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.