Related papers: On a characterization theorem in the space $\mathb…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
We construct spaces of quantum increasing sequences, which give quantum families of maps in the sense of Soltan. We then introduce a notion of quantum spreadability for a sequence of noncommutative random variables, by requiring their joint…
Given a collection $\{\lambda_1, \dots, \lambda_n\} $ of real numbers, there is a canonical probability distribution on the set of real symmetric or complex Hermitian matrices with eigenvalues $\lambda_1,\ldots,\lambda_n$. In this paper, we…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…
The fiducial is not unique in general, but we prove that in a restricted class of models it is uniquely determined by the sampling distribution of the data. It depends in particular not on the choice of a data generating model. The…
We establish a non-Archimedean analogue of Koksma's theorem. For a local field F of characteristic zero, we prove that the sequence ([{\alpha}x^n]) is uniformly distributed in the valuation ring O for almost every x with |x|_p>1. In the…
We describe a method for inferring linear causal relations among multi-dimensional variables. The idea is to use an asymmetry between the distributions of cause and effect that occurs if both the covariance matrix of the cause and the…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
We characterize semicircular distribution by the freeness of linear and quadratic forms in noncommutative random variables from a tracial $W^*$-probability space with relaxed moment conditions.
We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
The characteristic variety plays an important role in the analysis of the solution space of partial differential equations and exterior differential systems. This article studies the linear span of this variety, measuring its dimension via…
Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
We consider a random walk on a homogeneous space $G/\Lambda$ where $G$ is $\mathrm{SO}(2,1)$ or $\mathrm{SO}(3,1)$ and $\Lambda$ is a lattice. The walk is driven by a probability measure $\mu$ on $G$ whose support generates a Zariski-dense…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…