Related papers: The generalized Gaussian log-Minkowski problem
This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
Existence of symmetric (resp. asymmetric) solutions to the $L_p$ Gaussian Minkowski problem for $p\leq 0$ (resp. $p\geq 1$) will be provided. Moreover, existence and uniqueness of smooth solutions to the problem for $p>n$ will also be…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
We describe positive generalized functionals in Gaussian Analysis. We focus on distribution spaces larger than the space of Hida Distributions. It is shown that a positive distribution is represented by a measure with specific growth of its…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
We propose a Stein characterization of the Kummer distribution on (0, $\infty$). This result follows from our observation that the density of the Kummer distribution satisfies a certain differential equation, leading to a solution of the…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
Combining distributions is an important issue in decision theory and Bayesian inference. Logarithmic pooling is a popular method to aggregate expert opinions by using a set of weights that reflect the reliability of each information source.…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.
Some problems with the recent stimulating proposal of a ``Gauge Theory of Finance'' by Ilinski and collaborators are outlined. First, the derivation of the log-normal distribution is shown equivalent both in information and mathematical…
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image…
By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct…
It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…
We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration…
Information physics considers physical laws to result from the consistent quantification and processing of information about physical phenomena. In previous efforts, one of us (Knuth) has shown that a simple model of particles that directly…
We are able to rederive in a very simple way the standard generalized Wick's theorem for overlaps of mean field wave functions by using the extension of the statistical Wick's theorem (Gaudin's theorem) in the appropriate limits.
In this paper the Orlicz-Minkowski problem for torsional rigidity, a generalization of the classical Minkowski problem, is studied. Using the flow method, we obtain a new existence result of solutions to this problem for general measures.
In this talk an introduction to generalized parton distributions is given. Recent developments are shortly reviewed, including non-perturbative calculations, phenomenological aspects and evaluation of higher order perturbative and power…