1. Hereditary and Lacunary Limit Theorems in Probability and Analysis

Ioannis Karatzas, Columbia University

In the spirit of the celebrated Komlos theorem, we develop versions of the Weak and of the Hsu-Robbins-Erdos Laws of Large Numbers which are valid along appropriate (“lacunary”) subsequences of arbitrary sequences of random variables with bounded moments; as well as along all further (“hereditary”) subsequences of said subsequences. We also review the strong connections of this subject with lacunary trigonometric series.

*Joint work with Walter Schachermayer, Vienna.

2. Non-Standard Dynamic Utility Maximization

Steven Kou, Boston University

This talk will survey recent research on non-standard dynamic utility maximization, where the utility function may not be concave or increasing. Examples include (1) nonconcave utility functions used in behavioral economics, (2) the goal problems in household finance, (3) dynamic mean-variance analysis, and (4) median and quantile maximization. The latter two also have time inconsistency issues.

3. Topics in Sequential Analysis and Martingales

Victor de la Pena, Columbia University

In this presentation I will discuss my collaborative work with Y.S. Chow and T. L Lai. In particular, I will review important extensions of Wald’s equation to cases involving denormalized U-statistics, including multilinear forms.  I will also discuss some aspects of joint work on Self-normalization with T. L. Lai

4. Exploratory Data Analysis, Confirmatory Data Analysis and Replication in the Same Observational Study: A Two Team Cross-Screening Approach to Studying the Effect of Unwanted Pregnancy on Mothers’ Later Life Outcomes

Dylan S. Small, Wharton School of University of Pennsylvania

Exploratory data analysis, confirmatory data analysis and replication are three important aspects of building strong evidence from observational studies.  Exploratory data analysis, confirmatory data analysis and replication are often thought of as being done on separate studies.  However, for settings where randomized experiments are impossible to conduct for ethical reasons and observational studies must be relied on, it is common that there is a data set with unique strengths.  We developed a two-team cross screening approach that allows for exploratory data analysis, confirmatory data analysis and replication to be done in the same observational study data set.  We apply the approach to study the effect of unwanted pregnancy on mothers’ later life outcomes using data from the Wisconsin Longitudinal Study.

*This is joint work with Samrat Roy, Marina Bogomolov, Ruth Heller, Amy Claridge and Tishra Beeson.

5. Sequential analysis of survival data

Gordan Lan, Johnson and Johnson

I will review the early termination of BHAT – a survival trial sponsored by NHLBI-NIH in 1982. Some of the technical problems in monitoring survival trials are still unsolved.  I would like to use heuristic explanations to illustrate why “proportional hazards assumption” cannot be valid in the trial setting.

6. Chow and Lai, 1960-1990

David Siegmund, Stanford University

I will begin by reviewing four papers of Chow and Robbins in the mid-1960s and three papers of Chow and Not-Robbins. I will then describe the rapid development of a model for sequential clinical trials in the 1970s motivated by the contributions of Armitage (1960, 1975) and leading to the contributions of Lai and Siegmund (1977, 1979). (See also Woodroofe, 1976.) Finally, I will discuss a number of subjectively selected papers of T. L. Lai, obtained (with one exception) before his move to Stanford in 1987.

7. A Personal Remembrance of Y. S. Chow and Tze Lai

William F. Stout, University of Illinois at Urbana-Champaign

This is an equal remembrance of both men, Y.S. as my thesis advisor and Tze as a wonderful research colleague both many years ago and very recently.  Both were people of great character and superb researchers and collaborators. The talk will be a mix of personal recollections/stories and how each man helped influence and shape my career, both as a probabilist and psychometrician.

8. Fast Algorithms for Estimating Covariance Matrices of Stochastic Gradient Descent Solutions

Wei-Biao Wu, University of Chicago

Stochastic gradient descent (SGD), an important optimization method in machine learning, is widely used for parameter estimation especially in online setting where data comes in stream. While this recursive algorithm is popular for the computation and memory efficiency, it suffers from randomness of the solutions. In this talk we shall estimate the asymptotic covariance matrices of the averaged SGD iterates (ASGD) in a fully online fashion. Based on the recursive estimator and classic asymptotic normality results of ASGD, we can conduct online statistical inference of SGD estimators and construct asymptotically valid confidence intervals for model parameters. The algorithm for the recursive estimator is efficient and only uses SGD iterates: upon receiving new observations, we update the confidence intervals at the same time as updating the ASGD solutions without extra computational or memory cost. This approach fits in online setting even if the total number of data is unknown and takes the full advantage of SGD: computation and memory efficiency.

*This work is joint with Wanrong Zhu and Xi Chen.

9. Change Point Detection in Hidden Markov Models

Cheng-Der Fuh, National Central University, Taiwan

In this talk, I give a brief summary of change point detection in general hidden Markov models, including single-molecule experiments, an epidemic model for the COVID-19 outbreak, financial time series and sensor networks. Then present a theoretical result, in which the pre-change distribution fθ0 is given, while the post-distribution fθ after change is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from fθ0 to fθ, under a restriction on the false alarms. I investigate theoretical properties of a weighted Shiryayev-Roberts-Pollak (SRP) change point detection rule, to show that it is second-order asymptotically optimal. To illustrate the method, I apply the results to linear state space models with simulation studies.

10. Latent Space Models for Dynamic Networks

Yuguo Chen, University of Illinois at Urbana-Champaign

Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. The model parameters provide insight into the structure of the network, and the visualization provided from the model gives insight into the network dynamics. In addition to discussing our model, we also highlight the contributions of Professor Tze Leung Lai to
sequential importance sampling methods and their applications.

11. Prediction of change-point probability and its application the credit rating migrations

Haipeng Xing, Stony Brook University

This talk introduces a generic predictive model for change-points by using the logistic modeling and the hidden Markov filtering approach. Based on this approach, a predictive model for structural breaks in credit rating transitions is developed, which uses firms’ credit rating records and observed and latent economic variables. Applying the model to the S&P 500 credit rating data and economic variables from 1986 to 2015, we find that the probabilities of structural breaks are positively correlated with changes in S&P 500 returns, as well as volatilities and changes of inflation, and negatively correlated with changes in corporate bond yield. The significance of other variables depends on whether latent variables are included in the study or not.