Related papers: Hyperbolic valued random variables and conditional…
This paper introduces a new idea for constructing operators associated with a certain class of probability measures. Special cases include several know classical and noncommutative probability. The main example is derived from Feller [30,…
The probabilistic interpretation of Laplace transforms is used to help to describe the Laplace Transform $L(s)$ of improper random variables. In particular, busy periods in queueing models are examined. The value of $L(0)$ is explained in…
Given a normalized state-vector $\psi $, we define the conditional expectation $\mathbb{E }_{\psi } (A | B ) $ of a Hermitian operator $A $ with respect to a strongly commuting family of self-adjoint operators $B $ as the best…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a…
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power…
We introduce Hyperbolic Prototype Learning, a type of supervised learning, where class labels are represented by ideal points (points at infinity) in hyperbolic space. Learning is achieved by minimizing the 'penalized Busemann loss', a new…
We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…
The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are…
This paper presents a new method for conditional probability density simulation. The method is design to work with unstructured data set when data are not characterized by the same covariates yet share common information. Specific examples…
This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local…
Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a non-negative integer. We treat both the Poisson and Negative Binomial families as models for the…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…