# Gaussian processes

Wednesday, June 17, 2015 - 2:00pm - 3:30pm

Laura Swiler (Sandia National Laboratories)

This lecture will discuss meta-models (also called surrogate models or emulators) and their role in emulation of computer models. This lecture will focus on one particular emulator, the Gaussian Process (GP) Model. We will discuss the functional form of the GP, how GPs differ from other models, how to estimate the parameters governing the GP, training set design, and software tools available. We will conclude with the use of GPs in various contexts: in experimental design, optimization, and calibration.

Wednesday, April 15, 2015 - 3:10pm - 4:00pm

Emanuel Indrei (Carnegie-Mellon University)

The so-called logarithmic Sobolev inequalities appear in various branches of statistical mechanics, quantum field theory, Riemannian geometry, and partial differential equations. In this talk, we discuss recent progress towards establishing sharp quantitative versions of the classical Gaussian log-Sobolev inequality. This is based on joint work with Max Fathi and Michel Ledoux.

Tuesday, April 14, 2015 - 2:50pm - 3:40pm

Intrinsic volumes of convex sets are natural geometric quantities that also play important roles in applications. In particular, the discrete probability distribution ${cal L}(V_C)$ given by the sequence $v_0,ldots,v_d$ of conic intrinsic volumes of a closed convex cone $C$ in $mathbb{R}^d$ summarizes key information about the success of convex programs used to solve for sparse vectors, and other structured unknowns such as low rank matrices, in high dimensional regularized inverse problems.

Tuesday, June 26, 2012 - 2:00pm - 3:15pm

Radoslaw Adamczak (University of Warsaw)

I will discuss results by R. Latala concerning tail behaviour of

multivariate polynomials in independent Gaussian variables and show

how when combined with

classical functional inequalities they give estimates for polynomials

and more generally smooth functions with bounded derivatives of higher

order for a more general class of non-necessarily product measures. I

will also present similar inequalities for polynomials of general

sequences of independent subgaussian

multivariate polynomials in independent Gaussian variables and show

how when combined with

classical functional inequalities they give estimates for polynomials

and more generally smooth functions with bounded derivatives of higher

order for a more general class of non-necessarily product measures. I

will also present similar inequalities for polynomials of general

sequences of independent subgaussian

Tuesday, June 19, 2012 - 3:30pm - 4:45pm

Benedek Valko (University of Wisconsin, Madison)

By the Hilbert-Polya conjecture the critical zeros of the Riemann zeta function correspond to the eigenvalues of a self adjoint operator. By a conjecture of Dyson and Montgomery the critical zeros (after a certain rescaling) look like the bulk eigenvalue limit point process of the Gaussian Unitary Ensemble. It is natural to ask if this point process can we described as the spectrum of a random self adjoint operator.

Monday, August 2, 2010 - 4:00pm - 4:30pm

Xiaobai Sun (Duke University)

We introduce numerical study on the discrete counterpart of Gauss'

theorem. The purpose is to seek and establish a third approach,

beside the analytical and the kernel-independent approaches,

for efficient dimension reduction and preconditioning of equations

initially in differential form. Integration is done locally,

or globally, using analytical/symbolic rules as

well as numerical rules and utilizing geometric information.

theorem. The purpose is to seek and establish a third approach,

beside the analytical and the kernel-independent approaches,

for efficient dimension reduction and preconditioning of equations

initially in differential form. Integration is done locally,

or globally, using analytical/symbolic rules as

well as numerical rules and utilizing geometric information.

Tuesday, June 12, 2007 - 11:00am - 12:30pm

Ronald DeVore (University of South Carolina)

Examples of performance for Gaussian and Bernoulli ensembles.

Thursday, March 8, 2007 - 9:00am - 9:50am

Thomas Richardson (University of Washington)

In the 1920's the geneticist Sewall Wright introduced a class of

Gaussian statistical models represented by graphs containing directed

and bi-directed edges, known as path diagrams. These models have been

used extensively in psychometrics and econometrics where they are

called structural equation models.

Gaussian statistical models represented by graphs containing directed

and bi-directed edges, known as path diagrams. These models have been

used extensively in psychometrics and econometrics where they are

called structural equation models.

Thursday, April 30, 2015 - 2:00pm - 2:50pm

Fedor Nazarov (Kent State University)

I will describe our joint work with Mikhail Sodin on the expected value of the number of nodal domains of various Gaussian ensembles and try to attract attention to some open questions in the area.

Monday, January 14, 2013 - 2:00pm - 2:50pm

Michael Cranston (University of California)

We consider large scale behavior of the solution set of values u(t,x) for x in the d-dimensional integer lattice of the parabolic Anderson equation. We establish that the properly normalized sums of the u(t,x), over spatially growing boxes have an asymptotically normal distribution if the box grows sufficiently quickly with t and provided intermittency holds. The asymptotic distribution of properly normalized sums over spatially growing disjoint boxes is asymptotically independent.