There are many non-Gaussian time series models available in the literature. Copula-based time series models are particularly relevant as they can handle serial tail dependence or the clustering of extreme observations. To date, mainly copula-based Markov time series models that extend the autoregressive time series model have been studied and applied. In this talk, I will consider non-Markovian copula-based time series models that can be viewed as an extension of Gaussian autoregressive moving average (ARMA) models. I derive distributional properties and discuss conditions for stationarity, as well as the asymptotic properties of the maximum-likelihood estimators. Finally, the probabilistic forecasting performance is evaluated.

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

DNA methylation is a key epigenetic mechanism governing gene regulation and cellular identity. Advances in high-throughput sequencing technologies have enabled detailed investigation of methylation landscapes across single cells and complex tissue mixtures. However, the sparsity and noise inherent in single-cell data, as well as the signal distortion in enrichment-based platforms, pose major analytical challenges. This thesis presents two novel statistical frameworks to address these limitations and advance the computational toolkit for DNA methylation analysis.

The first contribution is vmrseq, a probabilistic method and software for detecting variably methylated regions from single-cell bisulfite sequencing data. vmrseq integrates a smoothing-based strategy for candidate region identification with hidden Markov modeling to account for spatial correlation and technical noise. Through extensive benchmarking on synthetic and experimental datasets, vmrseq demonstrates improved precision and biological relevance in identifying methylation heterogeneity, supporting downstream analyses such as unsupervised clustering and cell-type-specific marker discovery.

The second contribution is decemedip, a hierarchical Bayesian model and software for cell type deconvolution of enrichment-based methylation data such as MeDIP-seq. By leveraging reference panels derived from alternative platforms and modeling the complex relationship between methylation levels, CpG density, and read counts, decemedip enables accurate estimation of cell type proportions with uncertainty quantification. Its performance is validated through simulations, cross-platform comparisons, and real-world applications involving patient-derived xenografts and circulating cell-free DNA from cancer cohorts.

Together, these methods address critical gaps in the analysis of high-throughput DNA methylation data, enabling robust detection of epigenetic heterogeneity across biological contexts. The associated open-source software implementations provide practical tools for future epigenomic research and potential clinical applications.

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

It is difficult to anticipate the myriad challenges that a predictive model will encounter once deployed. Common practice entails a reactive, cyclical approach: model deployment, data mining, and retraining. We instead develop a proactive longtail discovery process by imagining additional data during training. In particular, we develop general model-based longtail signals, including a differentiable, single forward pass formulation of epistemic uncertainty that does not impact model parameters or predictive performance but can flag rare or hard inputs. We leverage these signals as guidance to generate additional training data from a latent diffusion model in a process we call Longtail Guidance (LTG). Crucially, we can perform LTG without retraining the diffusion model or the predictive model, and we do not need to expose the predictive model to intermediate diffusion states. Data generated by LTG exhibit semantically meaningful variation, yield significant generalization improvements on numerous image classification benchmarks, and can be analyzed by a VLM to proactively discover, textually explain, and address conceptual gaps in a deployed predictive model.

Bio

David Hayden leads Perception AI Research at Cruise, where he focuses on generative and world models, foundation model alignment and guidance, longtail robustness, uncertainty quantification, and synthetic data. He has consulted on machine learning and computer vision for diverse industries including pharmaceuticals, retail, and competitive sports. His work has shipped to hundreds of driverless cars, ran live in stadiums of 40,000 people, supported seed and Series A rounds, and is published in top conferences and journals including ICML, CVPR, Neurips, and Nature. He previously founded Essistive Technologies, where he developed and licensed discreet note-taking tech for individuals with limited vision. David received a PhD at MIT working on interpretable machine learning and computer vision, with emphasis on behavior analysis, multi-object tracking, Bayesian nonparametrics for time-series, distributions on manifolds, and uncertainty to guide decision making. 

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

Variational inference with stochastic gradients, commonly called black-box variational inference (BBVI) or stochastic gradient variational inference, is the workhorse of probabilistic inference in the large data, large model regime. For a decade, however, the computational properties of VI have largely been unknown. For instance, under what conditions is BBVI guaranteed to converge, and is it provably efficient? In this talk, I will present recent theoretical results on VI in the form of quantitative non-asymptotic convergence guarantees for obtaining a variational posterior. Following this, I will demonstrate the usefulness of the theoretical framework by investigating the theoretical properties of various design choices and algorithmic modifications, such as parametrizations of variational approximation, variance-reduced gradient estimators such as sticking-the-landing, structured variational families, and beyond.

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 

Abstract: The first passage time (FPT) is a useful tool in stochastic modeling of many biological, physical, social and economic processes evolving with time. It refers to the time when a random process first passes a threshold, e.g., when the population of an endangered species reaches a certain critical level, or when the number of infected individuals with a disease reaches a limit. Other examples include the survival time of a cancer patient, failure time of a mechanical system, and default time of a business, etc.

We study the boundary crossing problem for jump-diffusion processes over a discontinuous boundary and provide a complete characterization on the FPT distributions. We derive new formulas for piecewise linear boundary crossing probabilities and density of Brownian motion with general random jumps. These formulas can be used to approximate the boundary crossing distributions for general nonlinear boundaries. The method can be extended to more general diffusion processes such as geometric Brownian motion and Ornstein-Uhlenbeck processes with jumps. The numerical computation can be done by Monte Carlo integration which is straightforward and easy to implement. Some numerical examples are presented for illustration.

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

Presentation 1

Time: 11:00am – 11:30am

Speaker: Xihan (Henry) Qian, UBC Statistics MSc student

Title:  Modeling Diatom Dynamics and Environmental Drivers Using Functional Regression and Rank-Based Model Selection

Abstract: In this project, we analyze the relationship between diatom concentrations and environmental drivers in the Salish Sea using functional data analysis (FDA). Daily measurements of solar radiation, wind speed, air temperature, and diatom levels from 2007 to 2024 are treated as smooth functions over time. To capture the delayed effects of environmental variables on diatom dynamics, we apply a historical functional linear model and estimate a time-varying coefficient surface using finite element basis functions defined over a triangular domain. Smoothness is enforced using directional roughness penalties. Two model selection strategies are compared: one based on the Bayesian Information Criterion (BIC), and another prioritizing predictive performance using mean squared error and rank correlation. We show how the choice of tuning parameters affects predictive accuracy and highlight patterns in the estimated effects of environmental variables on diatom levels.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Joey Hotz, UBC Statistics MSc student

Title: The Rocky Road Toward Effective Vanilla Bayesian Optimization in High-Dimensional Search Spaces

Abstract: Bayesian optimization (BayesOpt) is a well-established statistical methodology for efficiently finding the true optimum value of a black-box function. A common concern with Bayesian optimization is the "Curse of Dimensionality", as these methods often struggle for input spaces with many parameters unless the algorithm is adjusted accordingly. Despite the prevalence of these challenges, a recently published paper empirically demonstrated that under certain specifications for the surrogate model, the sole adjustment required to make Bayesian optimization effective for higher-dimensional problems is to simply scale the prior distribution for the model based on the dimensionality of the search space. In this presentation, we discuss the background, methodology, and findings of the aforementioned paper. Additionally, we significantly broaden the scope of their simulation study to a wider class of statistical models to evaluate the robustness of their stated result.

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

Abstract: Statistics education stands at a critical juncture as we navigate the intersection of traditional statistical theory, modern computational approaches, and emerging AI technologies. This talk examines how statisticians can reimagine curricula by embracing computation as foundational elements rather than afterthoughts. While traditional statistics education has prioritized theoretical frameworks and applications, computation has emerged as the backbone of contemporary data analysis—from data acquisition and wrangling to visualization, modeling, and communication. Now, AI tools are further transforming this landscape, creating both opportunities and challenges for statistics and data science educators. The presentation will outline a forward-looking curriculum model for introductory courses that balances statistical thinking, data science methods, and explicit computational instruction

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

Presentation 1

Time: 11:00am – 11:30am

Speaker: Sarah Masri, UBC Statistics MSc student

Title: Compartmental models and Hawkes processes: equivalence and computational advantages in epidemiological modelling

Abstract: Epidemiological modelling is crucial for understanding and responding to the spread of infectious diseases, helping public health officials assess the impact of interventions and inform policy decisions. Some prominent models within this field, such as the SIR and SEIR compartmental models, rely on unobserved measurements and can be computationally intensive. This thesis investigates the equivalence between the stochastic SIR and SEIR compartmental models and the Hawkes process, a self-exciting point process, in the epidemiological setting. The research demonstrates that, under specified conditions, the SIR and SEIR models can be interpreted as special cases of the finite population Hawkes process, offering a unified framework for disease modelling that does not rely on latent measurements. This thesis contributes to the growing body of literature on stochastic epidemic models by providing an alternative approach to complement compartmental models, highlighting how inference under the Hawkes process, when fitting the process to data, is consistent with the parameters associated with the SIR and SEIR models. The findings suggest that the Hawkes process can approximate some compartmental models, offering a promising tool for epidemiological modelling.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Christine Chuong, UBC Statistics MSc student

Title: Forecasting Influenza, COVID-19 and Respiratory Syncytial Virus Detections in Canada

Abstract: Respiratory illnesses such as influenza, respiratory syncytial virus, and COVID-19 result in many hospitalizations and deaths per year in Canada. Anticipating the behaviour of viruses can be challenging as behaviour can differ between seasons, so accurate forecasts of future behaviour can help reduce uncertainty. Modelling hubs can be a useful tool in collecting and evaluating multiple forecasts in one place. Hubs run forecasting challenges that invite teams to make weekly probabilistic short-term forecasts for illnesses of interest, but no national challenge predicting respiratory viruses exists in Canada. Using data on respiratory virus detections taken from historic reports and an interactive dashboard maintained by the Public Health Agency of Canada, we established a forecasting hub for the 2024-2025 respiratory illness season. We submitted forecasts for a climatological model using historical data and an ensemble of this climatological model and an autoregressive with exogenous covariate (ARX) model with the predicted climatological medians. Forecasts were evaluated using the absolute error of the predicted median, weighted interval score (WIS) and empirical coverage of prediction intervals.

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

Abstract: In complex systems such as financial networks, the failure of a single entity can trigger cascading effects that threaten the stability of the entire system, and this is known as the systemic risk. A common measure for quantifying systemic risk is CoVaR, the Value-at-Risk of the system conditional on the distress of a single component.

In this talk, I will present a new approach to CoVaR based on tail expansions of copulas. Tail expansions of copulas provide a systematic way to characterize the joint tail behavior of multiple dependent random variables. This characterization naturally integrates and extends classical extreme value theory, offering a more flexible and interpretable representation of extremal dependence.

I will highlight the theoretical value of tail expansions in understanding the asymptotic behavior of CoVaR and demonstrate their practical use in developing new extreme value estimation methods. The talk also includes an empirical study that illustrates how the proposed approach can be used to assess the systemic risk in the U.S. financial industry.

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

Abstract: We study the multilayer random dot product graph (MRDPG) model, an extension of the random dot product graph to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework. At every time point, we observe a realization from an MRDPG. Across layers, we assume fixed shared common node sets and latent positions but allow for different connectivity matrices. We propose efficient tensor algorithms under both fixed and random latent position cases to minimize the detection delay while controlling false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm based on density kernel estimation that is applicable to a wide range of scenarios, including stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online.