Appproximate/composite likelihood methods replace the full and often computationally intractable marginal likelihood function either with an approximation of it, or an entirely different surrogate objective function, that is simpler and computationally more scalable to work with. Research on this topic can range from empirical comparisons of (different flavors of) approximate/composite likelihood versus full likelihood techniques for performing model selection and prediction, to formulating novel approximate/composite likelihood theory and methods for correlated data analysis, and non-standard applications of approximate/composite likelihood methods for prediction of random effects, model-based clustering, sufficient dimension reduction, and spatio-temporal modeling.

I am interested in studying and developing computationally efficient approaches for model selection and model averaging/ensemble modeling, particularly in correlated data settings. Research may vary from reviewing and examining developments such as Bayesian synthesis prediction, optimal frequentist model-averaging in for mixed-effects models, and model selection using divide-and-conquer techniques, to the application of regularization, information criteria, screening, and model averaging/ensemble modeling techniques for all sorts of interesting correlated and multi-response data e.g., in the context of tensor and network analysis, covariance/correlation regression, generalized estimating equations, stacked species distribution models in ecology, and so on.

Many spatio-temporal processes are often inherently non-stationary, even after accounting for the effect of measured covariates. Motivated primarily by spatio-temporal multivariate abundance data in ecology, research on this topic can range widely from evaluating and comparing classic and state-of-the-art approaches to handling complex non-stationarity in spatial data such as fixed-rank kriging and coregionalization; translating such approaches to new-ish settings such as multi-response non-normal data in ecology and factor analytic models in agriculture, understanding the importance (or not) of sophisticated spatio-temporal methods for inference such as variable selection and classification, and developing software that implements such approaches in a user-friendly manner for practitioners.

I am interested in the areas of reduced rank regression and the more general framework of sufficient dimension reduction (SDR) for constructing (typically linear) combinations of the covariates, while still capturing the relationship between response/s and the a potentially large-number covariates. Research can range from formulating new methods for model-based SDR and single/mutli-index models, developing techniques to address key aspects regarding to choice of the rank and how to perform prediction, and applications of reduced rank regression/SDR in non-standard settings such as in joint species distribution modeling in ecology, spatio-temporal modeling, and correlated data settings where the dimension reduction operation itself may be random.

Research on this topic can vary widely, from reviewing and comparing current approaches to stacked and joint species distribution models in terms of different aspects of statistical and predictive inference, proposing novel advances to SSDMs/JSDMs motivated by specific ecological questions of interest. Examples include but are not limited to the study and development of SSDMs/JSDMs for computationally scalable analysis of spatio-temporal multivariate abundance data, JSDMs with directed species associations, and the use of marginal models such as Ising regression models and generalized estimating equations as an alternative to the current and popular (but slow!) random effects approaches.

Variational approximations are an increasingly popular approach for overcoming intractable marginal log-likelihood functions, thereby facilitating computationally scalable likelihood-based estimation and inference. Research in this topic may include developing new variational-inspired approaches for non-standard response types, and semiparametric/functional regression techniques, theoretical and/or empirical evaluations of variational approximations versus other likelihood based estimation procedures for variable selection and predictive inference, and combining variational approximations with techniques such as estimating equations and composite likelihood.