Population Genetics: - Admixture models; Hidden Markov Models. - Ancient DNA. - Summaries and tests for population structure. - Scalability to large datasets / sequencing data. Statistical and probabilistic modelling of social networks: - Fast approximate inference routines for Bayesian latent variable network models - Multiple-relations / multiview / multilevel network modelling. - Community finding and block modelling. - Link and covariate prediction. - Role analysis of nodes in a network via ego-network modelling. Inference Methodology: - Variational Bayes. - MCMC. - Integrated Nested Laplace Approximations (INLA). - EM algorithm. - Hidden Markov Models. Sentiment Analysis: - Modelling multiple imperfect annotations. - Model Based Clustering of annotators. Palaeoclimate Reconstruction: - Modelling multivariate, zero-inflated, constrained, spatial counts data. - Solution of Inverse Problems via inversion of Bayesian Hierarchical Models.