Chervyakov , "Simple Explicit Formulas for Gaussian Path Integrals with Time-Dependent Frequencies", (http://cds.cern.ch/record/348185/files/9803016.pdf )H. Kleinert, A. Chervyakov, "Simple explicit formulas for Gaussian path integrals with time dependent frequencies," Phys. Lett. A245, 345...
对于任意连续时间轴t∈连续时间轴T，ξt∼N(μt,σt2)，也就是对于一个确定的高斯过程而言，对于...
ii) Monte Carlo, 这个就是所谓的暴力破解，利用Bayesian formula，结果高斯先验（也就是我们的多维高斯...
(This article https://arxiv.org/ftp/arxiv/papers/1502/1502.05317.pdf explains how to proceed for the formula) I've seen this post https://www.comsol.com/blogs/the-nonparaxial-gaussian-beam-formula-for-simulating-wave-optics/ explaining how to do it in 2D. But in 3D there is not anymor...
The variance is obtained from the spectral density by the formula (5.13)σX2=Var[X(t)]=∫-ππ∫0∞SX(ω,θ)dωdθ≈∑j=1n∑k=1mSX(ωj,θk)ΔωjΔθk The statistical distribution of the wave elevation X = X(t) is therefore determined by the probability density function (PDF)...
The canonical points are shown to coincide with the nodes of a “generalized Gaussian quadrature formula” of the form ∫bau(t) σ(t)sign∏i=1n(t−xi)vidt≉∑i=1n∑j=0ν1−2aiju(j)(xi) +∑j=0ν0−1a0ju(j)(a)+∑j=0νn+1−1an+1ju(j)(b), (∗) which is ...
A novel method for estimating the shape factor of a generalized Gaussian probability density function (PDF) is presented and assessed. It relies on matching the entropy of the modeled distribution with that of the empirical data. The entropic approach is suitable for real-time applications and yiel...
, and V. Mallet ( 2009 ), Comparative study of Gaussian dispersion formulae within the Polyphemus platform: Evaluation with Prairie Grass and Kincaid experiments , J. Appl. Meteorol. , 48 ( 12 ), 2459 – 2473 , doi: 10.1175/2009JAMC2160.1 ....
We first review the concept of a multivariate Gaussian mixture and then describe how it can be used to model images. Supposeu= [u1,u2, …,un]Tis a column random vector whose PDF has the following form: (44)p(u)=∑k=1kπkpk(u) ...
Multivariate Gaussian Distribution In general, the PDF of multivariate Gaussian distribution (a.k.a. multivariate normal distribution, MVN) is as below: 1(√2π)ddet(Σ)1/2exp{12(x−μ)TΣ−1(x−μ)}1(2π)ddet(Σ)1/2exp{12(x−μ)TΣ−1(x−μ)} ...