Related papers: Shot Noise with Random Parameters
We introduce a method for non-uniform random number generation based on sampling a physical process in a controlled environment. We demonstrate one proof-of-concept implementation of the method that reduces the error of Monte Carlo…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
The article considers the Derrida-Retaux model with a random number of terms, i.e. a sequence of integer random variables defined by the relations $ X_{n + 1} = (X_n^{(1)} + X_n^{(2)} + ... + X_n^{(N_n)} - a)^{+}$, $n\ge 0$, where $X_n^{j}$…
When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order…
This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given…
We investigate current fluctuations in non-degenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. We present an exact solution of the non-linear kinetic equations in the regime of…
We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we…
Roll-call data analysis aims to estimate legislators' ideal points and quantify the associated uncertainty. Existing approaches either rely on Bayesian methods implemented via Markov chain Monte Carlo sampling or focus primarily on point…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory,…
The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small…
Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the…
In this paper, we study the matrix denosing model $Y=S+X$, where $S$ is a low-rank deterministic signal matrix and $X$ is a random noise matrix, and both are $M\times n$. In the scenario that $M$ and $n$ are comparably large and the signals…
In this paper, we begin our discussion with some of the well-known methods available in the literature for the estimation of the parameters of a univariate/multivariate stable distribution. Based on the available methods, a new hybrid…
This is a preprint of Chapter 2 in the following work: Marta Lewicka, A Course on Tug-of-War Games with Random Noise, 2020, Springer, reproduced with permission of Springer Nature Switzerland AG. We present the basic relation between the…
The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as…
In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…
The probability density function of Kerr effect phase noise, often called the Gordon-Mollenauer effect, is derived analytically. The Kerr effect phase noise can be accurately modeled as the summation of a Gaussian random variable and a…
Let $A_\pm>0$, $\beta\in(0,1)$, and let $Z^{(\alpha)}$ be a strictly $\alpha$-stable L\'evy process with the jump measure $\nu(\mathrm{d} z)=(C_+\mathbb{I}_{(0,\infty)}(z)+ C_-\mathbb{I}_{(-\infty,0)}(z))|z|^{-1-\alpha}\,\mathrm{d} z$,…
We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…