# Seminars

## Seminars 2015-2016

### Upcoming

Wednesday, February 10, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Speaker: Amir Dembo (Stanford University)

Title: Walking within growing domains: recurrence versus transience

Abstract: When is simple random walk on growing in time d-dimensional domains recurrent? For domain growth which is independent of the walk, we review recent progress and related universality conjectures about a sharp recurrence versus transience criterion in terms of the growth rate. We compare this with the question of recurrence/transience for time varying conductance models, where Gaussian heat kernel estimates and evolving sets play an important role. We also briefly contrast such expected universality with examples of the rich behavior encountered when monotone interaction enforces the growth as a result of visits by the walk to the current domain's boundary. This talk is based on joint works with Ruojun Huang, Ben Morris, Yuval Peres and Vladas Sidoravicius.

Wednesday, February 17, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Speaker: Joong-Ho (Johann) Won (Seoul National University)

Title: Computational approaches in data mining and portfolio selection

Abstract: This talk consists of two parts. In the first part, I will share my experience with the use of high-performance computing (HPC) in high-dimensional data mining problems, which are well known to be difficult both theoretically and computationally. I advocate parallelization as a practical solution to mitigate the computational difficulties, and show that a fair amount of parallelism can be achieved with small efforts by using commodity HPC systems. Success and failure stories of adopting graphics processing units (GPUs) for the fused lasso sparse regression and Hadoop MapReduce for graph algorithms are discussed. In the second part, I will discuss a use of numerical optimization in financial portfolio selection problems in the presence of parameter uncertainty. Robust optimization is employed to explicitly incorporate a model of parameter uncertainty in the problem formulation, and optimizes for the worst-case scenario. This part of the talk considers robust mean-variance portfolio selection involving a trade-off between the worst-case utility and the worst-case regret, or the largest difference between the best utility achievable under the model and that achieved by a given portfolio. I will show that while optimizing for the worst-case utility may yield an overly pessimistic portfolio, optimizing for the worst-case regret may result in a complete loss of robustness. Robust trade-off portfolio compromises these two extremes, enabling more informative selections. I will show that, under a widely used ellipsoidal uncertainty model, the entire optimal trade-off curve can be found via solving a series of semidefinite programs (SDPs), which are computationally tractable. I then extend the model to handle a union of finitely many ellipsoids, and show that trade-off analysis under this quite general uncertainty model also reduces to a series of SDPs. For more general uncertainties, I propose an iterative algorithm based on the cutting-set method.

Wednesday, March 2, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Speaker: György Terdik (UD Hungary & UCSB)

Title: A new covariance function for spatio-temporal data analysis with applications

Abstract: TBA

Wednesday, April 20, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Speaker: Sudipto Banerjee (UCLA)

Title: TBA

Abstract: TBA

### Past

Wednesday, January 20, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Davar Khoshnevisan (University of Utah)

Title: Dissipation and High Disorder

Abstract: We consider the "parabolic Anderson model" with delta initial function. This is a linear, infinite system of stochastic differential equations that arise in a vast number of physical models. The solution of this system models, among other things, the particle density of of an infinite system of independent random walks, which replicate [give birth] to new random walks according to a common [independent] space-time white noise environment, starting with one particle at the origin at time 0. We show that, when the underlying random walks move in 1 or 2 dimensions, the total number of particles vanishes as time goes to infinity. By contrast, in dimensions 3 or greater there is phase transition: If the variance of the noise is sufficiently high, then the total number of particles vanishes; and if the noise variance is not sufficiently high, then the total number of particles tends to a non-trivial random variable. This talk is based on joint work with Le Chen, Michael Cranston, and Kunwoo Kim.

Wednesday, January 6, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Nils Detering (University of Munich)

Title: Bootstrap percolation in inhomogeneous, directed random graphs and financial contagion

Abstract: Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds that threshold, the vertex gets infected as well and remains so forever. We perform a thorough analysis of bootstrap percolation on a novel model of directed and inhomogeneous random graphs, where the distribution of the edges is specified by assigning two distinct weights to each vertex, describing the tendency of it to receive edges from or to send edges to other vertices. Under the assumption that the limiting degree distribution of the graph is integrable we determine the typical fraction of infected vertices. Our model allows us to study settings that were outside the reach of current methods, in particular the prominent case in which the degree distribution has an unbounded variance. Among other results, we quantify the notion of "systemic risk", that is, to what extent local adverse shocks can propagate to large parts of the graph through a cascade, and discover novel features that make graphs prone/resilient to initially small infections. We show how our results can be used to study default contagion in a financial network. Furthermore, we discuss several statistical aspects related to our model.

Monday, January 4, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Ibrahim Ekren (ETH Zurich)

Title: Viscosity Solutions for Path-dependent PDEs

Abstract: In this talk, we define derivatives of functionals on the space of continuous paths and give an introduction to path-dependent partial differential equations (PPDEs). Since the space of continuous paths is not locally compact, we cannot rely on the theory of viscosity solutions for PDEs and need to develop a new approach. We focus on the path-dependent heat equation and link it to a control problem. We will also mention new developments, challenges and applications in this field. This talk is based on joint works with Christian Keller, Nizar Touzi and Jianfeng Zhang.

Wednesday, December 9, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Daniel Lacker (Brown University)

Title: Mean field limits for stochastic differential games

Abstract: Mean field game (MFG) theory generalizes classical models of interacting particle systems by replacing the particles with decision-makers, making the theory applicable in economics and other social sciences. Most research so far has focused on the existence and uniqueness of Nash equilibria in a model which arises intuitively as a continuum limit (i.e., an infinite-agent version) of a given large-population stochastic differential game of a certain symmetric type. This talk discusses some recent results in this direction, particularly for MFGs with common noise, but more attention is paid to recent progress on a less well-understood problem: Given for each n a Nash equilibrium for the n-player game, in what sense if any do these equilibria converge as n tends to infinity? The answer is somewhat unexpected, and certain forms of randomness can prevail in the limit which are well beyond the scope of the usual notion of MFG solution. A new notion of weak MFG solutions is shown to precisely characterize the set of possible limits of approximate Nash equilibria of n-player games, for a large class of models.

Wednesday, December 2, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Ian Duncan (PSTAT-UCSB)

Title: The Affordable Care Act at 5 years: an actuarial perspective

Abstract: The Affordable Care Act was passed in 2010 and fully-implemented in 2014. Prof. Duncan was on the board of the Massachusetts Health Connector Authority, predecessor of the ACA and was involved in both Massachusetts reform and the ACA implementation in Massachusetts. He continues to be involved with risk adjustment, one of the important actuarial aspects of the law. He will discuss the evolution of the ACA, its successes and some of the issues likely to emerge in future years and their implications for actuaries.

Wednesday, November 18, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Susan Cassels (Geography-UCSB)

Title: Mathematical models to inform effective home-use HIV testing strategies for men who have sex with men

Abstract: The U.S. Food and Drug Administration (FDA) approved the first over-the-counter home-use HIV test in 2012. Public health departments have started to implement programs to increase their use; however, the potential impact of these tests on the HIV epidemic among men who have sex with men (MSM) is unknown. Home-use HIV tests may reduce HIV incidence if used by MSM who would otherwise not test or if they increase rates of testing, diagnosis and treatment. However, home-use tests may increase transmission if men replace clinic-based tests with home-use tests because the relatively long window period of available tests can result in false-negative tests during acute infection when HIV-infected persons are most infectious. The aim of this research is to inform public health approaches to promote safe and effective home-use HIV testing strategies for diverse populations of MSM. Using dynamic HIV transmission modeling, we find that if home-use HIV tests replace clinic-based testing, HIV prevalence may increase among Seattle MSM, even if home-use tests result in increased testing. Using data from two different epidemiologic settings in the U.S., Seattle and Atlanta, future work will use stochastic network models to estimate how different strategies of home-use HIV testing at the individual and partnership levels affects HIV incidence.

Wednesday, November 4, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Tomoyuki Ichiba (PSTAT-UCSB)

Title: Walsh semimartingales and diffusions on metric graphs

Abstract: In this talk we shall discuss diffusions on metric graphs. We start with a change-of-variable formula of Freidlin-Sheu type for Walsh semimartingale on a star graph. In diffusion case we characterize such processes via martingale problem. As a consequence of folding/unfolding semimartingale, we obtain a system of degenerate stochastic differential equations and examine its solution. The stationary distribution, strong Markov property and related statistical problems are also discussed. Then we extend our considerations to diffusions on metric graphs. This talk is based on joint work with I. Karatzas, V. Prokaj and M. Yan.

Wednesday, October 28, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Tomasz J. Kozubowski (Mathematics and Statistics-University of Nevada, Reno)

Title: Wrapping, mixing, and estimation for directional data

Abstract: Directional statistics is an important area, with applications ranging from biology, through earth sciences, to meteorology and medicine. In the first part of the talk, we present a general scheme of generating circular distributions through wrapping linear distributions around a circle, and discuss its particular cases where the linear distribution is either Gaussian or exponential. We then introduce another scheme, where circular distributions are obtained by mixing, and study its relation to wrapping. We show that, in general, these two operations commute: wrapping a mixture of linear distributions corresponds to mixture of wrapped distributions. We explore this in detail, and show that a large number of wrapped circular distributions introduced in the literature can be defined and studied through mixtures of wrapped Gaussian or wrapped exponential distributions. In the second part of the talk, we discuss computational issues arising in estimating circular parameters, where maximum likelihood estimators are rarely available in explicit forms. We present new general methodology, which is based on likelihood and Bayesian principles and can be adapted to circular data.

Wednesday, October 21, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Michael Nava (PSTAT-UCSB)

Title: A Change-point Problem in Circular Statistics

Abstract: Change-point tests are meant to detect the point in time at which a sample of observations changes in the probability distribution from which they came. Suppose one has a set of independent vectors of measurements, observed in a time-ordered or space-ordered sequence. In our set-up, these observations are circular data and we are interested as to which point in time does the distribution change from having one mode to having more than one mode. In this work we model unimodality or bimodality with a mixture of two Circular Normal distributions, which admits both possibilities, albeit for different parameter values. Tests for detecting the change-point are derived using the generalized likelihood ratio method. We obtain simulated distributions and critical values for the appropriate test statistics in finite samples, as well as provide the asymptotic distributions, under some regularity conditions. We also tackle this problem from a Bayesian perspective.

Wednesday, October 14, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Howard Zail (Elucidor, LLC; New York, NY)

Title: Implementation of Bayesian Predictive Analytics for Insurance Product Pricing, Underwriting and Risk Management

Abstract: There has been an explosion of new and powerful Bayesian predictive analytics techniques and methodologies over the last twenty years, but the insurance industry has been very slow at adopting these methodologies in practice. This seminar will present a number of real problems faced by insurers or pension funds and show how these new techniques can be implemented to improve profitability and establish a more efficient capital management strategy. In particular, we will discuss utilizing the following methodologies in a cohesive framework: state space modeling, hierarchical models, efficient and large scale MCMC, feature selection, and probabilistic programming.

Wednesday, October 7, South Hall 5607F, 3:30-5:00 p.m., Refreshments served at 3:15 p.m.

Andrey Sarantsev (PSTAT-UCSB)

Title: Approximation of reflected diffusions by solutions of SDE

Abstract: Consider a reflected diffusion on the positive half-line. It has a hard barrier at zero, which it cannot penetrate. We approximate it by a soft barrier created by drift, that is, by a solution to an SDE. We also consider a mutlidimensional version of this problem.