Research

Spatial models for discrete data. My core methodological interest is developing statistical models for spatially- or network-dependent discrete outcomes — counts, ordinal responses, categorical and binary data — where classical tools (Gaussian processes, Markov random fields) either scale poorly to many locations (the “large n” problem) or break down when the response itself is high-dimensional (the “large p” problem), as with survey instruments that collect many discrete rating items per respondent, which are rarely modeled jointly despite sharing spatial and social structure. My mixtures of directed graphical models framework — an alternative to the intractable normalizing constants of undirected Markov random fields — is one example of this approach, and a foundation I’m building on toward identifiable inference in this joint large-n, large-p regime.

Identifiability. A throughline across this work is identifiability: many popular latent-variable spatial models (e.g., spatial generalized linear mixed models) are only partially identifiable, so their posteriors never concentrate on the truth even with infinite data. I study the assumptions — discreteness of latent structure, sparsity, hierarchical layering — that restore identifiability, since identifiable models are what let a fitted model be interpreted, not just used to predict.

Borrowing from machine learning, for inference rather than prediction. Deep learning relies heavily on graphical models — layers of latent variables connected by a directed graph — using representation-learning ideas like sparsity-inducing regularization to improve predictive accuracy. My goal is to adapt these same concepts toward a different end: understanding what constraints and induced sparsity on that graphical structure are necessary for identifiability, so the resulting model supports interpretation and valid uncertainty quantification rather than just prediction.

Applications. My dissertation applied this framework to survey data from the Adolescent Health and Development in Context (AHDC) study, developing a land-use filtering model for spatially predicting collective efficacy ratings in an urban setting. My current work at Hershey extends the same ideas to a new domain: pairing consumer choice models — discrete, high-dimensional data on what shoppers put in a basket — with tractable optimization for assortment decisions.