Markov chain Monte Carlo (MCMC) algorithms are foundational methods for Bayesian statistics. However, most MCMC algorithms are inherently sequential, and their time complexity scales linearly with the number of samples generated. Previous work on adapting MCMC to modern hardware has therefore focused on running many independent chains in parallel. Here, we take an alternative approach: we propose algorithms to evaluate MCMC samplers in parallel across the chain length. To do this, we build on recent methods for parallel evaluation of nonlinear recursions that formulate the state sequence as a solution to a fixed-point problem, which can be obtained via a parallel form of Newton's method. We show how this approach can be used to parallelize Gibbs, Metropolis-adjusted Langevin, and Hamiltonian Monte Carlo sampling across the sequence length. Moreover, we prove theoretical results that link the convergence rate of the fixed-point algorithm to the stability of the recursion, yielding sublinear time complexity for certain problems. Finally, to lower memory costs and reduce runtime in practice, we develop quasi-Newton methods that are generally applicable for parallel evaluation of nonlinear recursions. Across several examples, we demonstrate the simulation of up to hundreds of thousands of MCMC samples with only tens of parallel Newton iterations. We find that the proposed parallel algorithms accelerate MCMC, in some cases by more than an order of magnitude compared to sequential evaluation.

This colloquium series is sponsored in part by the Constance van Eeden Endowment.

This talk is part of the SCOPE Seminar series. SCOPE is CANSSI Ontario’s newest seminar series, connecting researchers and trainees with leading work in statistical sciences, biostatistics, and data science from Canada and beyond.

Abstract:

I will touch on various aspects of working with statistical models that add realism at the cost of losing full parameter identification.  Such models can arise naturally when we own up to limitations in how data are acquired. I will aim to convey the “look and feel” of Bayesian inference using partially identified models. Then, in line with the question posed in the title, I will try to shed light on the features and the bugs.

To join this seminar, please register here.

This event is part of a biweekly forum on how AI is changing mathematical research, teaching, and the profession, and on what mathematics contributes to AI. Organized by PIMS and the UBC Department of Mathematics, it is informal and experience-based: short presentations followed by open discussion, including what has not worked. Topics include AI tools in research practice, formalized mathematics and machine-assisted proof, teaching and assessment, authorship and disclosure, and the mathematical foundations of trustworthy AI. Open to faculty, postdocs, and graduate students in the mathematical sciences and neighbouring fields at UBC, with sessions hybrid so colleagues across the PIMS network can take part. 

Organizers: Deanna Needell, Andrew Rechnitzer, Özgür Yilmaz.

Abstract:

We will talk about the impact of LLM's and AI from a staff perspective. We will cover some of the terminology and how it maps on to policies and practices at an institution like UBC (using UBC an example, not everything will be UBC specific). We will also cover some local tools we have developed and implemented and some others that we have planned. 

To join this seminar virtually, please register here.

In many health research contexts researchers have a rich collection of variables on a cohort of participants but wish to obtain additional variables on a subsample. The additional variables might be new assays on stored samples, coding of open-text responses, or validation of electronic health records against clinical notes.  I will describe how thinking in terms of influence functions helps us come up with good sampling designs and efficient weighted analyses. I will also talk about the efficiency/robustness tradeoffs in using weighted analyses rather than semiparametric MLEs.

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

Assessing the risk of extreme events is important in fields such as environmental science, finance, and insurance. While univariate extreme value theory (EVT) provides a well-established framework for modeling and extrapolating rare events, the multivariate setting is more challenging under asymptotic independence between variables.

The Heffernan–Tawn (HT) conditional extremes model addresses this by characterizing a response variable’s distribution given that a covariate exceeds a high threshold. However, existing implementations estimate a single pair of location and scale normalizing parameters across the entire covariate space, which limits conditional extreme quantile estimation accuracy where the dependence structure varies across the conditioning space, particularly in data-sparse regions. To address this, the present work proposes a locally adaptive estimator for the HT model based on random-forest-derived adaptive neighbourhoods and weighted quantile regression. The proposed approach preserves the theoretical structure of the conditional extremes model while replacing restrictive global estimation with flexible, locally adaptive inference. 

A simulation study compares the proposed random-forest-weighted (RF) estimator against the global HT benchmark across five bivariate dependence structures spanning asymptotic independence and both strong and weak asymptotic dependence. The RF estimator achieves a consistent RMSE reduction over HT across all structures and target quantile levels ($\tau = 0.90, 0.95, 0.99$). The improvements are particularly pronounced under weak asymptotic dependence and at the most extreme quantile levels.

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

This talk is part of the Institute of Applied Mathematics (IMS) Seminar series. SCOPE connects researchers and trainees with leading work in statistical sciences, biostatistics, and data science from Canada and beyond. Organized with CANSSI Ontario’s partner universities, the series features accomplished researchers advancing theory, methodology, and innovative applications across interdisciplinary challenges.

Abstract:

Markov Chain Monte Carlo (MCMC) is a powerful algorithmic framework for sampling from complex probability distributions. Standard MCMC methods struggle with high-dimensional distributions containing well-separated modes, becoming trapped in local regions. Replica-exchange/Parallel tempering (PT) addresses this by using intermediate annealing distributions to bridge a tractable reference (e.g., Gaussian) and an intractable target distribution. However, classical PT is inflexible, fragile, hard to tune, and prone to performance collapse on challenging inference tasks.

This talk introduces non-reversible parallel tempering (NRPT), which provably dominates classical PT algorithms. We show that NRPT undergoes a sharp algorithmic phase transition with increased parallelism, becoming robust, easy to tune, and scaling efficiently to GPUs. I will then demonstrate how to further accelerate PT using neural transports such as normalising flows and diffusions. We demonstrate this framework across a variety of examples in Bayesian inference and inference-time control for diffusion models.

This talk is part of the Canadian Statistical Sciences Institute's (CANSSI) SCOPE Seminar series. SCOPE connects researchers and trainees with leading work in statistical sciences, biostatistics, and data science from Canada and beyond. Organized with CANSSI Ontario’s partner universities, the series features accomplished researchers advancing theory, methodology, and innovative applications across interdisciplinary challenges.

Abstract:

Unseen planets, brown dwarfs and stellar companions leave a faint imprint on the motion of their host star. The Hipparcos and Gaia space missions, together spanning 25 years, make this imprint measurable for over a hundred thousand nearby stars.

I will describe our reconstruction of the companions of 106,508 stars, which uses a catalogue we recently released (G23H). Each reconstruction is a trans-dimensional posterior over the number of companions and their orbits. Unlike a catalogue of detections, a posterior for every star, including the non-detections, can support demographic inference without detection thresholds. We are now developing a joint population model in which the population and the individual systems inform each other.

This project shows where Bayesian modelling stands today. Some things are now feasible at scale: exploring multimodal, ill-conditioned posteriors over mixed discrete and continuous parameters with variational non-reversible parallel tempering, implemented in our open-source library Pigeons, and iterating quickly on models written in domain-specific modelling languages. Other challenges remain open, from quantifying the effect of misspecification to managing the complexity of large workflows.

Joint work with William Thompson (NRC Herzberg), Dori Blakely (University of Victoria), Trevor Campbell (UBC) and the wider G23H team.

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In data science education, competency is built through hands-on manipulation of code and data. Traditional lecture slides often lack this kind of active learning, presenting static lines of code alongside their output instead. When live coding is needed, instructors often need to switch between the slides and a separate environment such as RStudio — one that students may need to install themselves just to reproduce the demonstration. This presentation demonstrates a workflow for creating slides that embed live, editable R code students can modify and execute directly within the slide itself, removing the friction of switching between lecture material and a separate coding environment. We use Quarto, the live-revealjs extension, and GitHub Pages to build a simple, reproducible example course website that instructors can clone and adapt for their own use.

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

This talk is one of the Statistics Teaching and Learning in Statistics and Data Science Seminar Series. 

Statisticians who use Bayes factors often complain that, somewhat awkwardly, their hypothesis testing and estimation results can disagree: a Bayes factor may favour the null hypothesis while the 95% credible interval excludes the null value. In this talk, I show that this apparent contradiction disappears once testing and estimation are required to use the same "implied prior model odds." Upon careful consideration, we see that using a Bayes factor for decision-making implicitly commits one to a mixture model and, when one's null is a point null, implicitly specifies a spike-and-slab prior. Such priors are not without their challenges. The resulting model-averaged posterior has an atom at the null value, its CDF has a jump, and credible intervals at conventional levels such as 95% may not exist at all. Moreover, if the frequentist p-value is held fixed while the sample size grows, the range of probability levels at which a credible interval can be defined steadily shrinks. This is a lesser-known correlate of the Jeffreys–Lindley paradox, one that carries the paradox from testing into interval estimation. All of this leads to a simple question: is a spike-and-slab prior (or, equivalently, a Bayes factor against a point null) ever a good idea?  

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