Marked Gibbs Point Processes with Unbounded Interaction: An Existence Result
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DOI: 10.1007/s10955-020-02559-3
Abstract: We construct marked Gibbs point processes in $${\mathbb {R}}^d$$ R d under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded.… read more here.
Keywords: point processes; processes unbounded; marked gibbs; interaction ... See more keywords
Construction of computer experiment designs using marked point processes
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DOI: 10.1007/s13370-020-00770-9
Abstract: This article offers a method for building computer experiment designs. This method is based on the theory of marked point processes, otherwise known as object processes. Those designs rely on both the distribution of points… read more here.
Keywords: point processes; computer experiment; marked point; experiment designs ... See more keywords
Cluster Expansions for GIBBS Point Processes
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DOI: 10.1017/apr.2019.46
Abstract: Abstract We provide a sufficient condition for the uniqueness in distribution of Gibbs point processes with non-negative pairwise interaction, together with convergent expansions of the log-Laplace functional, factorial moment densities and factorial cumulant densities (correlation… read more here.
Keywords: point processes; gibbs point; cluster expansions; expansions gibbs ... See more keywords
Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes
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DOI: 10.1017/etds.2020.123
Abstract: Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by… read more here.
Keywords: point processes; point; translation invariant; invariant kernels ... See more keywords
Local inhomogeneous weighted summary statistics for marked point processes
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Computational and Graphical Statistics"
DOI: 10.1080/10618600.2023.2206441
Abstract: We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture different kinds… read more here.
Keywords: weighted summary; marked point; local inhomogeneous; summary statistics ... See more keywords
ESCIP: An Expansion-Based Spatial Clustering Method for Inhomogeneous Point Processes
Sign Up to like & getrecommendations! Published in 2019 at "Annals of the American Association of Geographers"
DOI: 10.1080/24694452.2019.1625747
Abstract: Detecting irregularly shaped spatial clusters within heterogeneous point processes is challenging because the number of potential clusters with different sizes and shapes can be enormous. This research develops a novel method, expansion-based spatial clustering for… read more here.
Keywords: point processes; expansion based; method; spatial clustering ... See more keywords
Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes
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DOI: 10.1093/imrn/rnz168
Abstract: We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in various random matrix and statistical physics models.… read more here.
Keywords: gap; painlev hierarchy; point processes; solutions painlev ... See more keywords
Rate-Distortion Theory of Finite Point Processes
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DOI: 10.1109/tit.2018.2829161
Abstract: We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of… read more here.
Keywords: point processes; point; rate distortion; theory ... See more keywords
Local Entropy Statistics for Point Processes
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DOI: 10.1109/tit.2019.2941213
Abstract: Point processes are often described with functionals, such as the probability generating functional, the Laplace functional, and the factorial cumulant generating functional. These are used to facilitate modelling of different processes and to determine important… read more here.
Keywords: statistics point; local entropy; generating functional; point processes ... See more keywords
A Cramér Rao Bound for Point Processes
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DOI: 10.1109/tit.2022.3140374
Abstract: The Cramér Rao bound provides a minimum achievable variance or covariance for a parameter for a univariate or vector-valued parameter. Point processes often have parameters that are described by functions and the variance and covariance… read more here.
Keywords: cram rao; point processes; rao bound;
Imitation Learning of Neural Spatio-Temporal Point Processes
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Transactions on Knowledge and Data Engineering"
DOI: 10.1109/tkde.2021.3054787
Abstract: We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite the rapid… read more here.
Keywords: imitation learning; spatio temporal; model; point processes ... See more keywords