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, tr...

Creator:

Swiler, Laura (Sandia National Laboratories)

Created:

2015-06-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

I will discuss results by R. Latala concerning tail behaviour of multivariate polynomials in independent Gaussian variables and show how when combined withclassical 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 p...

Creator:

Adamczak, Radoslaw (University of Warsaw)

Created:

2012-06-26

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In the 1920's the geneticist Sewall Wright introduced a class ofGaussian statistical models represented by graphs containing directedand bi-directed edges, known as path diagrams. These models have beenused extensively in psychometrics and econometrics where they arecalled structural equation models.I will first describe the subclass of bow-free...

Creator:

Richardson, Thomas S. (University of Washington)

Created:

2007-03-08

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

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 ...

Creator:

Goldstein, Larry

Created:

2015-04-14

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The Gauss-Manin system of a function is a direct image in the category of D-modules. For the case of isolated singularities there are two Singular libraries to compute it: gmssing.lib for (local) isolated hypersurface singularities, gmspoly.lib for (global) tame polynomial functions. In both cases the Gauss-Manin system carries a rich structure:...

Creator:

Schulze, Mathias (Oklahoma State University)

Created:

2006-10-27

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed sta...

Creator:

Banerjee, Sudipto (University of California, Los Angeles)

Created:

2018-02-23

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

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.

Creator:

Nazarov, Fedor (Kent State University)

Created:

2015-04-30

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

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 interm...

Creator:

Cranston, Michael (University of California, Irvine)

Created:

2013-01-14

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

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 pro...

Creator:

Valko, Benedek (University of Wisconsin, Madison)

Created:

2012-06-19

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

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 ...

Creator:

Indrei, Emanuel (Carnegie Mellon University)

Created:

2015-04-15

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

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 analytic...

Creator:

Sun, Xiaobai (Duke University)

Created:

2010-08-02

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.