For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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130 views

How to perform nonlinear regression with correlated errors?

I have a nonlinear least squares problem, but the errors are correlated. I could use R's nls function to do the regression if the errors were independent, but I don't know the right way to handle ...
3
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776 views

Correlation and Regression Question

Two separate tests are designed to measure a students ability to solve problems. Several students are randomly selected to take both tests and the results are: $$ \begin{matrix} \text{Test A}(x) ...
2
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14 views

Detecting camera shake

I have a bunch of data captured from a worm tracker that consists of a B&W camera that stares down at a few dozen worms for an hour at a time. The tracker captures the outline of each worm ...
2
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0answers
54 views

Show that a function is log supermodular

I have been struggling with the following Let $X$ be finite and a poset $P = (X, \leq)$, and for any $A \subseteq X$ we can define the function $f_A$ on $\mathcal{P}(A)$ as follows $$ f_A(Y) = \#\{ ...
2
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0answers
56 views

Expectation of random variables

a) Show that $E\{X-E(X)\} = 0$ for any random variable $X$. b) Use the result in part (a) and the following equation to show that if two random variables are independent then they are uncorrelated, If ...
2
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0answers
56 views

When does convergence in distributions inply convergence in covariance?

Good Morning. Let $(X_n)_n$ and $(Y_n)_n$ be sequences of random variables converging in distribution respectively to $X$ e $Y$. Suppose $X_n,Y_n$ are equally distributed but dependent for all $n$, ...
2
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42 views

A vector with fixed correlation with existing vector, is it always possible?

Suppose we have a known vector $X$ in $R^n$, and for any vector $Y$ in $R^n$, we impose on it the restriction that it must have a fixed correlation coefficient $r$ with $X$: \begin{align*} ...
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31 views

Finding correlations between many unknown functions.

Given an arbitrarily large number of black-box functions of one variable, is it possible to produce expressions that approximate their relationships to each other over their shared domain? Is it ...
2
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55 views

Dimension free Concentration bounds for Martingales

Consider the following random process which is defined on $n$ numbers $0\leq x_1,\ldots,x_n\leq 1$: At each step, pick an arbitrary number, say $x_i$. Then randomly (and independently) change its ...
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47 views

Finding the empirical correlation from a covariance matrix

I have this covariance matrix with five variables $X_1$ through $X_5$ in that order. ...
2
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0answers
199 views

Pearson correlation and metric properties

Assuming that the data set was $z$-standardized to zero mean and unit variance (also assuming that it does not contain constant vectors). Then Pearson's r reduces to Covariance: $$\rho(X,Y) := ...
2
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93 views

Correlation between an event and a time series

I have a time series, e.g. the daily number of visitors on my blog. I have a set of events of some class, like the days when I made a new posting. I want to measure the effect of a new posting on the ...
2
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143 views

Correlated diffusion processes and covariance matrix

I'm really noob in maths topics so I hope you will excuse me if I use terms which aren't correct. I would like to simulate $n$ dimensional diffusion processes with $n$ noises. Each process has its ...
2
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213 views

Geometric interpretation of element by element division of one vector by another

This is my first post here, and I'm not a mathematician, so please go easy on me :) In statistics there is a geometric interpretation of correlation that uses basic vector geometry. This is fairly ...
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0answers
23 views

Generate correlated random numbers precisely

Let's assume I want to generate k samples of n random numbers, that are correlated according to a given correlation matrix C (e.g. $n = 3$): ...
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0answers
42 views

Using mutual information to estimate correlation between a continuous variable and a categorical variable

As for the title, the idea is to use mutual information, here and after MI, to estimate "correlation" (defined as "how much I know about A when I know B") between a continuous variable and a ...
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0answers
16 views

Autocorrelation Clarification

Could anyone help clarify a high level explanation of autocorrelation? I understand that it is a measure of correlation between a timeseries and a lagged version of the same series. If we have take ...
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0answers
11 views

Can correlation dimension of an attractor exceed the dimension of the space?

Here is the definition of the correlation dimension: http://en.wikipedia.org/wiki/Correlation_dimension Is there a proof that the correlation dimension cannon exceed the dimension of the space?
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46 views

Multiple regression and hypothesis test $H_0$:$\beta_2=0$

Multiple regression model $H_0$:$\beta_2=0$, $H_1$:$\beta_2 \neq 0$ where $\beta_2$ is the vector of elements ($\beta_2, \beta_3, \dots, \beta_k$) and $\beta$ is slope of regression line. Why it is ...
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41 views

Redundancies in covariance matrix

We know that covariance matrix is symmetrical. I have a vague intuition that there may be some other redundancies beyond that. For example, if A is correlated to B and B is correlated to C then A and ...
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26 views

Finding correlation of data with potentially hidden time lags

Let's say I have few independent variables plus multiple observables that I monitor over time for a system. I'd like to find out if there is any correlation between the observables and any of the ...
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0answers
73 views

Probability and correlation function, interpretation of a result

My question is originated from the paper ...
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65 views

Calculation of conditional joint probability given certain conditionals for data which aren't independent

The context of this problem is the estimation of the distribution of a parameter $v$ given sets of data $A$ and $B$, where $A$ and $B$ are not independent. Suppose I know $P(v | A)$ and $P(v | B)$. ...
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548 views

What do angle brackets ($\langle\rangle$ ) mean in mathematics/statistics (autocorrelations)?

Okay, so the logarithmic return on a stock is given by: $$r_τ (t) = \ln P(t+τ) - \ln P(t),$$ where τ is the interval of time. I have no problem calculating that. My question comes to the following ...
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37 views

Sorting Vectors based on their correlation

This problem [question]: Sort vectors according to their distance between them is about sorting vectors based on the distance between them. What about sorting vectors based on the correlation ...
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0answers
22 views

Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix.

I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
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163 views

Cross-Correlation (and finding Correlation error ) of two digital sequences.

In a IEEE paper, I saw a formula for WUInt(ti+1) as , Reference : ...
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0answers
86 views

Compute significance of Kendall tau-b?

I have so-far tried all ways of computing kendall tau significance (where there are ties) described here. However, none of them works good, even for relatively large vectors. I think the problem is ...
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0answers
111 views

Windowed Linear Correlation

$\DeclareMathOperator \Cov {Cov}$ $\DeclareMathOperator \Var {Var}$ $\DeclareMathOperator \E {E}$ Consider the following experiment: For $N\geq1$, consider $N$ black balls. Let us paint each black ...
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27 views

Dynamic Light Scattering

In DLS does the combination of the Time Average and Ensemble Average give a better statistical average than the results shown by each case considered separately ?
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151 views

Cross Correlation

The cross-correlation function is defined as follows if $\bar{f}$ is the complex conjugate of $f$ and we assume that $f$ is real, such that $\bar{f} = f$. $$ \begin{align} f \star g &= ...
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37 views

Sampling a distribution with restrictions: eliminating the correlation between two variables

I have a collection of 400.000+ word-pairs. Each word-pair has an association strength, which is a measure of how related the two words are to each other (as in cow-milk). Each word-pair also has a ...
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0answers
122 views

Correlated Random Numbers Between A Range

I am trying to generate random numbers within a range say 57 to 107 which are correlated by a factor of 0.8. The numbers are for illustration simplicity only.
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13 views

Cross correlation computations

What are useful ways/formula for calculating sample cross correlations (i.e. correlation factors between individual components of two different random variables). Say I have two sample matrices, $X$ ...
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6 views

Finding correct values based on information from two arrays

Consider the following scenario: Say, one machine is sending out a beep signal every 10 seconds in a very noisy environment. I have two sensors which detects these beeps independently. Device A is ...
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0answers
6 views

differetiate between linear and non-linear relationship between two variablesand and explain the effect of Fisher z)

In statistics and mathematics it is not unusual to make a distinction between the type of relation between two variables. Also, we use r many a time after Fisher z- transformation. In a meta-analytic ...
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0answers
16 views

Condition number of covariance matrix

I am interested in generating a covariance matrix of dimension say 100. I managed to get a correlation matrix with finite condition number. To construct a covariance matrix I need to have standard ...
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0answers
6 views

How to order a set of attributes such that their correlation matrix concentrates high correlation terms around the diagonal?

Suppose there are n attributes that are being tested for correlation with one another. We need to find the order in which these attributes must be placed along the rows as well as columns such that ...
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5 views

Similarity between two matrices/lattices

I'm looking at the evolution of matrix in time where every coefficient can only be +1 or -1, from physical point of view it could be an Ising model on finite lattice. I'm interested in a variable ...
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0answers
10 views

Correlation 4-point

I need to calculate $\langle x_{i}x_{j}x_{k}x_{l}\rangle $, where $$ \langle f(x) \rangle = \int e^{-\frac{1}{2}A_{ij}x^{i}x^{j} - \frac{\lambda }{4!}\sum_{i}x_{i}^{4}} f(x)d^{n}\mathbf x , $$ for ...
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16 views

Weighted Pearsons Correlation

I am a software engineer so please bare with me. I am currently calculating the ppmc coefficient of a series of data over unequal time periods. I wish to weight data that was recorded within the last ...
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0answers
22 views

Spatio-temporal triple correlation

I would like to simplify if possible the spatio-temporal triple correlation of the following function: $$f(\vec{x},t)=\delta(\vec{x}-\vec{x}_0(t)) \otimes f_p(\vec{x})$$ I define the triple ...
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0answers
20 views

What is correlated with what in a linear regression?

I'm trying to make sure I understand the ins and outs of a linear regression and am making a table for what is correlated with what, so just want to see if I have everything included. I'm looking at ...
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0answers
30 views

How to interpret autocorrelation of images?

Say we have a multiple grayscale images $I_i$ collected as a matrix $M = [I_1\ I_2\ I_3\ldots I_n]$ What exactly does its autocorrelation $R_{MM} = M M^T /{n}$ tell me? According to Wikipedia ...
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0answers
16 views

Principal Component Regression

Suppose that Z1, Z2 and Z3 are the principal components of a data set and Y is a vector of the response variable. The correlation coecients between Y and Z1, Z2 and Z3 are 0.25, -0.4 and 0.7, ...
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0answers
12 views

Indepedence of sample means of two orthogonal Gaussian vectors?

Suppose $\boldsymbol{x}_{1}$ and $\boldsymbol{x}_{2}$ are Gaussian vectors with each distinct but arbitrary means and covariances, i.e., the elements of each vector are generally intra-correlated. ...
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0answers
16 views

Find solution of correlation matrix equation

Suppose ${X}$~$N(0,\sigma^2\Sigma)$, with $\Sigma$ being unknown correlation matrix. How to find a solution of $\Sigma$, such that for $Z=\alpha'X$, we have $var(Z)=C$. (Suppose C is properly chosen ...
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0answers
26 views

Generating correlated random numbers from Normal Distributions

If I have a sequence taken from X~N (μ1 , σ1 ). Is it possible to generate a sequence of numbers drawn from Y~N (μ2 , σ2) such that X and Y have correlation ρ?
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21 views

Normalized cross-correlation in detail

I'm trying to implement a normalized cross-correlation algorithm but I don't get what in fact is this measure. What confuses is the wikipedia definition: $\frac{1}{n} \sum \frac{(f(x,y)- ...
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0answers
28 views

Correlation: How to extend it from pairs to further random variables?

How can one determine the correlation coefficients (or their intervals) between $n$ standard-normal random variables $X_i$, $i=1,...,n$, when $X_i$ correlates with $X_{i+1}$ with correlation ...