Computability of Probability Distributions and Characteristic Functions

Computability of Probability Distributions and Characteristic Functions

As a part of our works on effective properties of probability distributions, we deal with the corresponding characteristic functions. A sequence of probability distributions is computable if and only if the corresponding sequence of characteristic functions is computable. As for the onvergence problem, the effectivized Glivenko’s theorem holds. Effectivizations of Bochner’s theorem and de Moivr...

Computability of Probability Distributions and Distribution Functions

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We th...

Distances between probability distributions via characteristic functions and biasing

In a spirit close to classical Stein’s method, we introduce a new technique to derive first order ODEs on differences of characteristic functions. Then, using concentration inequalities and Fourier transform tools, we convert this information into sharp bounds for the so-called smooth Wasserstein metrics which frequently arise in Stein’s method theory. Our methodolgy is particularly efficient w...

Constrained probability distributions of correlation functions

Context. Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation. However, this has been shown to be insufficient. Aims. For the case of Gaussian random fields, we search for an exact probability distribution of correlation...

Characteristic functions of scale mixtures of multivariate skew-normal distributions