Bayesian Analysis of Exponential Random Graphs : Estimation of Parameters and Model Selection

摘要: This thesis presents Bayesian solutions to inference problems for three types of social network data structures: a single observation network, repeated observations on the same and developing through time.A is conceived as being structure consisting actors their interaction with each other. A common conceptualisation networks let be represented by nodes in graph edges between pairs that are relationally tied other according some definition. Statistical analysis large extent concerned modelling these relational ties, which lends itself empirical evaluation.The first paper deals family statistical models called exponential random graphs takes various structural features into account. In general, likelihood functions only known up constant proportionality. procedure performing using Markov chain Monte Carlo (MCMC) methods presented. The algorithm consists two basic steps, one an ordinary Metropolis-Hastings up-dating step used, another importance sampling scheme used calculate acceptance probability step.In number method reports given (or informants) others investigated framework. model contains ingredients: unknown link this actors. These take form probit functions. An intrinsic problem not identified, meaning there combinations values parameters observationally equivalent. Instead restrictions achieving identification, it proposed different equivalent posteriori. Estimation carried out Gibbs switching devise enables transitions posterior modal regions. main goal procedures provide tools comparisons specifications.Papers 3 4, propose longitudinal networks. premise overall change occurs consequence sequences incremental changes. Models evolution continuos-time chains meant capture dynamics. Paper MCMC exploring posteriors such chains. More specifically, unobserved in-between explicitly modelled thereby avoiding need deal explicit formulas transition probabilities. based parameter wider class than has been available before. 4 builds demonstrates how perform selection models.