Random Determinants, Mixed Volumes of Ellipsoids, and Zeros of Gaussian Random Fields

Autoregressive Gaussian Random Vectors of First Order

Skew-Gaussian Random Fields

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...

Gaussian Process Random Fields

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via pairwise potentials. The GPRF likelihood is a simple, tractable, and paralle...

Random Walks and Mixed Volumes of Hypersimplices

Below is a method for relating a mixed volume computation for polytopes sharing many facet directions to a symmetric random walk. The example of permutahedra and particularly hypersimplices is expanded upon.

On Expected Gaussian Random Determinants

The expectations of random determinants whose entries are real-valued, identically distributed, mean zero, correlated Gaussian random variables are examined using the Kronecker tensor products and some combinatorial arguments. This result is used to derive the expected determinants of X +B and AX +X ′B.