Related papers: About the probability distribution of a quantity w…
We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of $n$ distributions, given one single sample from each distribution. This paper studies mean estimation for entangled…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary…
Traditional meta-analysis assumes that the effect sizes estimated in individual studies follow a Gaussian distribution. However, this distributional assumption is not always satisfied in practice, leading to potentially biased results. In…
This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
For a given spatial distribution of the lenses and distribution of the transverse velocity of the lens relative to the line-of-sight, a probability distribution for the lens mass for a single observed event is derived. In addition, similar…
A mixture of variance-gamma distributions is introduced and developed for model-based clustering and classification. The latest in a growing line of non-Gaussian mixture approaches to clustering and classification, the proposed mixture of…
We present a series of closed-form maximum entropy upper bounds for the differential entropy of a continuous univariate random variable and study the properties of that series. We then show how to use those generic bounds for upper bounding…
The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach…
Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann- Gibbs form of the entropy ensures that…
For the purpose of causal inference we employ a stochastic model of the data generating process, utilizing individual propensity probabilities for the treatment, and also individual and counterfactual prognosis probabilities for the…
In the use and interpretation of $\log{N}$--$\log{S}$ distributions for gamma-ray bursts, burst peak flux has typically been used for $S$. We consider here the use of the fluence as a measure of $S$, which may be a more appropriate quantity…
Generating samples from limited information is a fundamental problem across scientific domains. Classical maximum entropy methods provide principled uncertainty quantification from moment constraints but require sampling via MCMC or…
Maxwell's velocity distribution is known to be universally valid across systems and phases. Here we present a new and general derivation that uses the central limit theorem (CLT) of the probability theory. This essentially uses the idea…
The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision…