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.

Structure and lipid interactions of membrane-associated glycosyltransferases : Cationic patches and anionic lipids regulate biomembrane binding of both GT-A and GT-B enzymes

This thesis concerns work on structure and membrane interactions of enzymes involved in lipid synthesis, biomembrane and cell wall regulation and cell defense processes. These proteins, known as glycosyltransferases (GTs), are involved in the transfer of sugar moieties from nucleotide sugars to lipids or chitin polymers. Glycosyltransferases from three types of organisms have been investigated; one is responsible for vital lipid synthesis in Arabidopsis thaliana (atDGD2) and adjusts the lipid content in biomembranes if the plant experiences stressful growth conditions. This enzyme shares many structural features with another GT found in gram-negative bacteria (WaaG). WaaG is however continuously active and involved in synthesis of the protective lipopolysaccharide layer in the cell walls of Escherichia coli. The third type of enzymes investigated here are chitin synthases (ChS) coupled to filamentous growth in the oomycete Saprolegnia monoica. I have investigated two ChS-derived MIT domains that may be involved in membrane interactions within the endosomal pathway. From analysis of the three-dimensional structure and the amino-acid sequence, some important regions of these very large proteins were selected for in vitro studies. By the use of an array of biophysical methods (e.g. Nuclear Magnetic Resonance, Fluorescence and Circular Dichroism spectroscopy) and directed sequence analyses it was possible to shed light on some important details regarding the structure and membrane-interacting properties of the GTs. The importance of basic amino-acid residues and hydrophobic anchoring segments, both generally and for the abovementioned proteins specifically, is discussed. Also, the topology and amino-acid sequence of GT-B enzymes of the GT4 family are analyzed with emphasis on their biomembrane association modes. The results presented herein regarding the structural and lipid-interacting properties of GTs aid in the general understanding of glycosyltransferase activity. Since GTs are involved in a high number of biochemical processes in vivo it is of outmost importance to understand the underlying processes responsible for their activity, structure and interaction events. The results are likely to be useful for many applications and future experimental design within life sciences and biomedicine.