Modeling event cascades using networks of additive count sequences

TL;DR

This paper introduces a new statistical model for networks of event count sequences based on a cascade structure, enabling analytic forms for distributions and parameter estimation.

Contribution

It develops a novel framework using additive distributions like Poisson and negative binomial for modeling event cascades in networks.

Findings

Analytic forms for marginal and conditional distributions of event cascades.

A statistical method for estimating model parameters from observed data.

Application of Poisson and negative binomial distributions in cascade modeling.

Abstract

We propose a statistical model for networks of event count sequences built on a cascade structure. We assume that each event triggers successor events, whose counts follow additive probability distributions; the ensemble of counts is given by their superposition. These assumptions allow the marginal distribution of count sequences and the conditional distribution of event cascades to take analytic forms. We present our model framework using Poisson and negative binomial distributions as the building blocks. Based on this formulation, we describe a statistical method for estimating the model parameters and event cascades from the observed count sequences.