Dynamic degree-corrected blockmodels for social networks: A nonparametric approach

A nonparametric approach to the modelling of social networks using degree-corrected stochastic blockmodels is proposed. The model for static network consists of a stochastic blockmodel using a probit regression formulation, and popularity parameters are incorporated to account for degree heterogeneity. We specify a Dirichlet process prior to detect community structure as well as to induce clustering in the popularity parameters. This approach is flexible yet parsimonious as it allows the appropriate number of communities and popularity clusters to be determined automatically by the data. We further discuss and implement extensions of the static model to dynamic networks. In a Bayesian framework, we perform posterior inference through MCMC algorithms. The models are illustrated using several real-world benchmark social networks

Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks

We investigate the effect of cadmium (a toxic environmental pollutant) on the correlation structure of a number of urinary metabolites using Gaussian graphical models (GGMs). The inferred metabolic associations can provide important information on the physiological state of a metabolic system and insights on complex metabolic relationships. Using the fitted GGMs, we construct differential networks, which highlight significant changes in metabolite interactions under different experimental conditions. The analysis of such metabolic association networks can reveal differences in the underlying biological reactions caused by cadmium exposure. We consider Bayesian inference and propose using the multiplicative (or Chung–Lu random graph) model as a prior on the graphical space. In the multiplicative model, each edge is chosen independently with probability equal to the product of the connectivities of the end nodes. This class of prior is parsimonious yet highly flexible; it can be used to encourage sparsity or graphs with a pre-specified degree distribution when such prior knowledge is available. We extend the multiplicative model to multiple GGMs linking the probability of edge inclusion through logistic regression and demonstrate how this leads to joint inference for multiple GGMs. A sequential Monte Carlo (SMC) algorithm is developed for estimating the posterior distribution of the graphs

Functional models for longitudinal data with covariate dependent smoothness

This paper considers functional models for longitudinal data with subject and group specific trends modelled using Gaussian processes. Fitting Gaussian process regression models is a computationally challenging task, and various sparse approximations to Gaussian processes have been considered in the literature to ease the computational burden. This manuscript builds on a fast non-standard variational approximation which uses a sparse spectral representation and is able to treat uncertainty in the covariance function hyperparameters. This allows fast variational computational methods to be extended to models where there are many functions to be estimated and where there is a hierarchical model involving the covariance function parameters. The main goal of this paper is to implement this idea in the context of functional models for longitudinal datsa by allowing individual specific smoothness related to covariates for different subjects. Understanding the relationship of smoothness to individual specific covariates is of great interest in some applications. The methods are illustrated with simulated data and a dataset of streamflow curves generated by a rainfall runoff model, and compared with MCMC. It is also shown how these methods can be used to obtain good proposal distributions for MCMC analyses