Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a multivariate response vector as a parsimonious quadratic function of explanatory variables. The approach is analogous to the mean regression model, and is similar to a factor analysis model in which the factor loadings depend on the explanatory variables. Using a random-effects representation, parameter estimation for the model is straightforward using either an EM-algorithm or an MCMC approximation via Gibbs sampling. The proposed methodology provides a simple but flexible representation of heteroscedasticity across the levels of an explanatory variable, improves estimation of the mean function and gives better calibrated prediction regions when compared to a homoscedastic model.Some key words: heteroscedasticity, positive definite cone, random effects.

Network models are widely used in social sciences and genome sciences. The latent space model proposed by (Hoff et al. 2002), and extended by (Handcock et al. 2007) to incorporate clustering, provides a visually interpretable model-based spatial representation of relational data and takes account of several intrinsic network properties. Due to the structure of the likelihood function of the latent space model, the computational cost is of order O(N2), where N is the number of nodes. This makes it infeasible for large networks. In this paper, we propose an approximation of the log likelihood function. We adopt the case-control idea from epidemiology and construct a case-control likelihood which is an unbiased estimator of the full likelihood. Replacing the full likelihood by the case-control likelihood in the MCMC estimation of the latent space model reduces the computational time from O(N2) to O(N), making it feasible for large networks. We evaluate its performance using simulated and real data. We fit the model to a large protein-protein interaction data using the case-control likelihood and use the model fitted link probabilities to identify false positive links.

We present a selective review of statistical modeling of dynamic networks. We focus on models with latent variables, specifically, the latent space models and the latent class models (or stochastic blockmodels), which investigate both the observed features and the unobserved structure of networks. We begin with an overview of the static models, and then we introduce the dynamic extensions. For each dynamic model, we also discuss its applications that have been studied in the literature, with the data source listed in Appendix. Based on the review, we summarize a list of open problems and challenges in dynamic network modeling with latent variables.

No abstract

Bovine tuberculosis (bTB) is a chronic disease of cattle that impacts productivity and represents a major public health threat. Despite the considerable economic costs and zoonotic risk consequences associated with the disease, accurate estimates of bTB prevalence are lacking in many countries, including India, where national control programmes are not yet implemented and the disease is considered endemic. To address this critical knowledge gap, we performed a systematic review of the literature and a meta‐analysis to estimate bTB prevalence in cattle in India and provide a foundation for the future formulation of rational disease control strategies and the accurate assessment of economic and health impact risks. The literature search was performed in accordance with PRISMA guidelines and identified 285 cross‐sectional studies on bTB in cattle in India across four electronic databases and handpicked publications. Of these, 44 articles were included, contributing a total of 82,419 cows and buffaloes across 18 states and one union territory in India. Based on a random‐effects (RE) meta‐regression model, the analysis revealed a pooled prevalence estimate of 7.3% (95% CI: 5.6, 9.5), indicating that there may be an estimated 21.8 million (95% CI: 16.6, 28.4) infected cattle in India—a population greater than the total number of dairy cows in the United States. The analyses further suggest that production system, species, breed, study location, diagnostic technique, sample size and study period are likely moderators of bTB prevalence in India and need to be considered when developing future disease surveillance and control programmes. Taken together with the projected increase in intensification of dairy production and the subsequent increase in the likelihood of zoonotic transmission, the results of our study suggest that attempts to eliminate tuberculosis from humans will require simultaneous consideration of bTB control in cattle population in countries such as India.