Related papers: Direct Inversion for the Squared Bessel Process an…
We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients of a principal curvature as a…
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…
The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range…
We present two methods, based on Chebyshev tensors, to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. These methods are implemented and run in a Monte Carlo engine to compute Dynamic Initial Margin…
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…
Statistical modeling of point patterns is an important and common problem in several areas. The Poisson process is the most common process used for this purpose, in particular, its generalization that considers the intensity function to be…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
In this paper, we propose a new exogenous model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox-Ingersoll-Ross (CIR) model with a perfect fit to the observed term-structure.…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…
Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-B\'enard convection serves as a paradigm for these flows, reproducing key features such as…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
In Bayesian inverse problems, one aims at characterizing the posterior distribution of a set of unknowns, given indirect measurements. For non-linear/non-Gaussian problems, analytic solutions are seldom available: Sequential Monte Carlo…
In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…
This paper studies the supremum of a chi-square process with trend over a threshold-dependent-time horizon. Under the assumption that the chi-square process is generated from a centered self-similar Gaussian process and the trend function…
The cumulants and moments of the log of the non-central chi-square distribution are derived. For example, the expected log of a chi-square random variable with v degrees of freedom is log(2) + psi(v/2). Applications to modeling probability…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…