Related papers: Variational non-Bayesian inference of the Probabil…
Quantitatively connecting properties of parton distribution functions (PDFs, or parton densities) to the theoretical assumptions made within the QCD analyses which produce them has been a longstanding problem in HEP phenomenology. To…
Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…
Parton distribution functions (PDFs) describe universal properties of bound states and allow us to calculate scattering amplitudes in processes with large momentum transfer. Calculating PDFs involves the evaluation of matrix elements with a…
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…
In this paper we suggest a consistent approach to derivation of generalized Fokker-Planck equation (GFPE) for Gaussian non-Markovian processes with stationary increments. This approach allows us to construct the probability density function…
Probability distribution functions (PDFs) of column densities are an established tool to characterize the evolutionary state of interstellar clouds. Using simulations, we show to what degree their determination is affected by noise,…
We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong $L^1$-convergence of a suitable deterministic particle approximation to weak…
We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It…
The Bayesian predictive density has complex representation and does not belong to any finite-dimensional statistical model except for in limited situations. In this paper, we introduce its simple approximate representation employing its…
We present a novel method for solving population density equations (PDEs), where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different…
This paper is concerned with stochastic systems whose state is a diffusion process governed by an Ito stochastic differential equation (SDE). In the framework of a nominal white-noise model, the SDE is driven by a standard Wiener process.…
We present an alternative, Bayesian method for large-scale reconstruction from observed peculiar velocity data. The method stresses a rigorous treatment of the random errors and it allows extrapolation into poorly sampled regions in real…
A probabilistic description is essential for understanding growth processes far from equilibrium. In this paper, we compute time-dependent Probability Density Functions (PDFs) in order to investigate stochastic logistic and Gompertz models,…
Both observational and theoretical research over the past decade has demonstrated that the probability distribution function (PDF) of the gas density in turbulent molecular clouds is a key ingredient for understanding star formation. It has…
The choice of data that enters a global QCD analysis can have a substantial impact on the resulting parton distributions and their predictions for collider observables. One of the main reasons for this has to do with the possible presence…
Time series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various timescales,…
In this paper the conditions are investigated for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the $1-$body probability density…
The non-Gaussian normal diffusion, i.e., the probability distribution function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical…
Complex systems display anomalous diffusion, whose signature is a space/time scaling $x\sim t^\delta$ with $\delta \ne 1/2$ in the Probability Density Function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g.,…
We present a general framework to treat the evolution of one-point probability distribution function (PDF) for cosmic density $\delta$ and velocity-divergence fields $\theta$. In particular, we derive an evolution equation for the one-point…