6
votes
Accepted
Computing square root of diag(u)-uu'?
Would a decomposition of the form $A = XX^T$ suffice? This would be enough, e.g., if the end goal is sampling from the Gaussian distribution with this given covariance.
If so, you can use the ...
- 3,225
5
votes
Accepted
Data for Tracy-Widom distribution
It's actually not all that complicated to calculate the Tracy-Widom CDF just from its definition: see On The Numerical Evaluation Of Fredholm Determinants by Folkmar Bornemann. The Wikipedia page ...
- 11.5k
4
votes
Beta function and integral value
I've tried to implement your equation
\begin{align}
f(a,b) = \frac{1}{2}\int_0^1 \left|\frac{p^{a-1}(1-p)^{b-1}}{\beta(a,b)}-1\right| \, \text{d}p,
\end{align}
using four different methods of ...
- 410
4
votes
How to define a dimensionless Objective function for determining how peaked a curve is?
Let $f(\omega)$ be your power spectrum. Then maybe something like
$$
\frac{\|f\|_{L^\infty}\|f\|_{L^0}}{\|f\|_{L^1}} = \frac{\mathrm{max}_{\omega\in\Omega} f(\omega)\cdot|\omega_{max}-\omega_{min}|}{\...
- 3,101
3
votes
Accepted
Reconstructing statistics of $x\otimes y$ from E[XX'], E[YY'] and E[XY']
(Converted to an answer from my comments and expanded.)
Basically you need to compute the fourth moments $E[x_i x_j y_k y_l]$ for all $i,j,k,l$, given the second moments. These fourth moments are not ...
- 12.6k
3
votes
Data for Tracy-Widom distribution
Mathematica has the TW distributions:
http://reference.wolfram.com/language/ref/TracyWidomDistribution.html
- 31
2
votes
Accepted
Verifying that ODE integration generates Theoretical Stationary distribution
In general, your type of question would be called a "multivariate goodness of fit test". If $F(x_1,\ldots,x_n)$ is the $n$-dimensional CDF for the theoretical distribution, and the random variables $(...
- 11.5k
2
votes
Accepted
Which statistical method should I use for comparing machine run-time of two algorithms?
This is a typical use case for a paired t-test. The idea is to consider only the runtime difference $\Delta t$ for each problem and test for the null hypothesis $E(\Delta t)=0$. For a step-by-step ...
- 481
2
votes
Best way to convert a sparse (containing zeros) covariance matrix into a correlation matrix?
What about the following?
Dinv = np.diag(1.0 / np.sqrt(np.diag(cov_matrix)))
corr = Dinv @ cov_matrix @ Dinv
The above avoids any division except by the diagonal ...
- 121
2
votes
SciPy ODR "Ordinary" Least Squares?
Based on the ODRPACK Documentation it seems clear that by "ordinary least squares", the authors mean least squares in which the errors are (considered to be) only in the dependent variables, ...
- 2,272
2
votes
Tools to compare two matrices with same dimensions
Welcome to Scicomp! You might be interested in the field of (multimodal) medical image registration. In medical contexts one often wants to register a CT image with an MR or PET-Scan. The amplitudes ...
- 3,065
1
vote
How to generate p Sample of GGM of dimension m, for parameter : the weight, the means and the covariance?
Pick an integer i at random with probability p_i, the i-th weight. Then sample from the corresponding multidimensional Gaussian ...
- 283
1
vote
Parameter explained by many distributions
Your question is ill-posed.
Take just the data points corresponding to one label. I think that when you say "for each label, we have several data distributions associated to it" that what ...
- 56.8k
1
vote
Weighted moving variance
I believe that we can compute using the vectorized form, assuming a vector of weights w and a vector of values x:
...
1
vote
How to optimize sampling for parameter estimation
The computational costs of sensitivity analysis for a considerably large simulation is attributed to two main phenomena. Firstly, as it's mentioned in the body of the question, due to a large number ...
- 41
1
vote
Accepted
Is there any robust criteria for this kind of outlier?
If the histogram you're displaying is representative than you could methods which are used for binarization in Image Processing.
For instance, using Otsu's Method will probably be a robust way to set ...
- 573
1
vote
Accepted
Using the PAST algorithm to find eigenvectors
If the identity matrix is a feasible solution, then clearly it is an optimal solution.
However, most of the time, the identity matrix is not a feasible solution.
$$W\in \mathbb{R}^{m \times d}$$
...
- 126
1
vote
Accepted
will this methodology end up giving me a nonsense regression equation.
That depends on (i) how many random samples you draw, and (ii) how good a regression you want to have. The point of finding the best fit regression is that you want the best model out of all possible ...
- 56.8k
1
vote
1-D turbulent energy spectra in homogeneous direction (non-isotropic)
I think there is something wrong with your program.
First, the fft(u).*conjg(fft(u)) is equal to fft(R), ...
- 11
1
vote
Accepted
Legendre expansion of $r(x) = f(x)/g(x)$ using a finite number of samples from $f(x)$ and $g(x)$
I believe you are asking how to compute
$$\frac{f(x)}{g(x)}\approx\sum_{n=0}^p a_n P_n(x).$$
You could interpolate your samples of $f$ and $g$ to the Gauss-Legendre quadrature points on $[-1,1]$, ...
- 1,031
1
vote
Data Analysis - Cooling Efficiency
An efficiency metric
You could use,
$$\eta = p_{\text{out}}/p_{\text{in}}$$
where the power out ($p_{\text{out}}$) is defined as the heat per second from the room to the environment, and, power in (...
- 5,439
1
vote
Accepted
Parameter identification for regression model
You can just write it as a least squares minimization problem. That leads to a quadratic problem that is easy to solve.
The problem is, in general, underdetermined since you only have $Nn$ equations, ...
- 56.8k
1
vote
Accepted
Using physical parameter as a Gaussian random variable in a simple Poisson problem
In the loop over your instances of 100 random values for $k$, you could write the value for $k$ into a file, and call your finite element code; the finite element code could then open the file, read ...
- 56.8k
1
vote
Accepted
Is resampling more accurate than block average for statistical analysis of data?
I guess that you are not actually interested in the variance, but in a confidence interval for your observable $\theta$. It should be noted that computing the confidence interval from the variance (i....
- 481
1
vote
Efficient calculation for L-Kurtosis?
You might be interested in the R package Lmoments. Here is the documentation for it, as well. According to it, the package is capable of computing at least L-scale, Lskewness, L-kurtosis.
While this ...
- 8,742
Only top scored, non community-wiki answers of a minimum length are eligible