Related papers: Daisy Models: Semi-Poisson statistics and beyond
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
In this work we introduce a semi-parametric Bayesian change-point model, defining its time dynamic as a latent Markov process based on the Dirichlet process. We treat the number of change point as a random variable and we estimate it during…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
Using classical field approximation we present the first study of statistical properties of one dimensional Bose gas with attractive interaction. The canonical probability distribution is generated with the help of a Monte Carlo method.…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
Simpson's paradox, a long-standing statistical phenomenon, describes the reversal of an observed association when data are disaggregated into sub-populations. It has critical implications across statistics, epidemiology, economics, and…
We study increasing subsequences (IS) for an ensemble of sequences given by permutation of numbers {1,2,...,n}. We consider a Boltzmann ensemble at temperature T. Thus each IS appears with the corresponding Boltzmann probability where the…
A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…
The production rate of the CP-odd Higgs boson in the Minimal Supersymmetric Standard Model is evaluated through next-to-leading order in the strong coupling constant. The divergent integrals are regulated using Dimensional Reduction, with a…
We propose a new type of quantum statistics, which we call inclusion statistics, in which particles tend to coalesce more than ordinary bosons. Inclusion statistics is defined in analogy with exclusion statistics, in which statistical…
Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
We construct an ensemble of second--quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one GOE or GUE statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely the…
The dynamics of time-reversible systems are statistically indistinguishable when observed forward or backward in time. A rich literature of statistical methods to distinguish irreversible dynamics from the reversible dynamics of linear,…
Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of…
Due to selection rules, new particles are sometimes discovered/predicted to be produced in pairs. In the current search for SUSY particles this will occur if R-parity is conserved. In local relativistic field theory, there can be identical…
It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson…
We study a 2+1 dimensional theory of bosons and fermions with an omega ~ k^2 dispersion relation. The most general interactions consistent with specific symmetries impart fractional statistics to the fermions. Unlike examples involving…