Related papers: Statistical duality of the Laplace distribution
I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…
We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution…
Causal effects are usually studied in terms of the means of counterfactual distributions, which may be insufficient in many scenarios. Given a class of densities known up to normalizing constants, we propose to model counterfactual…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
The main goals of this paper are: i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without…
A method is suggested to decompose the statistical and systematic uncertainties from the residues between the calculation of a theoretical model and the observed data. The residues and the parameters of the model can be obtained through the…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
In recent years, a range of measures of partial stochastic dominance have been introduced. These measures attempt to determine the extent to which one distribution is dominated by another. We assess these measures from intuitive, axiomatic,…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? I propose we utilize the posterior distribution of a causal effect and present the probability of the effect being greater…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.
In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…
Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…