I like anime, drinking tea, and occasionally doing some statistics.
University of New South Wales
BSc/BA (Honours I, Uni Medal), 2012
University of New South Wales
If you are a prospective student and/or if you have your own ideas and wish to collaborate, please get in touch! Most of these projects are also co-supervised, and can be catered depending on the level and interests of the student.
Composite likelihood is based on the idea of replacing the full and often computationally intractable marginal likelihood function with a surrogate objective function that is simpler to work. Research on this topic ranges widely, from empirical comparisons of (different flavors of) composite likelihood versus full likelihood techniques for performing variable selection, predictive inference, and robustness to various forms misspecification, to formulating novel composite likelihood techniques for models applied to high volume/dimensional correlated data, and developing methodology and associated theory for non-standard usages of composite likelihood such as prediction of random effects/latent variables, sufficient dimension reduction, and measurement error settings.
Joint species distributions models (JSDMs) refer to a general class of joint models for analyzing species communities. Research on this topic can vary widely, from reviewing and comparing current approaches to JSDMs in terms of different aspects of statistical and predictive inference, proposing novel advances to JSDMs motivated by specific ecological questions of interest. Particular focus will be given to JSDMs for the analysis of spatio-temporal multivariate abundance data, JSDMs with directed species associations, and the development of user-friendly software implementing JSDMs for ecologists.
This topic will focus on the development and study of computational efficient and statistically rigorous approaches for model/feature selection in complex, correlated data settings. Research may vary from reviewing and examining developments such as differential-geometric least angle regression, optimal frequentist model-averaging in for mixed-effects models, and variable selection using divide-and-conquer techniques, to the application of regularization, information criteria, and model-averaging methods for correlated data analysis e.g., in the context of tensor analysis, covariance/correlation regression, GEE-assisted inference for latent variable models, among others.
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.
This topic will investigate 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 novel approaches to model-based SDR and index models, developing techniques to answer key questions regarding to choice of the rank and aspects of inference such as prediction, and applications of reduced rank regression and SDR in non-standard settings such as in joint species distribution modeling in ecology, spatio-temporal modeling, measurement error, and time series analysis.
This topic will investigate variational approximations for overcoming intractable marginal log-likelihood functions and performing computationally efficient likelihood-based analysis. Research may include developing new variational-inspired approaches for complex latent variable models, spatio-temporal, and semiparametric/functional regression techniques (say), empirical evaluations of variational approximations versus other likelihood based estimation procedures for variable selection and robustness to misspecification, improving variational inference especially when it comes to uncertainty quantification and bias correction, and combining variational approximations with techniques such as estimating equations and composite likelihood.
CBFM: Spatio-temporal joint species distribution modeling using community-level basis functions
vagam: Variational approximations for generalized additive models