Unless otherwise noted, the Department of Statistics Seminar Series for the Spring 2023 semester will take place on Wednesdays at 3 PM EST. Please note that our public seminar series is abbreviated this term due to faculty recruitement season.
March 29, 2023
Nicole A. Lazar, Professor of Statistics at Penn State University
Title: Hypothesis Testing for Shapes Using Vectorized Persistence Diagrams
Abstract: Topological data analysis involves the statistical characterization of data shape. One of the key tools for this purpose is persistent homology, which can be used to summarize the relevant features. In this talk, I will start with a quick survey of the topological data analysis approach and the inferential challenges it poses. I will then introduce a two-stage hypothesis test for vectorized persistence diagrams represented in Euclidean space. The method is flexible, and can be applied to a wide variety of data types. Furthermore, the proposed procedure yields more accurate and informative inference compared to other hypothesis testing methods for persistent homology.
April 5, 2023 (via Zoom)
Xueying Tang, Assistant Professor of Mathematics at University of Arizona
Title: Modeling sparsity using log-Cauchy priors
Abstract: Sparsity is often a desired structure for parameters in high-dimensional statistical problems. Within a Bayesian framework, sparsity is usually induced by spike-and-slab priors or global-local shrinkage priors. The latter choice is often expressed as a scale mixture of normal distributions. It marginally places a polynomial-tailed distribution on the parameter. In general, a heavy-tailed prior with significant probability mass around zero is preferred in estimating sparse parameters. In this talk, we consider a general class of priors, with the log Cauchy priors as a special case, in the normal mean estimation problem. This class of priors is proper while having a tail order arbitrarily close to one. The resulting posterior mean is a shrinkage estimator, and the posterior contraction rate is sharp minimax. We also demonstrate the performance of this class of priors on simulated and real datasets.
April 19, 2023
Martin Lindquist, Professor of Biostatistics at Johns Hopkins University
Title: Individualized spatial topology in functional neuroimaging
Abstract: Neuroimaging is poised to take a substantial leap forward in understanding the neurophysiological underpinnings of human behavior, due to a combination of improved analytic techniques and the quality of imaging data. These advances are allowing researchers to develop population-level multivariate models of the functional brain representations underlying behavior, performance, clinical status and prognosis, and other outcomes. Population-based models can identify patterns of brain activity, or ‘signatures’, that can predict behavior and decode mental states in new individuals, producing generalizable knowledge and highly reproducible maps. These signatures can capture behavior with large effect sizes and can be used and tested across research groups. However, the potential of such signatures is limited by neuroanatomical constraints, in particular individual variation in functional brain anatomy. To circumvent this problem, current models are either applied only to individual participants, severely limiting generalizability, or force participants’ data into anatomical reference spaces (atlases) that do not respect individual functional topology and boundaries. Here we seek to overcome this shortcoming by developing new topological models for inter-subject alignment, which register participants’ functional brain maps to one another. This increases effective spatial resolution, and more importantly allow us to explicitly analyze the spatial topology of functional maps make inferences on differences in activation location and shape across persons and psychological states. In this talk we discuss several approaches towards functional alignment and highlight promises and pitfalls.
April 26, 2023
Snigdha Panigrahi, Assistant Professor of Statistics at University of Michigan
Title: Approximate selective inference via maximum likelihood
Abstract: Several strategies have been developed recently to ensure valid inferences after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this talk, we will address the problem of selective inference through approximate maximum likelihood estimation.
Our goal is to: (i) efficiently utilize hold-out information from selection with the aid of randomization, (ii) bypass expensive MCMC sampling from exact conditional distributions that are hard to evaluate in closed forms. At the core of our new method is the solution to a convex optimization problem which assumes a separable form across multiple learning queries during selection. We illustrate the potential of our method across wide-ranging values of signal-to-noise ratio in simulated experiments.
Tuesday, June 6, 2023
Jason Fine, Visiting Researcher at National Cancer Institute
Title: Emerging Areas for Competing Risks in Nested Case Control Studies
Abstract: This talk will overview some emerging statistical area for competing risks in nested case control studies, which are popular in cancer research. A key issue in the design of such studies is the definition of a "case". We consider an alternative "case" definition to the usual definition based on not having failed from any of the failure types of interest. Each failure type may have a marginal "case" definition. Issues of endpoint definition, efficiency and interpretability are presented, with a focus on unification of the two case definitions in a single modelling framework. A second issue is that it is common that many nested case control studies may be conducted using a common dataset. The potential for efficiency gain when combining data from nested case-control studies on different cancer types has not been fully explored. I will discuss a model speification based on Lunn-McNeil proportional risk model which can be applied in the nested case control setting. The main idea is that efficiency may be gained by specifying a single proportional hazards model which subsumes
data from the multiple nested case control studies. Large gains in efficiency may be achieved, particularly for event types which are rare. Finally, I consider the issue of secondary endpoints in competing risks nested case control studies, with a focus on tting Fine-Gray model for the cumulative incidence function using data from a standard nested case-control study, where the primary endpoint is the cause specific hazard function. I will heuristically sketch an approach based on weighting and describe some of the complicating factors which distinguish this analysis from previous analyses of secondary endpoints in nested case-control studies.
Please be sure to check back for updates, or email srh75@pitt.edu to be added to the Seminar Series mailing list. For any virtual seminars, a Zoom link will be sent to the mailing list.