Questions tagged [statistics]
The study of collection, organization, analysis, and interpretation of data.
97
questions
1
vote
1
answer
159
views
Beta function and integral value
I have two values $a$ and $b$ where $a \ge 0$ and $b \ge 0$ and I have to calculate the formula below.
$$
\frac{1}{2}\int_0^1\text{abs}\left[\left( \frac{p_i^{(a - 1)} \times (1 - p_i)^{(b - 1)}}{\...
0
votes
0
answers
40
views
Solving Symmetric/Hollow Matrix issue
I have a particular issue and need something creative or solution from calculus.
I have Symmetric/Hollow Matrix, a numbers are % of mismatch between them. Ideally, all of them should be 0, but I have ...
- 101
2
votes
1
answer
83
views
SciPy ODR "Ordinary" Least Squares?
Scipy.odr has a setting for "fit types", including one for ordinary least-squares. This matches with the documentation of ODRPACK (see p. 31, Computational method).
However, the package ...
- 21
-1
votes
1
answer
34
views
Parameter explained by many distributions
If we had, for example, labeled data, where for each entry (label) we have several data distributions associated to it, how can I get something meaningful from them?
Is this a solvable problem? Is ...
- 1
-1
votes
1
answer
69
views
Generating Rvs for a given PDf in python
Two random variables $X$ and $Y$ are distributed according to
\begin{align}
f_{XY}(x,y)= \begin{cases}
x+y & 0\leq x \leq 1, 0\leq y \leq 1 \\
0 & otherwise
\end{cases}
\end{align}
I ...
- 1
4
votes
0
answers
71
views
Efficient computation of marginalized multivariate normal likelihood
In general,if we know that the marginal Gaussian distribution for some variable $\textbf{x}$ and a conditional Gaussian distribution for some $\textbf{y}|\textbf{x}$ of the forms:
$$p(\textbf{x}) = \...
- 41
1
vote
1
answer
120
views
Define continuous, non-analytical pdfs in python
I am planning to do some basic algebra on continuous, non-analytical random variabels. I want to define their probability density functions as arrays x and f(x).
Yet, I was surprised to find out that ...
- 159
4
votes
1
answer
189
views
How to define a dimensionless Objective function for determining how peaked a curve is?
I have attached 2 plots for FFT spectra. One is considered good and one is bad.
The good one is classified on the basis of how closely spaced the frequencies and the bad is based on how multiple ...
- 41
2
votes
0
answers
155
views
Whi are chi-squared distributions in (C++) boost::random and C++ STL faster than in boost::math?
I am trying to generate random chi-squared numbers in C++, according to some degree of freedom (which can be a float). Several libraries can be used for that purpose, among which the C++11 Standard ...
- 153
2
votes
1
answer
201
views
Best way to convert a sparse (containing zeros) covariance matrix into a correlation matrix?
I have a $100$x$100$ covariance matrix that looks like this.
Some rows/cols are all-zero because those corresponding elements are not present in the sample from which covariance is calculated. I'm ...
- 151
2
votes
0
answers
124
views
Partial/Extended/Truncated Template Matching
So template matching using correlation is available in a lot of computational packages; OpenCV matchTemplate(), scipy.signal.correlate2d(), IPP CrossCorrNorm, etc.
But they all either evaluate ...
- 121
3
votes
1
answer
57
views
Reconstructing statistics of $x\otimes y$ from E[XX'], E[YY'] and E[XY']
I'm looking at random vectors $z$ of size $d^2$ which can be written as $z=x\otimes y$ where $x$,$y$ are random vectors in $\mathbb{R}^d$ with following second moments known -- $E[XX']$, $E[YY']$ and $...
- 1,799
7
votes
1
answer
227
views
Computing square root of diag(u)-uu'?
I need an efficient way to take square root of a matrix which is a sum of diagonal matrix and rank-1 matrix.
More specifically it's the following matrix
$$A=D-uu'=\text{diag}(u)-uu'$$
Where entries ...
- 1,799
1
vote
1
answer
636
views
Weighted moving variance
i have a time-series and, in analogy with exponentially weighted moving average, i would like to compute the exponentially weighted moving standard deviation or variance in an efficient, numerically ...
- 131
1
vote
0
answers
52
views
Fast convergence of smoothing of periodic noise
I have essentially periodic data from a simulation (not exactly periodic but is qualitatively fairly periodic), and I'd like to take an average or noise filter of some sort that I can get a well ...
- 2,059
3
votes
2
answers
215
views
How to optimize sampling for parameter estimation
I have a computer model with a number of parameters that need to be calibrated based on experimental results. It's also important to understand the sensitivity of the results to each parameter ...
- 41
2
votes
0
answers
118
views
difference between PLSA and LDA
What is the difference between Probabilistic Latent Semantic Analysis(pLSA) and Latent Dirichlet Allocation (LDA)?
- 21
0
votes
0
answers
73
views
how to estimate the number of people on a street within an hour?
I tried to use opencv to analyze a video filmed on the street.
But the problem is the performance is not enough.
I think the number of people must follow the poisson distribution.
So I want to ...
1
vote
0
answers
130
views
Why does the correlation function of this stochastic differential equation starts at different points?
I am working with the following differential equation:
The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term, with a reflecting wall boundary conditions.
After solving ...
- 11
2
votes
1
answer
210
views
Which statistical method should I use for comparing machine run-time of two algorithms?
I am comparing the run-time of two algorithm by solving different instance of the problems. Sample of my data:
...
- 23
2
votes
0
answers
31
views
Identifying the time window at which a meteorological factor influences tree growth the most
This is a problem I am encountering in a research project. I have thought of a naive approach to solve it which relies on many assumptions, is not guaranteed to work, and would be tedious and ...
- 121
0
votes
1
answer
66
views
Is there any robust criteria for this kind of outlier?
I have this data, and I need to detect the outliers.
The outliers are clearly visible on the borders (start and end, in red). And I only care for outliers present at the start or end.
I could easily ...
- 3
1
vote
0
answers
49
views
What is a performant clustering algorithm for approx 10,000 vectors of approx 30 dimension?
I have a set of real-valed vectors, for example
$S = \{v_1, v_2, ..., v_k\}$
$v_i = \begin{pmatrix} age_i \\ height_i \\ weight_i \\ ... \end{pmatrix}$
or whatever. Each vector has on the order of ...
- 111
1
vote
0
answers
23
views
Uniform distribution in 3D space [duplicate]
Posted this at math stack exchange as well, but alas no replies! So, I have been trying to find ways of distributing particles of spherical or other shape in 3D space, e.g. rectangular space. Random() ...
- 45
4
votes
1
answer
163
views
Using the PAST algorithm to find eigenvectors
I'm working on trying to extract the eigenvectors from a series of observations from a random variable, by using the PAST algorithm, see e.g. 6.2.3 in this book:
Large pdf.
I don't understand the ...
- 41
2
votes
1
answer
53
views
Verifying that ODE integration generates Theoretical Stationary distribution
I am trying to simulate an ODE, like $ \dot{x} = \xi(x) $ that should have a stationary distribution (a la Stat Mech). Assuming that my ODE algorithm generates time samples of my system state $ x $ ...
- 153
0
votes
2
answers
63
views
will this methodology end up giving me a nonsense regression equation.
I'm wondering if this is a valid methodology to find the best regression equation for a given data set.
User provides a rang of estimated value for some set of variables. Th algorithm uses the ...
- 103
1
vote
2
answers
541
views
Data for Tracy-Widom distribution
I have data for a random variable and I wish to test whether it conforms to the Tracy-Widom distribution. However, the T-W distribution is hard to compute. Is there a readly available table of its ...
- 113
2
votes
1
answer
925
views
1-D turbulent energy spectra in homogeneous direction (non-isotropic)
I am trying to compute the one-dimensional energy spectra for my channel-flow simulation. I have already written a post-processing script to achieve this; however, I need to validate my code before ...
- 103
2
votes
1
answer
77
views
Legendre expansion of $r(x) = f(x)/g(x)$ using a finite number of samples from $f(x)$ and $g(x)$
I have two finite sets of events $\{x_1, ..., x_N\}$ and $\{y_1, ..., y_N\}$ that are sampled from the PDFs $f(x)$ and $g(x)$, respectively, where $x \in [-1,+1]$. I want to estimate the Legendre ...
- 23
1
vote
1
answer
243
views
Data Analysis - Cooling Efficiency
I have a question as I am starting my dive into computational analysis.
I have a large set of data (~2 months) which includes the room temperature, HVAC status (heat/cool/off) and the location of ...
- 11
1
vote
1
answer
43
views
Parameter identification for regression model
Consider the following regression model :
Y = AX + BU
where the size of Y is $N \times n$, A is $N \times n$, X is $n \times n$, B is $N \times n$ and U is $n \times 1$.
The matrices X,Y and U are ...
- 21
2
votes
1
answer
73
views
Using physical parameter as a Gaussian random variable in a simple Poisson problem
I want to vary the input parameter of a physical dynamic mechanics problem, as a Gaussian Random variable and view the resulting Probability Density Function (PDF). I used the Finite Element Method to ...
- 347
2
votes
1
answer
401
views
Optimize custom probability distribution in Python [closed]
Consider random variables $X$ and $Y$, their distributions are given. $Z = f_a(X, Y)$ where $f(\cdot, \cdot)$ is a deterministic, not random function $f_a: \mathbb{R}^2 \to \mathbb{R}$ depending on a ...
- 121
7
votes
1
answer
299
views
Tikhonov (Ridge) Regression and Normalization
For a typical Ridge Regression method for solving an inverse problem
$$
\min_x ||A~x - b||^2 + \lambda^2||\Gamma~x||^2
$$
Which has an analytical solution of
$$
\hat{x}_{est}=(A^TA+\lambda^2 \Gamma^T\...
- 255
0
votes
2
answers
42
views
How are the outcomes that generated from different predictive models combined to get more accurate predictions?
The simple average is commonly used to combine the predictions out of different predictive models. Apart form the simple average, what are the other methods that can be used for combining the ...
- 111
6
votes
1
answer
471
views
Is resampling more accurate than block average for statistical analysis of data?
I'm working in laboratories where molecular dynamics data are almost always analysed usign block average as stated in the famous Allen and Tildesley book.
We divide the datas in blocks of size $M$ on ...
- 323
1
vote
0
answers
918
views
Generating Random Numbers in Fortran for Metropolis method
I am having a really hard time getting any kind of reliable / consistent result from my Metropolis code. I have torn it apart and am now examining just the randomness in my random number generator.
I ...
- 131
0
votes
1
answer
112
views
Force a line through the origin
What does it mean: to force a line through the origin?
I interpret this to be making (forcing) the intercept as (0,0) in the regression procedure of an x-y scatterplot, but am not sure.
- 1
0
votes
1
answer
5k
views
Normalize data so that the sum of squares = 1
In presenting geochemical data, I would like to try a statistical method that presents the data in an ISOCON diagram. This method requires scaling all the data to be the same distance from the origin (...
- 1
1
vote
0
answers
109
views
How to get mathematical model from a data set with MATLAB
I have some values imported from excel about the annual sell of a product, with 3 var:
month,
price,
sold items
I have seen how to plot a chart using curve fitting tool but I need to define a ...
- 111
8
votes
2
answers
1k
views
Sum over very small exponentials: Underflow
I am trying to compute (in C) a sum like
$S = \sum_i \exp( - a_i )$,
where $10^{4} < a_i < 10^{5}$ are approximately normal distributed. So even if I do the Log-Sum-Exp trick
$S = \exp(\...
- 83
0
votes
1
answer
44
views
Conditional Independence (Bayesian Network)
suppose you have this bayesian network: p(a,b,c) = p(c|b) p(b|a) p(a)
a -> b -> c
are a and c conditionally independent given b?
If yes, why are they independent? How can I show that?
- 111
4
votes
1
answer
3k
views
Is there a relationship between the covariance matrix and the partial derivative?
Suppose that there are $N$ pieces of data, each of which contains $M$ parameter values such that $N >> M$. If we put this information into matrix form ($N$ rows, $M$ columns) and then compute ...
- 2,109
1
vote
2
answers
337
views
Polynomial approximation
Is there any universal method to fill this matrix for any $n$ value:
$\textbf{A} = \left[ \matrix{n & \sum x_i & \sum x_i^2 & \cdots & \sum x_i^n \cr
\sum x_i & \sum ...
2
votes
1
answer
131
views
CFD turbulence modelling mean pressures vs peak pressures
I have been experimenting with using Autodesk CFD to investigate facade/ cladding pressures on a (rectangular) building, comparing results with cladding/ facades pressures pressures from design codes ...
- 121
-1
votes
1
answer
299
views
Problem using MATLAB `fminunc` [closed]
I am trying to find the minimum of this function. But I receive the following error when I run the script. What am I doing wrong:
...
- 1
2
votes
1
answer
79
views
Efficient calculation for L-Kurtosis?
I am doing some statistical signal analysis and was wondering if there are any C/Java packages that do L-moment calculations, specifically L-Kurtosis as I am wanting to do things such as ...
- 235
0
votes
1
answer
159
views
Can Box-Cox transformation be applied for data of this form?
I have data of the form:
X Y
3.53 0
4.93 50
5.53 60
6.21 70
7.37 80
9.98 90
16.56 100
And I want to find out $n$ so that this can be ...
- 119
1
vote
0
answers
127
views
How to curve fit an unknown function?
I have data which can be described by $y=f(x,z)$ where $z$ varies from 170 ~ 154. Now values given by $ks$ are known sample values that equals value given in the table header, $uks$ are unknown ...
- 119