# Questions tagged [statistics]

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

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295 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
715 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
54 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 ...
219 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 ...
124 views

### difference between PLSA and LDA

What is the difference between Probabilistic Latent Semantic Analysis(pLSA) and Latent Dirichlet Allocation (LDA)?
87 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
144 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 ...
261 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: ...
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 ...
67 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
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 ...
1 vote
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() ...
164 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 ...
54 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 $x$ ... 64 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
602 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 ...
1k 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 ...
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 ...
1 vote
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 ...
1 vote
47 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 ...
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 ...
426 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 ...
323 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\...
43 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 ...
500 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
933 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 ...
158 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.
6k 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
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(\...