20 papers · ranked by Valyu relevance
David Lüdke, Enric Rabasseda Raventós, Marcel Kollovieh, Stephan Günnemann
'Stephan Günnemann'] Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning models for point processes are predominantly constrained by…
Archit Verma, Siddhartha G. Jena, Danielle R. Isakov, Kazuhiro Aoki + 2 more
Multi-cellular organisms rely on spatial signaling among cells to drive their organization, development, and response to stimuli. Several models have been proposed to capture the behavior of spatial signaling in multi-cellular systems, but existing approaches fail to capture both the autonomous behavior of single cells…
Marian-Andrei Rizoiu, Young Lee, Swapnil Mishra, Lexing Xie
This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point processes. We then introduce the Hawkes process, its event intensity function, as…
Dirk P. Kroese, Zdravko I. Botev
Spatial processes are mathematical models for spatial data; that is, spatially arranged measurements and patterns. The collection and analysis of such data is of interest to many scientific and engineering disciplines, including the earth sciences, materials design, urban planning, and astronomy. Examples of spatial…
Nazanin Mehrasa, Ruizhi Deng, Mohamed A. Ahmed, Bo Chang + 4 more
'Thibaut Durand' 'Marcus A. Brubaker' 'Greg Mori'] Event sequences can be modeled by temporal point processes (TPPs) to capture their asynchronous and probabilistic nature. We propose an intensity-free framework that directly models the point process distribution by utilizing normalizing flows. This approach is capable…
Jakob Gulddahl Rasmussen
These short lecture notes contain a not too technical introduction to point processes on the time line. The focus lies on defining these processes using the conditional intensity function. Furthermore, likelihood inference, methods of simulation and residual analysis for temporal point processes specified by a…
Sean Bellew, Ian Flint, Yan Wang
Poisson processes have become a prominent tool in species distribution modelling when analysing citizen science data based on presence records. This study examines four distinct statistical approaches, each of which utilises a different approximation to fit a Poisson point process. These include two Poisson regressions…
Edward Appau Nketiah, Chenlong Li, Weihua Yang, Yingchuan Jing + 2 more
Space-time self-exciting point process models are introduced to capture the clustering features in crime datasets. It does particularly well in modeling social network datasets, crime and security datasets, financial datasets, and seismic datasets. However, there has been limited analysis of large crime datasets using…
Adam J. Peterson
The inhomogeneous Poisson point process is a common model for time series of discrete, stochastic events. When an event from a point process is detected, it may trigger a random dead time in the detector, during which subsequent events will fail to be detected. It can be difficult or impossible to obtain a closed-form…
Pierre Brémaud
The theme of this article is the sampling of cluster and iterated cluster point processes. It is partially a review, mainly of the Brix–Kendall exact sampling method for cluster point processes and its adaptation by Møller and Rasmussen to Hawkes branching point processes on the real line with light-tail fertility…
Long Tao, Karoline E. Weber, Kensuke Arai, Uri T. Eden
A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For neural spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem to assess the statistical properties of rescaled spike times.…
Patrick F. Bloniasz, Shohei Oyama, Emily P. Stephen
Neural electrophysiological recordings arise from interacting rhythmic (oscillatory) and broadband (aperiodic) biological subprocesses. Both rhythmic and broadband processes contribute to the neural power spectrum, which decomposes the variance of a neural recording across frequencies. Although an extensive body of…
Jarosław Klamut, Tomasz Gubiec, Geert Verdoolaege, Rosario Nunzio Mantegna
'Rosario Nunzio Mantegna'] In many physical, social, and economic phenomena, we observe changes in a studied quantity only in discrete, irregularly distributed points in time. The stochastic process usually applied to describe this kind of variable is the continuous-time random walk (CTRW). Despite the popularity of…
Andi Kresna Jaya, Nurtiti Sunusi, Erna Tri Herdiani
The point process model effectively represents the number of random events occurring over time through its intensity function. When events are of two types, a bivariate point process allows simultaneous analysis of each event’s intensity. This study develops a conditional intensity model for a non-homogeneous bivariate…
Ali Yousefi, Mohammad Reza Rezaei, Kensuke Arai, Loren M. Frank + 1 more
There is an increasing demand for a computationally efficient and accurate point process filter solution for real-time decoding of population spiking activity in multidimensional spaces. Real-time tools for neural data analysis, specifically real-time neural decoding solutions open doors for developing experiments in a…
Carl P. Dettmann
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson…
Marco Raberto, Fabio Rapallo, Enrico Scalas, Matjaz Perc
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting…
Nathan Gold, Martin G. Frasch, Christophe L. Herry, Bryan S. Richardson + 1 more
Experimentally and clinically collected time series data are often contaminated with significant confounding noise, creating short, noisy time series. This noise, due to natural variability and measurement error, poses a challenge to conventional change point detection methods. We propose a novel and robust statistical…
Yuji Kaiya, Ryo Tamura, Koji Tsuda
Kinetic models are widely used in simulating the relationship between the input space and the outcome space of a chemical process. Ignoring the computational cost, complete profiling, i.e., performing simulation at all grid points in the input space, would be the best way to understand the model, because it provides us…
Authors not listed
Quantities calculated from molecular simulations are often subject to an initial bias due to unrepresentative starting configurations. Initial data are usually discarded to reduce bias. Chodera's method for automated truncation point selection [J. Chem. Theory Comput. 2016, 12, 4, 1799–1805] is popular but has not been…