Questions tagged [statistics]

The study of collection, organization, analysis, and interpretation of data.

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4
votes
1answer
136 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
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0answers
32 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
44 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
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0answers
46 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 ...
0
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0answers
19 views

How to start coding for posterior inference

I am trying to implement the model given in http://proceedings.mlr.press/v84/andersen18a/andersen18a.pdf where they have used mean-field variational inference for posterior inference, but I want to ...
3
votes
1answer
50 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
142 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
166 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
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0answers
34 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
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2answers
195 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
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0answers
77 views

difference between PLSA and LDA

What is the difference between Probabilistic Latent Semantic Analysis(pLSA) and Latent Dirichlet Allocation (LDA)?
0
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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
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0answers
49 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
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1answer
124 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
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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
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0answers
43 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
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0answers
22 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
149 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
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2answers
60 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
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2answers
391 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
402 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
239 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
59 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
204 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
179 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
293 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
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0answers
696 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
41 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
3k 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 ...
7
votes
2answers
585 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
321 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
116 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
150 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
60 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
131 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
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0answers
109 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
510 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
405 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
242 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 ...
2
votes
2answers
112 views

fastest and most efficent way to count all combinations in many sets and sum them together

I am a Java programmer who has reached the limits of brute computer power. My relational database (and non relational databases) is not producing results quick enough and I have hit a bottleneck in ...
1
vote
1answer
214 views

What is the algorithm that matlab used in its built-in function 'pca'?

Do anyone know what is the algorithm that MATLAB used in its built-in function "pca"? I have the following data set: 148.9820 55.8438 210.2150 149.3030 56.8891 208.4280 151.4400 55....