Essays on Bayesian Inference for Social Networks

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

We are special, just the way we are!Listening to children's voices in an Inclusive Multicultural Environment

The aim of this research is to provide insight into how middle school learners experience an inclusive multicultural learning environment. Increasing diversity is challenging European educational systems, which have the arduous task to foster inclusion of learners with diverse educational needs. In order to explore the participants’ descriptions, a qualitative approach based on semi-structured interviews with six learners was employed. Learners’ positions in the educational scenery are central and unique; they are the main experts on their own situations and therefore precious contributors to educational research. Results have been discussed according to a sociocultural perspective. The analysis of my data suggests that the learners perceive their inclusive environment as beneficial. Moreover, they perceive their cultural diversity as strength, reckon social interaction and teamwork with peers as favorable conditions for learning, feel competent in multicultural communication and believe that respect and acceptance towards others are necessary common values. Some implications of multiculturalism in special education are discussed according to the results of a recent European study, which shows that in all the participating European countries, Sweden included, there is a consistent discrepancy in the proportions of learners with immigrant background within special education. Assessment methods developed for mono-cultural learners appear to be a valid reason why multicultural learners are over-or under-represented in special education. Research also shows that inclusion of diversity in educational environment enables the development of social skills in all learners.

Essays on the Economics of Networks Under Incomplete Information

Social networks constitute a major channel for the diffusion of information and the formation of attitudes in a society. Introducing a dynamic model of social learning, the first part of this thesis studies the emergence of socially influential individuals and groups, and identifies the characteristics that make them influential. The second part uses a Bayesian network game to analyse the role of social interaction and conformism in the making of decisions whose returns or costs are ex ante uncertain.