Related papers: On sampling and parametrization of discrete freque…
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes,…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be…
Linear dynamical relations that may exist in continuous-time, or at some natural sampling rate, are not directly discernable at reduced observational sampling rates. Indeed, at reduced rates, matricial spectral densities of vectorial time…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
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…
The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…
A protocol for distributed estimation of discrete distributions is proposed. Each agent begins with a single sample from the distribution, and the goal is to learn the empirical distribution of the samples. The protocol is based on a simple…
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
An important problem in physics concerns the analysis of audio time series generated by transduced acoustic phenomena. Here, we develop a new method to quantify the scaling properties of the local variance of nonstationary time series. We…
Recently Sasane defined a notion of evaluating a distribution at a point using delta sequences. In this paper, we explore the relationship between generalizations of his definition and the standard definition of distributional point values.…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…
It has been known for years how random height variations of a repeated nano-scale structure can give rise to smooth angular color variations instead of the well-known diffraction pattern experienced if no randomization is present. However,…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…