Tagged Questions

83 views

Distribute Monte Carlo samples among dimensions

Simplified problem: Given a $d$-times nested convolution of an input function $g(x):\mathbb{R}\mapsto \mathbb{R}$ with the same band-limited smooth function $f(x):\mathbb{R}\mapsto \mathbb{R}$. I am ...
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1k views

Generating samples of a multivariate cauchy distribution

The question is very simple: Do you know an efficient algorithm to generate samples of the multivariate cauchy distribution ...
2k views

Inverting Hessian matrix

I need to invert a Hessian matrix to calculate the covariance matrix. The matrices are fairly large, typical sizes are (300x300), or values of that order. In general, the Hessian is very ...
616 views

how to deal with bad-scaled covariance matrix?

Hi, When Aetkin linear model is used, problem holder has to provide weight matrix which is defined as $\Sigma^{-1/2}$. As far as the covariance matrix is always positive-defined the raising to the ...
276 views

Estimating a multinomial sum

I have the following sum \sum_{r_1=q+1}^{\tau}\dots\sum_{r_\lambda=q+1}^{\tau}{\tau\choose r_1,\dots,r_\lambda,\tau-r_1-\dots -r_\lambda} (\Lambda-\lambda)^{\tau-r_1-\dots-r_\lambda} ...
1k views

Polynomial Regression/Least Squares

I have a couple questions on the same topic: 1) Does ordinary linear least squares have a generally defined confidence interval. I know that you can determine the confidence interval of each term, ...
686 views

Random, Linear, Homogeneous Difference Equations and Time Integration Methods for ODEs

Most methods (that I know of) of numerically approximating the solution of ODEs are "general linear methods". For this type of method, the so-called 'linear stability' is examined by applying the ...
492 views

O(n^2) algorithm to approximate the sum of the log of the singular values of a matrix

Given an $M \times N$ matrix of rank $N$ ($M \ge N$) with $i^{th}$ singular value $\sigma_i$, does their exist an $O(M^2)$ algorithm for approximating the sum $H =\sum_{i=1}^N \log(\sigma_i)$ with ...