Statistical Methods for Samples of Interaction Networks
Creators: name: Bolt, George
Publisher: name: Lancaster University
Year: 2023
Subjects: Network data
Network science
Bayesian statistics
Markov chain Monte Carlo (MCMC)
Distance measures

description: Network data arises through the observation of relational information
 between a collection of entities. An ubiquitous example of such data are
 social networks, where friendships amongst a sample of people are
 observed. However, there has begun to appear other subtly different forms
 of data which also fit this description. Notably, work in the literature
 has recently considered when (i) the units of observation within a network
 are edges or paths, often referred to as interaction networks, with
 examples such as emails between people or a series of page visits to a
 website by a user, and (ii) one observes a sample of networks, for
 example, in neuroscience applications, brain scan data of a single patient
 is often processed into a network representation, with a multi-patient
 study thus leading to a sample of networks.
 
 
 However, the intersection of (i) and (ii) has presently not been
 considered, that is, where a sample of interaction networks are observed.
 For example, one might observe a sample of users navigating the same
 website. Use of currently proposed methods to analyse such data would
 either be inappropriate or require one to first aggregate data into
 another form, incurring a potential loss of information. Motivated by this
 gap in the literature, this thesis proposes statistical methods suitable
 for the analysis of samples of interaction networks.
 
 
 In this regard, two main contributions are made. Firstly, the problem of
 measuring the distance between two interaction networks is considered.
 Distances are an incredibly useful and versatile tool, opening to door to
 a variety of analytical methodologies, such as dimension reduction and
 clustering algorithms. Secondly, building upon this work, the problem of
 summarising a sample of interaction networks is considered. Of particular
 focus is obtaining analogues of the mean and variance in this non-trivial
 scenario, that is, where data points are themselves interaction networks.
 To this end, a novel Bayesian modelling framework is proposed. Given a
 user-specified distance measure, we construct Gaussian-like distributions
 over the space of interaction networks, that is, models parameterised via
 location and scale. This approach raises significant computational
 challenges; not only are resulting posterior distributions
 doubly-intractable, but the parameter space includes the space of
 interaction networks, which is both discrete and multidimensional. As
 such, specialised Markov chain Monte Carlo (MCMC) algorithms are developed
 which circumvent these issues, facilitating parameter inference for the
 proposed models. Crucially, the location and scale parameters provide
 analogues of the mean and variance, respectively, resulting in the desired
 summary measures.
 
 
 Across both pieces of work, simulation studies are undertaken to confirm
 the efficacy of proposed methods and to explore their properties.
 Additionally, their practical applications are illustrated through example
 analyses of two open-source datasets: (i) an in-play football dataset
 released by StatsBomb, and (ii) a dataset of user interactions with the
 location-based social network Foursquare.