15 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…
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…
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…
Viola Priesemann, Oren Shriki, Francesco P. Battaglia
The finding of power law scaling in neural recordings lends support to the hypothesis of critical brain dynamics. However, power laws are not unique to critical systems and can arise from alternative mechanisms. Here, we investigate whether a common time-varying external drive to a set of Poisson units can give rise to…
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…
Sultan Hussain, Anwar Zeb, Akhter Rasheed, Tareq Saeed
This work is devoted to a stochastic model on the spread and control of corona virus (COVID-19), in which the total population of a corona infected area is divided into susceptible, infected, and recovered classes. In reality, the number of individuals who get disease, the number of deaths due to corona virus, and the…
Xuhua Xia, Daria Sanna
Classical branching-process theory, developed by Galton and Watson in the nineteenth century and later refined by Fisher and Haldane, provides the formal framework for quantifying the fate of new mutants, new viral and bacterial pathogens, new colonization of invasive species, etc. It is a powerful tool to quantify and…
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…
Moinak Bhaduri
Hidden Markov models (HMMs), especially those with a Poisson density governing the latent state-dependent emission probabilities, have enjoyed substantial and undeniable success in modeling natural hazards. Classifications among these hazards, induced through quantifiable properties such as varying intensities or…
Scott R Kegler
Injury-related mortality rate estimates are often analyzed under the assumption that case counts follow a Poisson distribution. Certain types of injury incidents occasionally involve multiple fatalities, however, resulting in dependencies between cases that are not reflected in the simple Poisson model and which can…
Paul J. Hurtado, Adam S. Kirosingh
In this paper we generalize the Linear Chain Trick (LCT; aka the Gamma Chain Trick) to help provide modelers more flexibility to incorporate appropriate dwell time assumptions into mean field ODEs, and help clarify connections between individual-level stochastic model assumptions and the structure of corresponding mean…
Neha Gupta, Arun Kumar, Nikolai Leonenko
In this article, we introduce the Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular, we discuss the space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Skellam process by independent stable…
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…
Noa Malem-Shinitski, César Ojeda, Manfred Opper, Udo Von Toussaint + 1 more
'Philip Broadbridge'] Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible…
Fangshu Cui, Bo Yuan
Background One central building block of population genetics is the fixation probability. It is a probabilistic understanding of the eventual fate of new mutations. Moreover, the fixation probability of new beneficial mutations plays an important effect on the adaptation of populations to environmental challenges.…