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A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…

Statistics Theory · Mathematics 2024-06-11 Antonio Di Noia , Marzia Marcheselli , Caterina Pisani , Luca Pratelli

The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches:…

Geophysics · Physics 2007-05-23 C. Godano , L. de Arcangelis

Causality plays a central role in understanding interactions between variables in complex systems. These systems often exhibit state-dependent causal relationships, where both the strength and direction of causality vary with the value of…

Data Analysis, Statistics and Probability · Physics 2025-08-05 Álvaro Martínez-Sánchez , Adrián Lozano-Durán

This paper discusses different needs and approaches to establishing ``causation'' that are relevant in legal cases involving statistical input based on epidemiological (or more generally observational or population-based) information. We…

Methodology · Statistics 2009-09-29 K. Mengersen , S. A. Moynihan , R. L. Tweedie

In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential…

Probability · Mathematics 2018-06-28 V. Yu. Korolev , A. K. Gorshenin , S. K. Gulev , K. P. Belyaev , A. A. Grusho

Many causal processes have spatial and temporal dimensions. Yet the classic causal inference framework is not directly applicable when the treatment and outcome variables are generated by spatio-temporal point processes. We extend the…

Methodology · Statistics 2022-06-09 Georgia Papadogeorgou , Kosuke Imai , Jason Lyall , Fan Li

We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as…

Probability · Mathematics 2026-03-24 Nikolaos Kolliopoulos , Martin Larsson , Zeyu Zhang

The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…

Methodology · Statistics 2025-07-15 Jimmy Lederman , Aaron Schein

We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…

Statistics Theory · Mathematics 2013-05-09 Paul Doukhan , William Kengne

Conflict prediction is a vital component of path planning for autonomous vehicles. Prediction methods must be accurate for reliable navigation, but also computationally efficient to enable online path planning. Efficient prediction methods…

Robotics · Computer Science 2023-02-28 Christian E. Roelofse , Corné E. van Daalen

We describe and contrast two distinct problem areas for statistical causality: studying the likely effects of an intervention ("effects of causes"), and studying whether there is a causal link between the observed exposure and outcome in an…

Statistics Theory · Mathematics 2021-04-02 A. Philip Dawid , Monica Musio

We investigate structural features and processes associated with the onset of systemic conflict using an approach which integrates complex systems theory with network modeling and analysis. We present a signed network model of cooperation…

Social and Information Networks · Computer Science 2022-03-10 Megan Morrison , J. Nathan Kutz , Michael Gabbay

Causal inference with interference is a rapidly growing area. The literature has begun to relax the "no-interference" assumption that the treatment received by one individual does not affect the outcomes of other individuals. In this paper…

Methodology · Statistics 2015-03-06 Tyler J. VanderWeele , Eric J. Tchetgen Tchetgen , M. Elizabeth Halloran

The perceived randomness in the time evolution of "chaotic" dynamical systems can be characterized by universal probabilistic limit laws, which do not depend on the fine features of the individual system. One important example is the…

Mathematical Physics · Physics 2016-09-21 Carl P. Dettmann , Jens Marklof , Andreas Strömbergsson

We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system…

Chaotic Dynamics · Physics 2021-04-26 Konstantin Clauß , Felix Kunzmann , Arnd Bäcker , Roland Ketzmerick

Analysis of wars and conflicts between regions has been an important topic of interest throughout the history of humankind. In the latter part of the 20th century, in the aftermath of two World Wars and the shadow of nuclear, biological,…

General Economics · Economics 2021-07-05 Devansh Bajpai , Rishi Ranjan Singh

The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…

Data Analysis, Statistics and Probability · Physics 2009-11-10 Gary C. Hill

Inspired by previous works on human dynamics, we collect the temporal statistics of the article creation by three Western scientists and an Eastern writer. We investigate the distributions of the time intervals between the creations of…

Physics and Society · Physics 2012-04-02 Na Li , Han Yan , Wen-Yao Zhang , Yu-Jian Li , Zhen-Dong Xi , Bing-Hong Wang

Historical episodes such as the World War I "live-and-let-live" system and the Christmas Truce of 1914 demonstrate that opposing military units can establish spontaneous, local cooperation even in extreme conflict environments. Such…

Theoretical Economics · Economics 2026-03-20 Leonardo Becchetti , Franceso Salustri , Nazaria Solferino

The interaction of all mobile species with their environment hinges on their movement patterns: the places they visit and how frequently they go there. In human society, where the prevalent form of cohabitation is in cities, the highly…

Physics and Society · Physics 2020-02-17 Markus Schläpfer , Michael Szell , Hadrien Salat , Carlo Ratti , Geoffrey B. West
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