Abstracts for the morning speakers

Here are the titles and abstracts for the morning speakers.

Prof. Luis Carvalho

Title: Bayesian centroid estimation for discrete inference: theory and

applications

Abstract:

Maximum likelihood estimators have traditionally dominated discrete inference

for a long time. In the first talk we apply statistical decision theory to

derive a new contender that minimizes a posterior generalized Hamming loss:

the centroid estimator. Since this loss is more refined, this estimator better

identifies and accounts for regions of high concentration of posterior

probability in the parameter space. We discuss both specific constraints of

interest and broad conditions under which this optimization problem becomes

computationally tractable and provide further generalizations to centroid

estimation. In the second talk we illustrate centroid estimation with

applications to land cover classification, genome-wide association studies

(GWAS), and community detection.

Prof. Henry Lam

Title: A robust approach to assessing input model uncertainty

Abstract: Sensitivity analysis for stochastic systems that arise in engineering and finance is typically carried out

via derivative estimation, which critically requires parametric model

assumptions. In many situations, however, we want to evaluate model

misspecification effect beyond certain parametric family of models, or

in some cases, there plainly are no parametric models to begin with.

Motivated by such deficiency, in this talk we will propose a sensitivity analysis

framework that is parameter-free, by using statistical distances such as Kullback-Leibler

divergence and chi-square distance as a measure of model discrepancy, and obtain well-defined

derivative estimators. These estimators are robust in that they

automatically choose the worst (and best)-case directions to move

along in the (typically infinite-dimensional) model space. They

require little knowledge to implement; the distributions of the

underlying random variables can be known up to, for example, black-box

simulation. The first part of the talk will cover the basic formulation and methodology to construct these estimators.

In the second part, we will generalize the framework in several directions, including sensitivity with respect to input serial dependency,

steady-state estimation and the incorporation of moment equations.

Prof. Konstantinos Spiliopoulos

Talk 1:

Title: Metastability and Monte Carlo Methods for Multiscale Problems

Abstract: Rare events, metastability and Monte Carlo methods for

stochastic dynamical systems have been of central scientific interest for many years now. In this talk we focus on rough energy landscapes, that are modeled as multiscale stochastic dynamical systems perturbed by small noise.

Large deviations deals with the estimation of rare events. Depending on the type of interaction of the fast scales with the strength of the noise we get differen t behavior, both for the large deviations and for the corresponding Monte Carlo methods.I will describe how to design asymptotically provably efficient importance sampling schemes for the estimation of associated rare event probabilities, such as exit probabilities,hitting probabilities, hitting times,

and expectations of functionals of interest. Standard Monte Carlo methods perform poorly in these kind of problems in the small noise limit. In the presence of multiple scales one faces additional difficulties and straightforward adaptation of importance sampling schemes for standard small noise diffusions will not produce efficient schemes. We resolve this issue and demonstrate the theoretical results by examples and simulation studies. Time permitting we will discuss construction of efficient Monte Carlo methods for the related problem of escape from a stable equilibrium point.

Talk 2:

Title: Systemic risk in large financial networks

Abstract: The past several years have made clear the need to better understand the behavior of risk in large interconnected financial networks. Interconnections often make a system robust, but they can act as conduits for risk. In this talk, I will present recent results on modeling the dynamics of correlated default events in the financial market. An empirically motivated system of interacting point processes is introduced and we study how different types of risk, like contagion and exposure to systematic risk, compete and interact in large-scale systems. A law of large numbers for the loss from default is proven and used for approximating the distribution of the loss from default in large, potentially heterogeneous portfolios. Fluctuation analysis and conditional Gaussian approximations are used to improve the approximations. Then, large deviations theory allows us to capture the tail of the distribution and quantify large portfolio losses. Numerical results illustrate the accuracy of

the approximations. The results give insights into how different sources of default correlation interact to generate typical and atypical portfolio losses.