23 papers · ranked by Valyu relevance
Thomas A. Trikalinos, Yuliia Sereda, Abhik Ghosh
We introduce the nhppp package for simulating events from one dimensional non-homogeneous Poisson point processes (NHPPPs) in R fast and with a small memory footprint. We developed it to facilitate the sampling of event times in discrete event and statistical simulations. The package’s functions are based on three…
Pradeep Vishwakarma
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes. In particular, we propose and study a point process, namely, the generalized…
Thomas A Trikalinos, Yuliia Sereda
We introduce the nhppp package for simulating events from one dimensional nonhomogeneous Poisson point processes (NHPPPs) in R. Its functions are based on three algorithms that provably sample from a target NHPPP: the time-transformation of a homogeneous Poisson process (of intensity one) via the inverse of the…
Nicolas Lanchier
Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also true for multi-dimensional Poisson point processes. In contrast, the proof of…
Renaud Alie, David A. Stephens, Alexandra M. Schmidt
Many models for point process data are defined through a thinning procedure where locations of a base process (often Poisson) are either kept (observed) or discarded (thinned). In this paper, we go back to the fundamentals of the distribution theory for point processes and provide a colouring theorem that characterizes…
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…
Anand Srinivasan, Steph Hohn, Raymond E. Goldstein
Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly distributed and consistent with gamma distributions. We propose an explanation…
Peter Harremoës, Sebastian Deffner
Since the seminal work of Kolmogorov, probability theory has been based on measure theory, where the central components are so-called probability measures, defined as measures with total mass equal to 1. In Kolmogorov’s theory, a probability measure is used to model an experiment with a single outcome that will belong…
Wray Buntine, Narayanaswamy Balakrishnan
Hierarchical stochastic processes, such as the hierarchical Dirichlet process, hold an important position as a modelling tool in statistical machine learning, and are even used in deep neural networks. They allow, for instance, networks of probability vectors to be used in general statistical modelling, intrinsically…
Alexander Gnedin, Svante Janson, Yaakov Malinovsky
> We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collectors and dixie cup problems. We show that as the number of boxes tends to infinity, the distribution of the maximal occupancy count does…
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…
Lasse Leskelä
This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical formulas for Kullback–Leibler divergences, R´enyi divergences, Hellinger distances, and…
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…
Nicoletta D’Angelo, Giada Adelfio, Jorge Mateu, Ottmar Cronie
for spatial point pattern intensity estimation Authors: ['Nicoletta D’Angelo' 'Giada Adelfio' 'Jorge Mateu' 'Ottmar Cronie'] Second-order statistics play a crucial role in analysing point processes. Previous research has specifically explored locally weighted second-order statistics for point processes, offering…
Dani Gamerman, Marcel de Souza Borges Quintana, Mariane Branco Alves, Carlos Alberto De Bragança Pereira + 2 more
'Carlos Alberto De\xa0Bragança\xa0Pereira' 'Paulo Canas Rodrigues' 'Mark Andrew Gannon'] Many techniques have been proposed to model space-varying observation processes with a nonstationary spatial covariance structure and/or anisotropy, usually on a geostatistical framework. Nevertheless, there is an increasing…
Siyi Wang, Xu Wang, Chenlong Li, Augustine Wong + 1 more
Rampant terrorism poses a serious threat to the national security of many countries worldwide, particularly due to separatism and extreme nationalism. This paper focuses on the development and application of a temporal self-exciting point process model to the terror data of three countries: the US, Turkey, and the…
Authors not listed
Stochastic Simulation Algorithms (SSA) are a cornerstone in simulating Free Radical Polymerization (FRP) due to their accuracy and reliability. However, computational inefficiency remains a challenge for large-scale and complex polymerization systems. This work introduces a novel stochastic simulation algorithm…
Authors not listed
Relation between triple point temperature and the Rydberg constant based on the semi-phenomenological approach is found. To explain squared number 17 set in factor of proportionality, we use the Poisson distribution to be valid for some groups of thermal vibrations in pure water. We formulate a theorem explaining…
Authors not listed
Classical molecular dynamics (MD) simulation is the most computationally efficient way to model large molecular systems atomistically for extended periods; however, due to fixed forcefield parameters, incorporating on-the-fly quantum reactions is not straightforward. Reactive Step-Based Molecular Dynamics (RSMD) is a…
Murray G. Efford, David Fletcher
Spatially explicit capture–recapture models are used widely to estimate the density of animal populations. The population is represented by an inhomogeneous Poisson point process, where each point is the activity centre of an individual and density corresponds to the intensity surface. Estimates of density that assume…
Authors not listed
The screening of chemical libraries is an essential starting point in the drug discovery process. While some researchers desire a more thorough screening of drug targets against a narrower scope of molecules, it is not uncommon for diverse screening sets to be favored during early stages of drug discovery. However, a…
Fernando Alcalde Cuesta, Gustavo Guerberoff, Álvaro Lozano Rojo
In this paper, we study the absorption and fixation times for evolutionary processes on graphs, under different updating rules. While in Moran process a single neighbour is randomly chosen to be replaced, in proliferation processes other neighbours can be replaced using Bernoulli or binomial draws depending on 0 < p ≤…
Mark Sinzger-D’Angelo, Heinz Koeppl
Cellular processes are open systems, situated in a heterogeneous context, rather than operating in isolation. Chemical reaction networks (CRNs) whose reaction rates are modelled as external stochastic processes account for the heterogeneous environment when describing the embedded process. A marginal description of the…