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.

Kvinnligt och manligt på sociala medier : En kvantitativ studie om medieanvändning och negativa känslor

In the present study the use and experience of using social media was examined in men and women in order to evaluate a possible relationship to gender. Particular emphasis was placed upon negative emotions. A questionnaire was constructed and submitted via Facebook by an online survey. There were 61 women and 50 men who completed the questionnaire. It was found that women and men used social media similarly with regard to frequency and the kind of social media they approached. Both genders used social media on a daily basis and both had profiles on the most popular social network sites as Facebook, Instagram, YouTube and Snapchat. The main purpose for using social media was to maintain already established friend relationships and to take part of other peoples content. A majority of the women but not the men used blogs, whereas a majority of the men but not the women used Twitter more frequently. The study also indicated a sex difference concerning the contents they took part of in the social media. More women took part of content that was related to a female stereotypic image whereas more men took part of content that was related to a male stereotypic image. There was no gender difference concerning contents such as fashion, entertainment, humour, news or politics. In the women there was a significant relationship between the use of social media and negative emotions. However, in the men, such a relationship was not found. The results indicate that more women tend to experience negative emotions when active on social media. More women experienced life as meaningless and boring, as well as stress after consuming contents in social media. They also did compare their life with others on social media leaving them with negative feelings. Such relationships could not be found in the men. In conclusion the present study indicated that for many aspects the use of social media is similar in women and men. However there seems to be a difference with regard to the experience of negative emotions in relation to the use of social media in women but not in men.