Questions tagged [statistics]
The study of collection, organization, analysis, and interpretation of data.
93
questions
-1
votes
1answer
36 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 ...
4
votes
0answers
54 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}) = \...
1
vote
1answer
63 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 ...
4
votes
1answer
146 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 ...
2
votes
0answers
62 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 ...
2
votes
1answer
93 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 ...
2
votes
0answers
51 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 ...
3
votes
1answer
56 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 $...
6
votes
1answer
167 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'$$
Where entries ...
1
vote
1answer
340 views
Weighted moving variance
i have a time-series and, in analogy with exponentially weighted moving average, i would like to compute the exponentially weighted moving standard deviation or variance in an efficient, numerically ...
1
vote
0answers
41 views
Fast convergence of smoothing of periodic noise
I have essentially periodic data from a simulation (not exactly periodic but is qualitatively fairly periodic), and I'd like to take an average or noise filter of some sort that I can get a well ...
3
votes
2answers
204 views
How to optimize sampling for parameter estimation
I have a computer model with a number of parameters that need to be calibrated based on experimental results. It's also important to understand the sensitivity of the results to each parameter ...
1
vote
0answers
87 views
difference between PLSA and LDA
What is the difference between Probabilistic Latent Semantic Analysis(pLSA) and Latent Dirichlet Allocation (LDA)?
0
votes
0answers
28 views
how to estimate the number of people on a street within an hour?
I tried to use opencv to analyze a video filmed on the street.
But the problem is the performance is not enough.
I think the number of people must follow the poisson distribution.
So I want to ...
1
vote
0answers
71 views
Why does the correlation function of this stochastic differential equation starts at different points?
I am working with the following differential equation:
The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term, with a reflecting wall boundary conditions.
After solving ...
2
votes
1answer
150 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:
...
2
votes
0answers
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 ...
0
votes
1answer
63 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 ...
1
vote
0answers
45 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 ...
1
vote
0answers
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() ...
4
votes
1answer
156 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 ...
2
votes
1answer
44 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 $ ...
0
votes
2answers
61 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 ...
1
vote
2answers
456 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 ...
2
votes
1answer
520 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 ...
2
votes
1answer
69 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 ...
1
vote
1answer
240 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 ...
1
vote
1answer
33 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 ...
2
votes
1answer
61 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 ...
2
votes
1answer
265 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 ...
6
votes
1answer
213 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\...
0
votes
2answers
41 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 ...
6
votes
1answer
353 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 ...
1
vote
0answers
796 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 ...
0
votes
1answer
46 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.
0
votes
1answer
4k 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
vote
0answers
108 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 ...
8
votes
2answers
798 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(\...
0
votes
1answer
41 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?
4
votes
1answer
2k 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 ...
1
vote
2answers
327 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
1answer
120 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 ...
-1
votes
1answer
159 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:
...
2
votes
1answer
64 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 ...
0
votes
1answer
138 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 ...
1
vote
0answers
112 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 ...
0
votes
1answer
59 views
Best path for estimation
I have a Cartesian grid (100x100) in which some of the points are known (30 out of 10,000) and the rest are unknown. I want to use the known points and estimate the other cells. Is there any ...
2
votes
1answer
538 views
How to prevent overflow and underflow in the Euclidean distance and Mahalanobis distance
I was working in my project when I was struck by the question of whether it would be necessary, or at least cautious, prevent overflow and underflow in the calculation of these two distances.
I ...
1
vote
0answers
524 views
How to choose (and many) threshold in Eigenface?
I edited my question trying to make it as short and precise.
I am developing a prototype of a facial recognition system for my Graduation Project. I use Eigenface and my main source is the document ...
0
votes
2answers
260 views
Statistical analysis of optimization algorithms
If we optimize some parameter using 4 optimization algorithms, 2 of which are population based (say A and B) and 2 trajectory methods (single point search)(say C and D); what statistical test can be ...
