The Savage Dissertation Award

My PhD research focuses on developing Bayesian methods for inferring structured mathematical infectious disease models within modern probabilistic computing languages to characterize disease spread. By capturing fine-scale transmission dynamics of multi-type epidemics, my work extends beyond traditional homogeneous models to account for complex, structured interactions across populations. Central to this approach, the framework provides a fully generative structured model for latent infections and their resulting observations - including deaths, recorded cases, and seroprevalence surveys - which are essential for quantifying uncertainty in epidemic trajectories and guiding targeted interventions in population subgroups. A key contribution is the development of an age- and time-specific Bayesian transmission model that links real-time mobile phone mobility data to COVID-19 mortality data through human contact patterns and then uses this rich relationship to identify demographic groups driving SARS-CoV-2 transmission in the United States. These findings, published in Science and presented at leading conferences, provide crucial insights for targeted public health interventions and vaccination strategies. To address computational challenges in Bayesian inference for large-scale epidemic models, I introduced a non-parametric spatial prior using a low-rank, two-dimensional Gaussian process projected by regularized B-splines. This method enhanced computational efficiency while preserving predictive accuracy. Embedded within a Bayesian hierarchical framework, it was used to estimate the impact of SARS-CoV-2 vaccination coverage on mortality trends in the United States. This research was published in Bayesian Analysis and presented at the ISBA World Meeting. 

Models that involve intractable normalising constants represent a major computational challenge to statistical inference, since the computation of intractable normalising constants requires numerical integration of complex functions over large or possibly infinite sets, which can be impractical. In particular, Bayesian inference for intractable models demands a specially tailored algorithm to bypass evaluation of two nested intractable normalising constants originating from posterior and model simultaneously. This thesis addresses this computational challenge through the development of a novel generalised Bayesian inference approach built on a Stein discrepancy, called SD-Bayes. Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer desirable properties to resulting generalised posteriors, such as robustness to model misspecification. In this context, the Stein discrepancy selected as the loss function circumvents evaluation of normalising constants of models and produces generalised posteriors that are accessible using standard Markov chain Monte Carlo algorithms. On a theoretical level, we show posterior consistency, asymptotic normality, and global bias-robustness of generalised posteriors. It is shown that generalised posteriors equipped with global bias-robustness demonstrate a strong insensitivity to an irrelevant outlier mixed in data, that is, a simple yet common setting of model misspecification. For intractable models in continuous domains, we derive a useful special case of the Stein discrepancy, called kernel Stein discrepancy, to be combined with SD-Bayes. The resulting SD-Bayes demonstrates strong global bias-robustness and enables fully conjugate inference for exponential family models. We provide numerical experiments on a range of intractable distributions, including applications to kernel-based exponential family models and non-Gaussian graphical models. For intractable models in discrete domains, we establish another useful special case of the Stein discrepancy, called discrete Fisher divergence, to be combined with SD-Bayes. The resulting SD-Bayes benefits from its efficient computational cost and absence of user-specified hyperparameters that can be difficult to choose in the discrete case. In addition, a new approach to calibration of generalised posteriors through optimisation is considered, independently of SD-Bayes. Applications are presented on lattice models for discrete spatial data and on multivariate models for count data, where in each case the methodology facilitates generalised Bayesian inference at efficient computational cost. 

Stick-breaking has a long history and represents the most popular procedure for constructing random discrete distributions in Statistics and Machine Learning. In particular, due to their intuitive construction and computational tractability they are ubiquitous in modern Bayesian nonparametric inference. Most widely used models, such as the Dirichlet and the Pitman-Yor processes, rely on iid or independent length variables. Here we pursue a completely unexplored research direction by considering exchangeable and Markov length variables and investigate the corresponding general class of stick-breaking processes. We derive conditions ensuring that the associated species sampling process is proper and has full topological support, two fundamental desiderata for Bayesian nonparametric models. We also analyze the stochastic ordering of the weights and provide a new characterization of the Pitman-Yor process as the only stick-breaking process invariant under size-biased permutations, under mild conditions. Moreover, we identify notable subclasses of the new stick-breaking processes, that enjoy appealing properties and include Dirichlet, Pitman-Yor and Geometric priors as special cases. Our findings further include distributional results that allow us to develop computational algorithms for posterior inference. Interesting methodological implications are drawn from numerical implementations of Markov stick-breaking processes. 

Species sampling models are a broad class of discrete Bayesian nonparametric priors that model the sequential appearance of distinct tags, called species or clusters, in a sequence of labeled objects. Over the last 50 years, species sampling priors have found much success in a variety of settings, including clustering and density estimation. However, despite the rich theoretical and methodological developments, these models have rarely been used as tools by applied ecologists, even though their primary investigation often involves the modeling of actual species. This dissertation aims to partially fill this gap by elucidating how species sampling models can be useful to scientists and practitioners in the ecological field, especially in species discovery and clustering applications. In particular, we will present (i) a general Bayesian framework inspired by the Dirichlet process to model accumulation curves, which summarize the sequential discoveries of distinct species over time; (ii) a Bayesian nonparametric taxonomic classifier (BayesANT), which predicts the taxonomic affiliation of DNA sequences sampled from the environment while also accounting for potential species novelty; and (iii) a prior for the Dirichlet process precision parameter (the Stirling-gama) that allows for transparent elicitation in clustering applications, such as finding subcommunities of ants in a colony.  

Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this talk, we propose a Bayesian mixed membership model for functional data. Using the multivariate Karhunen-Loève theorem, we derived a scalable representation of Gaussian processes that maintains data-driven learning of the covariance structure. The work is primarily motivated by studies in functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). In this context, our work formalizes the clinical notion of "spectrum" in terms of feature membership proportions. In addition, we discuss an extension of our framework to allow for covariate-dependent modeling structures. Within this framework, we established a set of sufficient conditions for ensuring the identifiability of the mean, covariance, and allocation structure up to a permutation of the labels. Using this covariate-dependent framework, we were able to gain novel insight into the developmental changes of neural activity as children age. Specifically, we found that typically developing children had a more prominent shift in peak alpha frequency, which has been shown to be a biomarker of neural development.