# Seminars

## Seminars 2015-2016

### Upcoming

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.

### Past

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.