Bayesian Analysis of Network Data : Model Selection and Evaluation of the Exponential Random Graph Model

Faculty/Professorship: Statistics and Econometrics  ; Fakultät Sozial- und Wirtschaftswissenschaften: Abschlussarbeiten 
Author(s): Körber, Julian
Publisher Information: Bamberg : opus
Year of publication: 2018
Pages: XVI, 235 ; Illustrationen, Diagramme
Supervisor(s): Rässler, Susanne; Fischbach, Kai  ; Gerrits, Lasse
Language(s): English
Dissertation, Otto-Friedrich-Universität Bamberg, 2018
DOI: 10.20378/irbo-51620
Licence: German Act on Copyright 
URN: urn:nbn:de:bvb:473-opus4-516206
The exponential random graph model (ERGM) is a class of stochastic models for network data widely applied in statistical social network analysis. The ERGM can be used to model a wide range of social processes. However, it is generally difficult to estimate due to its intractable normalizing constant. Markov chain Monte Carlo maximum likelihood (MCMC-ML) ERGM estimation is available but tends to be numerically unstable due to model degeneracy of particular specifications. Bayesian ERGM estimation is robust to model degeneracy and is a practical alternative to the MCMC-ML approach.
Bayesian model selection is based on the Bayes factor which is the ratio of marginal likelihoods of concurring models. The research aim of this thesis is to estimate the marginal likelihood of the ERGM class using path sampling which is also called thermodynamic integration. Power posterior sampling is a discretized version of thermodynamic integration using a fixed path of tempering steps to transition from the prior distribution to the posterior distribution of interest. In this thesis, power posterior sampling is used both to integrate over the parameter space of the ERGM posterior distribution of interest and to yield an estimate of the respective intractable ERGM normalizing constant. Existing approaches of estimating the ERGM marginal likelihood rely on a non-parametric density approximation or a Laplace approximation. The proposed power posterior exchange algorithm with explicit evaluation of the likelihood (PPEA-EEL) does not require such approximations and yields a valid estimate of the ERGM marginal likelihood.
As the PPEA-EEL is a computationally expensive approach involving many MCMC samples, new graphical methods to evaluate power posterior samples are developed.
In this thesis a brief introduction to random graphs and network dependencies is given. The ERGM class is discussed and various dependency assumptions are illustrated. MCMC-ML ERGM estimation is applied to policy networks in Ghana, Senegal and Uganda. Bayesian ERGM estimation and Bayesian model selection are discussed. An overview is given on methods of estimating the marginal likelihood originating from importance sampling, namely bridge sampling, path sampling and power posterior sampling. The PPEA-EEL is applied to social network data and the numerical stability of the approach is evaluated.
GND Keywords: Soziales Netzwerk; Bayes-Verfahren; Zufallsgraph; Netzwerk <Graphentheorie>; Netzwerkanalyse <Soziologie>
Keywords: Bayesian Model Selection, Exponential Random Graph Model, Social Network Analysis
DDC Classification: 310 Statistics  
RVK Classification: QH 253     QH 333   
Type: Doctoralthesis
Year of publication: 7. June 2018

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