Related papers: A Bayesian Probability Calculus for Density Matric…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…
The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate…
As described quantum mechanically, an experimental trial parses into "a preparation" expressed by a density operator and "a measurement" expressed by a set of detection operators, one for each measurable event. A density operator and a…
In this paper we give a formula for the probability that $n$ random points chosen under the uniform distribution in a disk are in convex position. While close, the formula is recursive and is totally explicit only for the first values of…
It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}\Psi probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
Decision theory does not traditionally include uncertainty over utility functions. We argue that the a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…