Recovering counterfactual distributions is an important goal in causal inference. In recent years, there has been a growing literature on transport-based models that directly model transport maps between outcome distributions. These methods avoid specifying full data-generating processes and are therefore more robust to mis-specification. The multivariate nonlinear difference-in-differences (DiD) model is one such example. It recovers counterfactual distributions using optimal transport when the treatment is discrete. This approach, however, does not readily generalize to continuous treatments. In this talk, we extend the nonlinear DiD to a continuous treatment setting using cocycles, which are constructed using a different class of transport maps. We propose an estimator for the average treatment effect on the treated and conduct simulation experiments to empirically study its convergence. We also investigate whether having anchoring treatment groups can result in faster convergence and answer that in the negative based on the simulation results.

To join this seminar virtually, please request Zoom connection details from hr.ops@stat.ubc.ca. 

Telemetry data offer unprecedented opportunities to study wildlife behaviour, but extracting ecological insights from these complex processes requires advanced statistical methods. Using narwhal (Monodon monoceros) movement data as a case study, my PhD develops novel statistical methods to address three key challenges in animal movement analysis. First, while hidden Markov models (HMMs) provide a natural and powerful framework for inferring latent behavioural states from movement data, selecting the number of hidden states in such models is a notoriously difficult task. Common information criteria perform poorly in selecting the number of states under model misspecifications. I build upon a double penalized maximum likelihood estimator (DPMLE) for simultaneous estimation of the number of states and parameters of non-stationary HMMs. Through simulations and the narwhal case study, I show that the DPMLE outperforms traditional methods under misspecifications and enables more realistic modelling of movement data. Second, as human activities expand across wildlife habitats, quantifying behavioural responses to disturbances is crucial for conservation. I introduce a lasso-penalized threshold HMM that jointly estimates the distance at which animals react to a stimulus and ensures this distance threshold corresponds to a meaningful behavioural shift. Results suggest that narwhal react to vessels up to 4 km away, reducing movement persistence and spending more time in deeper waters. To my knowledge, this is the first model-based estimate of a disturbance threshold in movement ecology. Third, understanding habitat selection requires methods robust to location error inherent in animal tracking data. I extend the Langevin diffusion habitat selection model to accommodate error-prone observations, using automatic differentiation and the Laplace approximation for efficient maximum-likelihood estimation, providing the first Template Model Builder (TMB) implementation capable of handling covariates depending on latent variables. Simulations indicate that the proposed method performs better than conventional two-step procedures, which tend to produce estimates biased towards zero. Application to narwhal data reveals a stronger selection signal towards deeper water under my approach. Together, the methods developed in my dissertation advance the statistical toolkit for movement ecology and beyond, as the frameworks developed here are broadly applicable to time series analysis across a wide range of fields.

To join this seminar virtually, please request Zoom connection details from hr.ops@stat.ubc.ca. 

A treatment benefit predictor is a function that maps patient characteristics to a putative treatment benefit for that patient. Such predictors support the optimization of individualized treatment decisions, a central idea of precision medicine. However, evaluating the predictive performance of a treatment benefit predictor is challenging, as we often cannot observe each individual's treatment benefit. This work theoretically underpins common predictive metrics and demonstrates conceptual and practical evaluation of prespecified treatment benefit predictors in the target population. At a conceptual level, we define the estimands of a set of predictive performance metrics. A particular measure of discrimination is used as an illustrative example to reveal methodological concerns on multiple fronts. We describe how to evaluate a treatment benefit predictor using observational data from the target population and explore how predictive performance metrics may change when confounding is not fully controlled. In practice, we propose and implement estimation methods for evaluating the predictive performance of treatment benefit predictors, assessing their reliability through simulation studies. We illustrate their practical use in real-world observation data, including cohort construction and modeling strategies. Overall, this work helps bridge the gap between predictive modeling and causal inference, providing a framework for evaluating treatment benefit predictors using predictive performance metrics.

To join this seminar virtually, please request Zoom connection details from hr.ops@stat.ubc.ca. 

Symmetry plays a central role in the sciences and in statistics. Yet, identifying distributional symmetry from a single sample of data can be challenging. Inferential tools for group symmetry of a probability measure exist in the form of hypothesis tests, but analogous tools for the symmetry of a conditional distribution are absent from the literature. This thesis initiates the study of nonparametric tests for equivariance and invariance of a conditional distribution under the action of a locally compact group. By characterizing conditional symmetry in terms of a conditional independence statement, we leverage the existing conditional randomization testing framework to construct consistent randomization tests for conditional symmetry. We instantiate such tests using kernel methods and derive finite-sample power lower bounds. Furthermore, we show that kernel-based tests for invariance of a probability measure can be unified with our tests under the conditional randomization framework, extending our theoretical results to those tests. We evaluate our tests for conditional symmetry on synthetic examples and demonstrate their use in particle physics applications.

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca. 

Non-reversible parallel tempering (NRPT) is an effective algorithm for sampling from distributions with complex geometry, such as those arising from posterior distributions of weakly identifiable and high-dimensional Bayesian models or Gibbs distributions in statistical mechanics. In this work we introduce methods for the automated tuning of NRPT and establish convergence results that explain its observed empirical success. A central feature of all methods that we consider is that they can be fully automated and are robust, enabling them to be used in software with minimal hassle for the user, as evidenced by their application to open problems in astrophysics by our collaborators. Furthermore, the methods are all parallelizable and scale well with modern computational resources.

We begin with a study of how to bridge NRPT and variational inference in order to obtain more effective samplers. To do so, we introduce a generalized annealing path connecting the posterior to an adaptively tuned variational reference, where the reference is tuned to minimize the forward (inclusive) KL divergence to the posterior. To easily tune a general class of such variational families, we introduce AutoGD: a gradient descent method that automatically adapts its learning rate at each iteration. Our theory establishes the convergence of AutoGD, recovering the optimal rate of gradient descent (up to a constant) for a broad class of functions. Finally, to shed light on the empirical success of NRPT, we establish its uniform (geometric) ergodicity under a model of efficient local exploration. We obtain analogous ergodicity results for classical reversible parallel tempering, providing new evidence that NRPT dominates its reversible counterpart. 

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca. 

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca. 

Variational inference (VI) approximates a target distribution within a chosen family that permits i.i.d. sampling and tractable density evaluation. Because the approximation is obtained by minimizing a divergence to the target, its best achievable quality is constrained by the family’s expressiveness. Yet greater flexibility does not guarantee better results: the optimization landscape is typically highly non-convex, so the theoretical optimum is rarely attained in practice. Consequently, VI generally lacks the asymptotic exactness of Markov chain Monte Carlo (MCMC)—the ability to achieve arbitrarily accurate inference given sufficient computation, regardless of tuning.

In this talk, I will introduce mixed variational flows (MixFlows): a framework for constructing tuning-free, asymptotically exact variational families using measure-preserving dynamical systems. The key methodological advance is a way to use involutive MCMC kernels to build variational flows, yielding families that inherit MCMC-level convergence guarantees while retaining VI’s tractability (i.i.d. sampling and closed-form density evaluation).

I will also discuss how tools from chaotic dynamical systems illuminate the propagation of probabilistic error through \emph{inexact} flows—errors that arise from finite-precision arithmetic and numerical discretization—providing practical guidance for when flow-based approximations remain reliable in spite of numerical instability. 

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca. 

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selectingan appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods—AutoStep MCMC—that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is π-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca.

The relative risk (RR) offers interpretation and comparison advantages over the Odds Ratio (OR) used in logistic regression. However, its direct estimation in high-dimensional settings is challenging. Common approaches, such as penalized log-binomial and Poisson regression, are built on parameters that are variationally dependent, while newer, variation-independent models have been limited by estimators not designed for high-dimensional or sparse data.

To address this, this project built on previous penalized RR models to implement a faster penalized estimator for the variation-independent relative risk model. The contributions include an efficient implementation in C++, the use of an Adaptive Step Size FISTA algorithm for robust optimization, and a comprehensive evaluation of different penalization strategies and model specifications. Through simulation studies, the proposed estimator is shown to be a robust tool for high-dimensional analysis. It demonstrates better predictive accuracy and the ability to identify relevant predictors in sparse scenarios correctly.

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca. 

Estimating the parameters of disease transmission models is an important component in analyzing disease outbreaks and inferring transmission networks. The introduction of genetic data into disease transmission models has enabled more detailed inference, particularly through phylogenetic trees derived from the genetic data. Existing approaches often rely on a single phylogenetic tree to subset transmission trees from a set of possible transmission trees inferred from epidemiological data. However, such methods typically do not account for the uncertainty inherent in phylogenetic reconstruction. This thesis introduces a Sequential Monte Carlo-Expectation Maximization (SMC-EM) framework that explicitly incorporates uncertainty in transmission and phylogenetic trees. We treat these trees as latent variables and use observed genetic sequences, sampling times, and epidemiological data to inform the model. Our method constructs transmission and phylogenetic trees sequentially, conditioned on infection times, and updates parameter estimates iteratively via a variant of the EM algorithm. We evaluate the performance of the proposed method through extensive simulation studies and demonstrate its applicability using a real-world outbreak dataset. The results indicate that the SMC-EM approach provides improved parameter estimates while effectively capturing the uncertainty in latent tree structures. 

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca.