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We study random vectors of the form $(\operatorname {Tr}(A^{(1)}V),...,\operatorname {Tr}(A^{(r)}V))$, where $V$ is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the $A^{(\nu)}$ are…
Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to demonstrate that the…
We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. Unlike current…
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
A criterion is given for a type in a finite rank stable theory to be (almost) internal to a given nonmodular minimal type. The motivation comes from results of Campana which give criteria for compact complex analytic spaces to be algebraic…
In [11] it has been proved some variational formula on the Legendre-Fenchel transform of the cumulant generating function (the Cram\'er function) of Rademacher series with coefficients in the space $\ell^1$. In this paper we show a…
We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard…
Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent…
Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing…
The celebrated union-closed conjecture is concerned with the cardinalities of various subsets of the Boolean $d$-cube. The cardinality of such a set is equivalent, up to a constant, to its measure under the uniform distribution, so we can…
We perform the canonical analysis of the Holst action for general relativity with a cosmological constant without introducing second-class constraints. Our approach consists in identifying the dynamical and nondynamical parts of the…
We study the interpretability of conditional probability estimates for binary classification under the agnostic setting or scenario. Under the agnostic setting, conditional probability estimates do not necessarily reflect the true…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
To each associative unitary finite-dimensional algebra over a normal base, we associative a canonical multiplicative function called its determinant. We give various properties of this construction, as well as applications to the topology…
Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.
Based on entropy and symmetrical uncertainty (SU), we define a metric for categorical random variables and show that this metric can be promoted into an appropriate quotient space of categorical random variables. Moreover, we also show that…
We introduce a theory of non-commutative $L^{p}$ spaces suitable for non-commutative probability in a non-tracial setting and use it to develop stochastic analysis of Grassmann-valued processes, including martingale inequalities, stochastic…
In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give…