Related papers: Interval probability density functions constructed…

A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to its mean value over a short interval or over an arithmetic progression, with the interval as short as possible or the modulus as…

We introduce a generalization of the Young integration on self-similar sets defined in a closed interval and give a sufficient condition of its integrability. We also prove integration by substitution, integration by parts and term-by-term…

We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…

We consider the problem of fitting a probability density function when it is constrained to have a given number of modal intervals. We propose a dynamic programming approach to solving this problem numerically. When this number is not…

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…

We consider the numerical evaluation of one dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan (1998). In their approach higher order derivatives of one dimensional densities are used, which…

The problem of exactly generating a general random process (target process) by using another general random process (coin process) is studied. The performance of the interval algorithm, introduced by Han and Hoshi, is analyzed from the…

We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without…

This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…

The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…

Let a sequence of iid. random variables $\xi_1,...,\xi_n$ be given on a measurable space $(X,\cal X)$ with distribution $\mu$ together with a function $f(x_1,...,x_k)$ on the product space $(X^k,{\cal X}^k)$. Let $\mu_n$ denote the…

We introduce a new class of real-valued monotones in preordered spaces, injective monotones. We show that the class of preorders for which they exist lies in between the class of preorders with strict monotones and preorders with countable…

We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…

We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…

We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…

We consider some random iterated function systems on the interval and show that the invariant measure has density in $\mathcal{C}^\infty$. To prove this we use some techniques for contractions in cone metrics, applied to the transfer…

Let $[a,b]\subset\mathbb{R}$ be a non empty and non singleton closed interval and $P=\{a=x_0<\cdots<x_n=b\}$ is a partition of it. Then $f:I\to\mathbb{R}$ is said to be a function of $r$-bounded variation, if the expression…

Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole…

Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have…