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The technique of wrapping of a univariate probability distribution is very effective in getting a circular form of the underlying density. In this article, we introduce the circular (wrapped) version of xgamma distribution and study its…
Galaxy populations at different cosmic epochs are often linked together by comoving cumulative number density in observational studies. Many theoretical works, however, have shown that the number densities of tracked galaxy populations…
We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…
We present an improved formula for the anomalous radial velocity of the star during planetary transits due to the Rossiter-McLaughlin (RM) effect. The improvement comes from a more realistic description of the stellar absorption line…
We present RoadMapping, a full-likelihood dynamical modelling machinery that aims to recover the Milky Way's (MW) gravitational potential from large samples of stars in the Galactic disk. RoadMapping models the observed positions and…
We study the probability distribution function (PDF) of relative velocity between two different dark matter halos (i.e. pairwise velocity) with a set of high-resolution cosmological $N$-body simulations. We investigate the pairwise velocity…
We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in MOND, using the N-body code N-MODY, which is a particle-mesh based code with a numerical MOND potential solver developed by Ciotti,…
The transport of positive quantities underlies countless physical processes, including fluid, gas, and plasma dynamics. Discretizing the associated partial differential equations with Galerkin methods can result in spurious nonpositivity of…
We propose a fast algorithm for evaluating the moments of Bingham distribution. The calculation is done by piecewise rational approximation, where interpolation and Gaussian integrals are utilized. Numerical test shows that the algorithm…
We consider the problem of computing L1-distances between every pair ofcprobability densities from a given family. We point out that the technique of Cauchy random projections (Indyk'06) in this context turns into stochastic integrals with…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log-likelihood and its gradient and Hessian. We estimate the gradient and…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
We present a new method for extracting the true 3-d velocity and density fields from the nonlinear redshift--space projected density field. The method is based on the nonlinear, nonlocal transformation of the density field. We assume a…
Fredholm integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. They model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear…
The majority of terrestrial direct detection experiments for Dark Matter (DM) rely on the Standard Halo Model (SHM), which assumes the local DM velocity distribution follows a Maxwell-Boltzmann distribution. However, galaxy mergers can…
The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations. FMM groups…
We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…
We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since…