arXiv subjects

Darren J Wilkinson

Publications and source records attributed to Darren J Wilkinson.

9 recordsLinked to original sources

arXiv2019

A Review of Stochastic Block Models and Extensions for Graph Clustering

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the type of the graph, the clustering approach, the inference approach, and whether the number of groups is selected or estimated. We also review models that combine block modelling with topic modelling and/or longitudinal modelling, regarding how these models deal with multiple types of data. How different approaches cope with various issues will be summarised and compared, to facilitate the demand of practitioners for a concise overview of the current status of these areas of literature.

stat.ML↗

arXiv2019

A hierarchical model of non-homogeneous Poisson processes for Twitter retweets

We present a hierarchical model of non-homogeneous Poisson processes (NHPP) for information diffusion on online social media, in particular Twitter retweets. The retweets of each original tweet are modelled by a NHPP, for which the intensity function is a product of time-decaying components and another component that depends on the follower count of the original tweet author. The latter allows us to explain or predict the ultimate retweet count by a network centrality-related covariate. The inference algorithm enables the Bayes factor to be computed, in order to facilitate model selection. Finally, the model is applied to the retweet data sets of two hashtags.

stat.AP↗

arXiv2018

A Social Network Analysis of Articles on Social Network Analysis

A collection of articles on the statistical modelling and inference of social networks is analysed in a network fashion. The references of these articles are used to construct a citation network data set, which is almost a directed acyclic graph because only existing articles can be cited. A mixed membership stochastic block model is then applied to this data set to soft cluster the articles. The results obtained from a Gibbs sampler give us insights into the influence and the categorisation of these articles.

stat.AP↗

arXiv1997

BAYES-LIN: An object-oriented environment for Bayes linear local computation

BAYES-LIN is an extension of the LISP-STAT object-oriented statistical computing environment, which adds to LISP-STAT some object prototypes appropriate for carrying out local computation via message-passing between clique-tree nodes of Bayes linear belief networks. Currently the BAYES-LIN system represents a rather low-level set of tools for a back-end computational engine, together with diagnostic graphics for understanding the effects of adjustments on the moral graph. A GUI front end, allowing interactive formulation of DAG models could be easily added, but is currently missing from the system. This document provides a very brief introduction to the system, by means of a work-through of two example computations, followed by a list of variables, functions, objects and methods provided by the system.

physics.data-an↗

arXiv1996

Local computation of influence propagation through Bayes linear belief networks

In recent years there has been interest in the theory of local computation over probabilistic Bayesian graphical models. In this paper, local computation over Bayes linear belief networks is shown to be amenable to a similar approach. However, the linear structure offers many simplifications and advantages relative to more complex models, and these are examined with reference to some illustrative examples.

bayes-an↗

arXiv1996

Bayes linear variance adjustment for time series

This paper exhibits quadratic products of linear combinations of observables which identify the covariance structure underlying the univariate locally linear time series dynamic linear model. The first- and second-order moments for the joint distribution over these observables are given, allowing Bayes linear learning for the underlying covariance structure for the time series model. An example is given which illustrates the methodology and highlights the practical implications of the theory.

bayes-an↗

arXiv1995

Bayes linear covariance matrix adjustment

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated with examples of adjustments for some common problems. The problem of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be amenable to a similar approach. Diagnostics for matrix adjustments are also discussed.

bayes-an↗

arXiv1995

Bayes linear adjustment for variance matrices

We examine the problem of covariance belief revision using a geometric approach. We exhibit an inner-product space where covariance matrices live naturally --- a space of random real symmetric matrices. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability specifications.

bayes-an↗

arXiv1995

Bayes linear covariance matrix adjustment for multivariate dynamic linear models

A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects which facilitates such adjustment. This approach helps to make the analysis simple, tractable and robust. To illustrate the methods, a simple model is developed for a time series representing sales of certain brands of a product from a cash-and-carry depot. The covariance structure underlying the model is revised, and the benefits of this revision on first order inferences are then examined.

bayes-an↗