Abstract: The celebrated, and much maligned, method of maximum likelihood is enjoying a modest revival for semiparametric models.  For shape constrained density and regression problems, and for mixture models and compound decision problems nonparametric maximum likelihood offers an efficient and tuning-parameter-free computational strategy.  Reweighted forms of quantile regression that borrow strength across nearby quantiles can also be formulated in likelihood terms.  Several variants of these unusual likelihoods will be reviewed, stressing some open problems.

Itinerary for the lecture:

3:30pm - Announcement the Anderson Award Winners

3:40pm - 'Remembering R.L. Anderson' by Dr. David Allen

3:50pm - Introduction of Dr. Koenker by Dr. Carlos Lamarche

4:00pm - R.L. Anderson Lecture - Unlikely Likelihoods

5:00pm - Event Wrap-Up

Abstract: Multilayer networks continue to gain significant attention in many areas of study, particularly, due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socio-environmental ecosystems. However, clustering of multilayer networks, especially, using the information on higher order interactions of the system entities, yet remains in its infancy. We discuss a new topological approach for multilayer network clustering, based on the rationale to group nodes not using the pairwise connectivity patterns or relationships between observations recorded at two individual nodes, but based on how similar in shape their local neighborhoods are at various resolution scales.  We quantify shapes of local node neighborhoods using persistence diagrams and then consider either single linkage or k-means forms of topological clustering, which allows us to systematically account for the important heterogeneous higher-order properties of node interactions within and in-between network layers and to integrate information from the node neighbors. In case of topological k-means, we also show that casting it into an empirical risk minimization framework using reproducing kernel Hilbert spaces allows us to derive clustering stability guarantees, similarly to the Euclidean k-means, i.e., property that most existing topological clustering methods lack. We illustrate our topological clustering methods in application to climate-insurance and COVID-19 data.

Abstract: In this talk, I will present a Bayesian framework for registration of real-valued functional data.  I will introduce function registration and its statistical setup, as well as a series of transformations, developed under a differential geometric framework, that simply the data and functional parameters.  Approximate draws from the posterior distribution are obtained using a novel Markov chain Monte Carlo (MCMC) algorithm which is well suited for estimation of functions.  Both simulated and real datasets will be presented to illustrate the proposed approach.

Abstract: In many statistical applications, subject matter knowledge or theoretical considerations suggest that two distributions should satisfy a stochastic order, with samples from one distribution tending to be larger than those from the other. In these situations, incorporating stochastic order constraints can lead to improved inferences. This talk will introduce mixture representations for distributions satisfying a likelihood ratio order. To illustrate the practical value of the mixture representations, I’ll address the problem of density estimation for likelihood ratio ordered distributions. In particular, I'll propose a nonparametric Bayesian solution which takes advantage of the mixture representations. The prior distribution is constructed from Dirichlet process mixtures and has large support on the space of pairs of densities satisfying the monotone ratio constraint. With a simple modification to the prior distribution, we can also test the equality of two distributions against the alternative of likelihood ratio ordering. I’ll demonstrate the approach in two biomedical applications.

Abstract: With the advent of continuous health monitoring with wearable devices, users now generate their unique streams of continuous data such as minute-level step counts or heartbeats. Summarizing these streams via scalar summaries often ignores the distributional nature of wearable data and almost unavoidably leads to the loss of critical information. We propose to capture the distributional nature of wearable data via user-specific quantile functions (QF) and use these QFs as predictors in scalar-on-quantile-function-regression (SOQFR). As an alternative approach, we also propose to represent QFs via user-specific L-moments, robust rank-based analogs of traditional moments, and use L-moments as predictors in SOQFR (SOQFR-L). These two approaches provide two mutually consistent interpretations: in terms of quantile levels by SOQFR and in terms of L-moments by SOQFR-L. We also demonstrate how to deal with multi-modal distributional data via Joint and Individual Variation Explained (JIVE) using L-moments. The proposed methods are illustrated in a study of association of digital gait biomarkers with cognitive function in Alzheimer’s disease (AD). Our analysis shows that the proposed methods demonstrate higher predictive performance and attain much stronger associations with clinical cognitive scales compared to simple distributional summaries.

Abstract: The estimation of the spatio-temporal dynamics of animal behavior processes is complicated by nonlinear interactions among individuals and with the environment. Agent-based methods allow for defining simple rules that generate complex group behaviors, but are statistically challenging to estimate and assume behavioral rules are known a priori. Instead of making simplifying assumptions across all anticipated scenarios, inverse reinforcement learning provides inference on the short-term (local) rules governing long term behavior policies or choices by using properties of a Markov decision process. We use the computationally efficient linearly-solvable Markov decision process (LMDP) to learn the local rules governing collective movement. The estimation of the immediate and long-term behavioral decision costs is done in a Bayesian framework. The use of basis function smoothing is used to induce smoothness in the costs across the state space. We demonstrate the advantage of the LMDP for estimating dynamics for a classic collective movement agent-based model, the self propelled particle model. Then, we present the first data application of IRL using the introduced methodology for collective movement of guppies in a tank and estimate trade offs between social and navigational decisions. Lastly, a brief discussion on the connections to traditional resource selection functions in ecology demonstrates the future potential advantage of LMDPs for inference on behavioral decisions as a result of an accumulation of behavioral costs.

Please join us as we celebrate the many contributions of Dr. Mai Zhou on the occasion of his retirement from the University of Kentucky. Dr. Zhou joined the Dr. Bing Zhang Department of Statistics in 1989 after completing his degree at Columbia University and spending time in visiting positions at MIT and UNC-CH. Dr. Zhou served as DGS and DUS during his time in the department and he developed an international reputation for his work on empirical likelihood, survival analysis, and semiparametrics. He was an early user and advocator of R. For over 30 years, Dr. Zhou has been the consummate professional and colleague.

The celebration will be very informal.  After a brief welcome by Dr. Rayens, Dr. Zhou will reflect on what he considers to be the contributions to research, teaching, and R that he is most proud of, or at least had the most fun with.   At the conclusion of these remarks, Dr. Regina Liu, Distinguished Professor of Statistics at Rutgers University, will share some memories.   Dr. Liu and Dr. Zhou were doctoral classmates at Columbia.  Following Dr. Liu’s remarks, we will open the floor to Dr. Zhou’s former students, many of whom will be in attendance, then to former colleagues and friends.