To design Bayesian studies, criteria for the operating characteristics of posterior analyses—such as power and the Type I error rate—are often assessed by estimating sampling distributions of posterior probabilities via simulation. In this work, we propose an economical method to determine optimal sample sizes and decision for such studies. Using our theoretical results that model posterior probabilities as a function of the sample size, we assess operating characteristics throughout the sample size space given simulations conducted at only two sample sizes. These theoretical results are used to construct bootstrap confidence intervals for the sample sizes and decision criteria that reflect the stochastic nature of simulation-based design. The broad applicability and wide impact of our methodology is illustrated using two clinical examples.

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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.

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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. 

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Nature-metaheuristics have been widely used in engineering, computer science and artificial intelligence to tackle various types of challenging optimization problems for decades and are increasingly used across disciplines. Interestingly, metaheuristics seem to be still relatively underused in the statistical research community.

I present an overview of nature-inspired metaheuristics and describe their main appealing features, which are their speed, flexibility, availability of codes in different platforms, and ease of implementation and usage. Above all, they are virtually assumptions free, enabling us to apply these general-purpose algorithms to tackle all kinds of high-dimensional optimization tasks. I will highlight some recent applications of these algorithms to construct theory-based early phase clinical trials, that are more realistic and flexible for dose response studies. If time permits, I will provide demonstrations to show how the codes work to find user-tailored optimal experimental designs.

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Bio: Professor Wong is a Professor at UCLA since 1990 and over the years, he has done collaborative work in dentistry, environment health science, rheumatology, and various domains in oncology, including in the design and analysis of cancer control and prevention trials for controlling Hepatitis B among Asians, colorectal cancer for Hispanics, and fighting obesity and promoting health of minorities at workplace. His main methodology research is in the construction of model-based optimal experimental designs for various biostatistical applications. His recent interests are in the applications of nature-inspired metaheuristics to tackle challenging estimation and design problems in toxicology, clinical trials and other areas of statistics. He has delivered more than 250 presentations globally, including recent short courses in design at Seoul National University and at the Toxicology Center in TU Dortmund University in Germany. Professor Wong has received grant awards from NSF and private foundations, along with several R01 grant awards from NIH as a principal investigator. He is fellow of the American Statistical Association, the Institute of Mathematical Statistics, the American Association for the Advancement of Science, an elected member of the International Statistical Institute and a full member of the Sigma Xi - The Scientific Research Honor Society. He has also just completed a 3-year Yushan Scholarship Award from the Ministry of Education in Taiwan.

In computer experiments, Gaussian process (GP) models are widely employed for emulation. However, when both qualitative and quantitative factors are involved, especially when qualitative factors have many categories, GP-based emulation becomes challenging, and existing methods can become unwieldy due to the curse of dimensionality. Motivated by computer experiments for the design of a cooling system, we introduce a new tree-based GP model for emulating computer codes with high-cardinality qualitative factors, referred to as the category tree GP (ctGP). The proposed approach incorporates a tree structure to partition the categories of the qualitative factors, after which GP or mixed-input GP models are fitted to the simulation outputs within the leaf nodes. The splitting rule is designed to reflect the cross-correlations among the categories of the qualitative factors, which a recent theoretical study has identified as a key component for improving prediction accuracy, and a pruning procedure based on cross-validation error is introduced to further ensure strong predictive performance. An application to the design of a cooling system demonstrates that the proposed method not only yields substantial computational gains and accurate predictions, but also offers meaningful insights into the system by uncovering an interpretable tree structure. Furthermore, in this cooling system design problem, the computer code is capable of generating multiple responses in addition to a single objective response; to accommodate this, we extend the ctGP framework to handle multiple responses by introducing an additional categorical variable that indicates which response is associated with each experimental point. Finally, we complete the cooling system design study by addressing the corresponding global optimization problem using Bayesian optimization with ctGP and an expected-improvement-type criterion.

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Bio: Ray-Bing Chen is a Professor in the Institute of Statistics and Data Science at National Tsing Hua University. He received his Ph.D. in Statistics from the University of California, Los Angeles in 2003. Prof. Chen’s research interests include statistical and machine learning, statistical modeling, computer experiments, and optimal design. His work has been published in leading journals such as the Annals of Applied Statistics, Journal of Computational and Graphical Statistics, Statistics and Computing, Technometrics, Journal of Quality Technology and Computational Statistics and Data Science. In recognition of his contributions to the field, he was elected as an Elected Member of the International Statistical Institute in 2020.

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Biostatistics is a field that requires multi-disciplinary collaboration between statisticians, medical professionals and other subject-domain experts. Over the last several years, BC Children’s Hospital Research Institute (BCCHRI) has built a biostatistics core to provide expertise to their research community on development of appropriate study design and analysis methods for clinical and public health research. This talk will outline the experience of leading the biostatistics unit, key skills for success in applied settings when working with non-statistical collaborators, and the tension between theoretical best practice and the constraints of real-world data. Examples of projects from BCCHRI will be used to illustrate statistical techniques and challenges. 

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Jeff Bone is the Biostatistical Lead at BC Children’s Hospital Research Institute. In this role, he provides methodological input to clinical and epidemiological research studies across a range of disciplines, supervises analysts and trainees, and provides community education. He has a PhD in Women’s and Children’s Health (UBC) focused on statistical methods and modelling in perinatal epidemiology, an MSc in Statistics (UBC) and BSc (Hons) in Mathematics and Statistics (UVic). His current areas of statistical research include analysis of population level data, causal inference for observational data and design and analysis of randomized controlled trials. His main areas of applied work are in perinatal epidemiology, obstetrics, and pediatric diabetes.

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. 

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Building data literacy requires intentional design—both inside and outside the classroom. As statistics educators, we are uniquely positioned to help learners not only analyze data but also communicate, question, and connect with it in meaningful ways. This talk will explore several initiatives that promote inclusive and engaging approaches to developing data literacy across different educational levels.

First, I will discuss a range of outreach activities designed to introduce statistical thinking to elementary and secondary students through play, storytelling, and authentic data contexts. These activities—ranging from constructing visualizations using the Spotify API to exploring sampling methods with geodes and “dinosaur fossils”—have been implemented at events such as Florence Nightingale Day and Pursue STEM. Such initiatives align with calls to cultivate early data literacy and “real-world statistical reasoning” among pre-tertiary learners (Ben-Zvi & Garfield, 2004; Ridgway, 2016).

Second, I will highlight innovations in postsecondary statistics education, focusing on the integration of Universal Design for Learning (UDL) principles (CAST, 2018) in a large third-year course (STA304: Surveys, Sampling, and Observational Data). Through flexible grading, grace period, and generative AI policies, the course design supports diverse learners while maintaining academic rigor. Student feedback illustrates how flexibility can enhance motivation, equity, and engagement—findings that echo recent work on inclusive assessment and learning autonomy in statistics education (Engel, 2017).

Together, these projects demonstrate how flexibility, communication, and creativity can support inclusive data literacy education across age groups. By integrating outreach and UDL-informed teaching, we can expand access to data-driven inquiry and foster a more diverse and data-confident generation of learners.

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Bayesian hypothesis testing using the Bayes factor is an alternative to hypothesis testing based on the p-Value. They are especially useful if one considers the p-postulate, which suggests that equal p-values, irrespective of sample size, should represent equal evidence against a null hypothesis, false. Bayes factors can, however, be computationally intensive and require a prior distribution. We define an extension of Jeffrey's approximate objective Bayes factor (eJAB) based on a generalization of the unit information prior. Its computation requires nothing more than the p-value and the sample size and it provides a measure of evidence that allows one to interpret the p-value in light of the associated sample size through the lens of an approximate Bayes factor corresponding to an objective prior. We apply eJAB to reexamine the evidence from 71,130 clinical trial findings with particular attention to contradictions between Bayes factors and NHST—i.e., instances of the Jeffreys–Lindley paradox (JLP). Our findings reflect increasing evidence in the literature of problematic clinical trial design and results.

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