Friday, February 22, 2019 — 10:30 AM EST

Equilibrium recoveries in insurance markets with limited liability

In this talk, I will talk about optimal insurance in partial equilibrium in case the insurer is protected by limited liability, and the multivariate insured risk is exchangeable. I focus on the optimal allocation of remaining assets in default, and show existence of an equilibrium in the market. In such an equilibrium, perfect pooling of the risk in the market occurs, but a protection fund is needed to charge levies to policyholders with low realized losses. If policyholders cannot be forced ex post to pay a levy, the constrained equal loss rule is used in equilibrium. This rule gained particular interest in the literature on bankruptcy problems. Moreover, in absence of a regulator, the insurer will always invest all its assets in the risky technology. The welfare losses if other recovery rules are used in case of default are illustrated; a different recovery rule can substantially effect the profit of the insurer. This talk will be based on a working paper on SSRN.  

Thursday, February 14, 2019 — 1:00 PM EST

* PLEASE NOTE: This seminar has been cancelled. 

Propensity scores and missing data, with application to research on effects of prenatal alcohol exposure 

We discuss challenges in analysing data from several epidemiological cohort studies designed to explore the association between prenatal alcohol exposure and child development. After Professors Sandra and Joseph Jacobson briefly describe the broader context, Professor Ryan will give a brief overview of the statistical challenges. Dr. Akkaya will then go into more detail, describing the approaches we have been taking, using propensity score analysis to adjust for potential confounders.  She will briefly review propensity score methods and their extension to application with continuous predictors, such as the amount of alcohol consumed by the mother during pregnancy.  She will then discuss extensions we have developed, using multiple imputation, to handle missing and misspecified covariates in this context.  In particular, she will describe a strategy for incorporating variables that have a two-part or semi-continuous structure.  This arises in our setting, for example, since many women will have zero exposure (meaning they are non-drinkers or abstainers), while there will then be a wide and long-tailed distribution of exposure levels among those who drink.   Two-part or semi-continuous variables also arise among the potential confounding variables in our study, for example, use of cocaine and other drugs during pregnancy.

Tuesday, February 5, 2019 — 4:00 PM EST

Space-filling Designs for Computer Experiments and Their Application to Big Data Research

Computer experiments provide useful tools for investigating complex systems, and they call for space-filling designs, which are a class of designs that allow the use of various modeling methods. He and Tang (2013) introduced and studied a class of space-filling designs, strong orthogonal arrays. To date, an important problem that has not been addressed in the literature is that of design selection for such arrays. In this talk, I will first give a broad introduction to space-filling designs, and then present some results on the selection of strong orthogonal arrays.

The second part of my talk will present some preliminary work on the application of space-filling designs to big data research. Nowadays, it is challenging to use current computing resources to analyze super-large datasets. Subsampling-based methods are the common approaches to reducing data sizes, with the leveraging method (Ma and Sun, 2014) being the most popular. Recently, a new approach, information-based optimal subdata selection (IBOSS) method was proposed (Wang, Yang and Stufken, 2018), which applies the design methodology to the big data problem. However, both the leveraging method and the IBOSS method are model-dependent. Space-filling designs do not suffer this drawback, as shown in our simulation studies.

Friday, February 1, 2019 — 4:00 PM EST

From Random Landscapes to Statistical inference

Consider the problem of recovering a rank 1 tensor of order k that has been subject to additive Gaussian Noise. It is information theoretically possible to recover the tensor with a finite number of samples via maximum likelihood estimation, however, it is expected that one needs a polynomially diverging number of samples to efficiently recover it. What is the cause if this large statistical-to-algorithmic gap? To understand this interesting question of high dimensional statistics, we begin by studying an intimately related question: optimization of random homogenous polynomials on the sphere in high dimensions. We show that the estimation threshold is related to a geometric analogue of the BBP transition for matrices. We then study the threshold for efficient recovery for a simple class of algorithms, Langevin dynamics and gradient descent. We view this problem in terms of a broader class of polynomial optimization problems and propose a mechanism or success/failure of recovery in terms of the strength of the signal on the high entropy region of the initialization. We will review several results including joint works with Ben Arous-Gheissari and Lopatto-Miolane. 

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