Colloquium

Presentation Title: Volatility Imparities in S&P 100 Index Options

Abstract:  The Standard & Poor's 100 Index (S&P 100 Index) trades both American and European-style options, which is atypical as most underlying trade options with only one of these features. As such, the options on the S&P 100 Index can be empirically assessed for adherence to prevailing theoretical results. One particular result, due to R. Myneni (1992, AOAP), establishes that the price of an American put option can be decomposed into its early-exercise premium (EEP) and the price of the corresponding European put option. This result suggests that option-implied measures of volatility should adhere to this decomposition. The present study investigates the extent of parity in the option-implied volatility signals between American and equivalently structured (same strike and tenor) European put options on the S&P 100 Index. Leveraging statistical process control, we document the extent of agreement in the implied volatilities of S&P 100 American and European put options during a time frame that spans before, during, and after the Global Financial Crisis (GFC, approximately 2007-2009). We further augment our study to investigate the statistical agreement between the market price of volatility risk of American and equally specified European put options on the S&P 100 Index. Our results indicate that parity between these volatility signals generally hold, thus adhering to theory, but notable statistical departures are evident, particularly during periods of extreme financial distress, thus affording likely profitable arbitrage opportunities.

Presentation Title: From Concept to Practice: Real-World Applications of Digital Twins for Health

Abstract:  Digital Twins for Health (DT4H) are virtual representations of individuals or health systems that are continuously updated with real-world data. Once largely theoretical, DT4H technologies are now moving into practice and transforming fields including medicine, public health, dentistry, and social work. This presentation will introduce the concept of DT4H and explain how digital twins are constructed through the integration of data, computational algorithms, AI/ML models, and feedback loops. Real-world examples will be highlighted, including applications in precision medicine, chronic disease management, drug development, and health resource allocation. Particular attention will be given to the essential role of data science and statistics in ensuring data quality, developing robust models, and validating outcomes. The talk will also examine challenges, opportunities, and ethical considerations in the adoption of digital twins. By the end, the audience will gain a clear understanding of how DT4H is being applied today and the pathways it opens for advancing patient care and public health.

The Maroon Door

418 N Main St, Blacksburg, VA 24060

Presentation Title: From Synthesis to Trust: Advanced Statistical Methods for Trustworthy Generative AI in Biomedical Imaging Studies

Abstract: Generative AI has rapidly transformed the biomedical imaging field by enabling image synthesis, helping address challenges of limited data availability, privacy, and diversity in biomedical research. Yet, the adoption of AI-generated images in biomedical studies requires rigorous methods to ensure their reliability for downstream analysis. In this talk, I will introduce novel and rigorous nonparametric approaches that strengthen the trustworthiness and statistical validity of synthetic biomedical imaging data. We develop simultaneous confidence regions to rigorously quantify uncertainty and detect meaningful differences between synthetic and original imaging data. To further enhance fidelity and utility, we propose a transformation that aligns the mean and covariance structures of synthetic images with those of the originals. I will also discuss methods for imputing missing imaging phenotypes using generative models and demonstrate how joint analysis of observed and imputed traits enhances inference while accounting for imputation error. Extensive simulations and applications to brain imaging data validate the proposed framework, demonstrating how these methods empower rigorous statistical inference and promote trustworthy advances in biomedical imaging.

Time: 11 am-12 pm, Friday, September 26, 2025

Location: Multipurpose Room, the Graduate Life Center

Presentation Title: Quantile Slice Sampling

Abstract: We propose and demonstrate a novel, effective approach to simple slice sampling. Using the probability integral transform, we first generalize Neal's shrinkage algorithm, standardizing the procedure to an automatic and universal starting point: the unit interval. This enables the introduction of approximate (pseudo-) targets through a factorization used in importance sampling, a technique that has popularized elliptical slice sampling. Reasonably accurate pseudo-targets can boost sampler efficiency by requiring fewer rejections and by reducing target skewness. This strategy is effective when a natural, possibly crude approximation to the target exists. Alternatively, obtaining a marginal pseudo-target from initial samples provides an intuitive and automatic tuning procedure. We consider pseudo-target specification and interpretable diagnostics. We examine performance of the proposed sampler relative to other popular, easily implemented MCMC samplers on standard targets in isolation, and as steps within a Gibbs sampler in a Bayesian modeling context. We extend to multivariate slice samplers and demonstrate with a constrained state-space model. R package qslice is available on CRAN.

Presentation Title: Democratizing Methods

Abstract: The past few decades have seen an explosion in the development of freely available software to implement statistical methods and algorithms to help explore and analyze data. However, researchers tend to assume that releasing software packages implementing specific methods is sufficient for ensuring that the tools are adopted and used correctly. Typically, very little attention is paid to the user experience. This in turn means that the tools do not get used, are used incorrectly, or the results are misinterpreted. This talk will present a case study for how software development could be different by describing a causal analysis tool that scaffolds the user experience. I will discuss lessons learned through user studies and experimental evidence. I conclude with calls to action for those that develop methods and software. 

Presentation Title: Conformal Prediction for Time Series and Spatial Data

Abstract: Conformal prediction (CP) provides a powerful, distribution-free framework for constructing prediction intervals with finite-sample coverage guarantees. However, many CP methods rely on the assumption of data exchangeability, which is typically violated in time series due to temporal dependence. This has motivated a growing body of work aimed at extending CP to the time-series setting. Another computational challenge comes from handling multi-dimensional time-series. In this talk, I will review recent advances in conformal prediction for time series, including our own contributions to a general framework for constructing distribution-free prediction intervals for time series that wrap around a given black-box algorithm. The new approach relaxes the exchangeability assumption and considers the temporal dependence of data. Theoretically, we establish marginal and conditional coverage guarantees based on temporal mixing, which comes with certain width optimality in some cases. Methodologically, we propose computationally efficient procedures based on ensemble predictors that are closely related to standard CP, yet tailored for time series. Finally, I will discuss a recent extension to spatial data by considering spatial mixing. 

Presentation Title: Leveraging deep learning for spatiotemporal interpolation

Abstract:  Gaussian Process (GP) models are the workhorse of spatial statistics.  They provide provably optimal prediction and a robust framework for statistical inference.  However, fitting GPs usually requires unrealistic assumptions such as stationarity, i.e., the process behaves similarly across the spatial domain, and even with this overly simplistic assumption the computation is not scalable.  We consider a nonstationary model based on a latent dimension expansion and show that this model permits an arbitrarily precise spectral approximation. For computation, we place the model in the deep learning architecture and use variational Bayesian deep learning to fit the model to millions of observations in minutes.  While the variational Bayesian approach is fast to fit, to ensure valid uncertainty quantification we develop a local conformal inference step.  We study the theoretical properties of this approach, empirically compare performance against benchmarks and apply the method to spatiotemporal interpolation of global daily aerosol optical depth.

Presentation Title: Statistical Shape Analysis of Complex Natural Structures

Abstract: Statistical modeling and analysis of structured data is a fast-growing field in Statistics and Data Science. Rapid advances in imaging techniques have led to tremendous amounts of data for analyzing imaged objects across several scientific disciplines. Examples include shapes of cancer cells, botanical trees, human biometrics, 3D genome, brain anatomical structures, crowd videos, nano-manufacturing, and so on. Shapes are relevant even in non-imaging data contexts, e.g., the shapes of COVID rate curves or the shapes of activity cycles in lifestyle data. Imposing statistical models and inferences on shapes seems daunting because the shape is an abstract notion and one requires precise mathematical representations to quantify shapes. This talk has two parts. In the first part, I will present some recent developments in "elastic representations" of structures such as functions, curves, surfaces, and graphs. In the second part, I will focus on statistical analyses: computing shape summaries, estimation under shape constraints, hypothesis testing, time-series models, and regression models involving shapes.

Presentation Title: Simulation-based Uncertainty Quantification for Remote Sensing Inverse Problems

Abstract: Remote sensing data provide a vast trove of information about Earth systems. These data are inferred from electromagnetic spectra observed by Earth-orbiting instruments using computational algorithms that approximately solve the following inverse problem. Given a spectrum, find the best estimate of the underlying true geophysical state that gave rise to it. The algorithms typically start with an initial guess for the true state, and iteratively try to minimize cost functions based on differences between predicted spectra from a deterministic forward model, and spectra actually observed. This set-up incorporates many important aspects related to uncertainty quantification for complex physical-statistical systems including intractable likelihoods, unknown physics, parameter calibration, computational demands, etc. The remote sensing problem is also inherently spatial, which is both a curse, in that it usually involves massive amounts of data, and a blessing in that it makes dimension reduction possible if we can learn and quantify spatial structure. In this talk I will discuss recent work that demonstrates how we leverage simulation-based inference (Cranmer, Brehmer, and Louppe, 2020), spatial statistical modeling with Gaussian processes (Cressie and Wikle, 2012; Paciorek and Schervish, 2006; Sainsbury-Dale, Zammit-Mangion, and Huser, 2024), and conditional spatial simulation to obtain robust uncertainty estimates for the output of a remote sensing data processing pipeline. If time permits, I will also show results of some preliminary work to quantify and incorporate model discrepancy.