Modelling Populations of Interaction Networks via Distance Metrics

TL;DR

This paper introduces a Bayesian framework for modeling interaction network populations using distance metrics, enabling statistical analysis of complex relational data with specialized inference methods.

Contribution

It proposes a novel Bayesian modeling approach for interaction networks based on distance metrics, including tailored MCMC inference schemes for complex posterior distributions.

Findings

Method effectively analyzes simulated data

Application demonstrates insights on social network data

Inference schemes handle doubly-intractable distributions

Abstract

Network data arises through observation of relational information between a collection of entities. Recent work in the literature has independently considered when (i) one observes a sample of networks, connectome data in neuroscience being a ubiquitous example, and (ii) the units of observation within a network are edges or paths, such as emails between people or a series of page visits to a website by a user, often referred to as interaction network data. The intersection of these two cases, however, is yet to be considered. In this paper, we propose a new Bayesian modelling framework to analyse such data. Given a practitioner-specified distance metric between observations, we define families of models through location and scale parameters, akin to a Gaussian distribution, with subsequent inference of model parameters providing reasoned statistical summaries for this non-standard data structure. To facilitate inference, we propose specialised Markov chain Monte Carlo (MCMC) schemes capable of sampling from doubly-intractable posterior distributions over discrete and multi-dimensional parameter spaces. Through simulation studies we confirm the efficacy of our methodology and inference scheme, whilst its application we illustrate via an example analysis of a location-based social network (LSBN) data set.