the way how to use the test to distinguish between two realisations of general random sets. The family of metrics on the space of distributions of random convex compact sets is constructed using the theory of N-distances and characteristic functions of random convex compact sets. Further, the approximation of the metrics through its finite dimensional counterparts is proposed, which lead to a new statistical test for testing equality in distribution of two random convex compact sets. Then, it is described how to approximate a realisation of a general random set by a union of convex compact sets, and it is shown how to determine whether two realisations of general random sets come from the same process using the constructed test. The procedure is justified by an extensive simulation study.

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Section: Approximation Of N-distance Based On Samplementioning

confidence: 99%

“…They can describe and explain many events, e.g. behaviour of cells in organisms (see [16], [9]), particles in materials (see [8], [21]) or presence of different plants (see [3], [19]). Therefore it is useful to develop methods for their statistical analyses.…”

Section: Introductionmentioning

confidence: 99%

Testing equality in distribution of random convex compact sets via theory of N-distances and its application to assessing similarity of general random sets

Gotovac,

Helisová

2018

Preprint

Self Cite

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“…In recent years, random sets have been developed as a valuable tool for modelling various phenomena in many fields of science such as dynamics of cells in organisms (Mrkvička and Mattfeldt, 2011;Hermann et al, 2015), presence of different plants in ecosystems (Diggle, 1981;Møller and Helisová, 2010) or particles in materials (Helisová, 2014;Neumann et al, 2016). In order to describe and explain these events, a wide range of random set models are introduced.…”

Section: Introductionmentioning

confidence: 99%

Similarity Between Random Sets Consisting of Many Components

Đogaš

2019

Image Anal Stereol

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Random sets play an essential role in modelling several phenomena in biology, medicine and material science. However, sometimes it is hard to describe them using a specific model. Therefore it can also be difficult to classify them or to compare their realisations. This contribution proposes a similarity measure between two random sets whose realisations consist of many components based on just one realisation of each of them. The similarity measure is obtained in a non-parametric way taking into account the shapes and the positions of the components. The procedure is justified by a simulation study and consequently applied to real biomedical data of histological images of mammary tissue.

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“…As a model, random sets can describe and explain many events. Some examples are dynamics of cells in organisms (Mrkvička and Mattfeldt, 2011;Hermann et al, 2015), particles in materials (Helisová, 2014;Neumann et al, 2016) or the presence of different plants in ecosystems (Diggle, 1981;Møller and Helisová, 2010).…”

Section: Introductionmentioning

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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Modeling, Statistical Analyses and Simulations of Random Items and Behavior on Material Surfaces

Cited by 4 publications

References 8 publications

Testing equality in distribution of random convex compact sets via theory of N-distances and its application to assessing similarity of general random sets

Testing equality in distribution of random convex compact sets via theory of N-distances and its application to assessing similarity of general random sets

Similarity Between Random Sets Consisting of Many Components

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

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