Data, events, processes, etc, are non-independent if knowledge of 1 provides some information about the state or value of the other.

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random effect with high variability in record numbers per factor level

I'm dealing with a large observational data set, where I have yield values (response variable) nested within farm and location. When farm and location are included in a random intercept model, both ...
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0answers
3 views

Covariance between non symmetrical matrices with a unidirectional composition

I am trying to explain variation in why some researchers go to certain places and not others by analyzing how many articles scientists from one publish about another location. My matrix is ...
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1answer
40 views

100-Dollar Game Responses as Predictor

Outcome = Feature Sentiment Participants will rate on 1-5 point scale how much like a particular feature. Potential Predictors = Developments A - E Participants will be asked to imagine they have ...
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5answers
355 views
+100

On the importance of the i.i.d. assumption in statistical learning

In statistical learning, implicitly or explicitly, one always assumes that the training set $\mathcal{D} = \{ \bf {X}, \bf{y} \}$ is composed of $N$ input/response tuples $({\bf{X}}_i,y_i)$ that are ...
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1answer
30 views

The likelihood function of related samples

I know how to get the likelihood function for two independent samples from normal distribution. What will happen to the likelihood function if the samples are related? What will be its form?
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2answers
50 views

Probability distribution of the subtraction of two dependent non-gaussian distributions

I have two dependent,correlated non-gaussian random variable X and Y. I want to calculate probability distribution of Z=X-Y. For independent distribution, I know the equation is as follows, What ...
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1answer
48 views

How to reconcile results from many incremental hypothesis tests?

I'm considering a series of controlled experiments (e.g. A/B tests) measuring the performance of a system. Each time a change to the system is found significant (via statistical inference) the test ...
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0answers
13 views

Can you compare the means of two nonindependent sets of data that are not paired?

I am doing within-group comparisons of monkey movement behaviour (e.g., daily path length, home range size) because I want to determine if their behaviour is different in the dry versus the wet ...
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1answer
28 views

Testing the independence of a time series

I’d like to test whether my time series of consecutive payments is independent or not and thought that since this is a pretty common condition in statistics it should be easy. Well, turns out is isn’t ...
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1answer
11 views

What methods can be used for tractable computation of probabilities for evolutionary model of non-independent entities?

I'm trying to extend a simple model which works as follows. We have n 'original' entities which each have a colour. This population evolves by the following events, which occur at exponential rates: ...
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1answer
33 views

Can nonlinear regression with least squares estimations be used for testing hypotheses with data containing dependent observations?

I counted the number of animals of a certain species in 6 fixed locations on a monthly basis for 18 months. I now would like to test the effects of location, starting density, and time on the dynamics ...
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1answer
43 views

Exemple of real-life non-linear correlation in time series?

I am looking for a dataset of 'real-life' time series that exhibits non-comonotonic / non-countermonotonic dependence. I am not looking for the textbook X^2 correlation, but interesting yet real ...
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1answer
16 views

generating random matrix

My problem is this: I have a matrix with three columns. I created a second matrix with only two columns where column1 is the first column (col1) from the first matrix and column2 = ...
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1answer
19 views

model to predict variable evolution

Suppose that I have a set of variables X1 X2 and X3 that explain the evolution of a ...
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0answers
37 views

Lack of independence - how to analyze data from a time-series that are spatially correlated?

I am dealing with a species distribution. From aerial imagery, the species' presence has been assessed at specific locations by identifying the presence/absence of the species of interest under 9500 ...
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0answers
36 views

Tail dependence of mixture copulas

I am currently using (multivariate) mixture copulas to model a financial data set. The mixture has two components as follows: $$C_{mixture}=wC_1+(1-w)C_2$$ where $C_1$ and $C_2$ are copulas. I have ...
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0answers
15 views

Kendall's tau for extreme copulas: extreme-t and Hüsler-Reiss

I am looking for formulas to calculate Kendall's tau ($\tau_\mathrm{C}$) from copula parameter (or vice versa). I am interested in extreme-t and Hüsler-Reiss copulas. It is not an issue if numerical ...
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1answer
51 views

How do I test for independence with non-exclusive categorical variables?

Introduction I have a categorical contingency table with many rows and a binary outcome, which I count: ...
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19 views

how to maximize strength of inference in non-independent data

I have a large set of vectors, each one describing the shape of a different object. Each vector has 25 categorical descriptors for the shape of the object, with each position on the vector having ...
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0answers
44 views

Expanding Joint probability distribution function having dependent random variables

Let $Z_1$ and $Z_2$ denotes two dependent random variables defined as \begin{align} Z_1&=\frac{XY}{aX+bY+c}\\ Z_2&=\frac{XY}{uX+vY+w} \end{align} where $X$ and $Y$ are independent ...
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12 views

How to determine if events are joint or disjoint?

Two events recorded for two dice throws : 1. odd,even (P = 1/2) 2. 1,2,3,4,5,6 (P = 1/6) As these events are joint the probability of dice1 being odd and dice2 ...
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0answers
24 views

If distance correlation $DCOR(X,Y) = 0.5$ then are X and Y dependent or independent?

If distance correlation $DCOR(X,Y) = 0.5$ then are $X$ and $Y$ statistically dependent or independent? What about when $DCOR(X,Y) > 0$, are they statistically dependent for sure even when it's less ...
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1answer
14 views

How to deal with non-independent data when comparing populations across a range of distances

I am trying to figure out how to carry out an analysis but am having trouble finding any information. I am interested in finding out whether values of sensitivity across populations are more similar ...
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1answer
48 views

Misguiding data relationship between Y and X?

Background: I am currently surveying a number of articles related to subject of urban sprawl. One of the things that I have come across multiple times in the literature (a thing which seems to bother ...
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22 views

Correctly determine alpha for repeating statistical test in non-independent (interpolated) timeseries data

Problem I have timeseries of measurements of which I also have determined the standard deviation of the noise. My goal is to determine whether or not the measurement is significantly different from 0 ...
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0answers
34 views

Panel attrition, strict exogeneity and cluster correction

I'm analyzing a panel of Dutch municipalities (N=485, T=10), in which my variable of interest is a dummy variable that shows whether in a given year the municipality has paid parking or free parking ...
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1answer
44 views

EM algorithm with dependent observations

I am trying to implement an EM algorithm for dependent observations. Specifically, I am dealing with families where the hidden variables $Z$ of the children are dependent on the hidden variables of ...
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22 views

Which statistical test to apply for non-related variables

I have two variables, travel time to health facilities and density of violent crimes in a particular city, I need a test that I can use to statistically quantify if there is any relationship between ...
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1answer
19 views

Do I use a dependent or independent T-Test with this experimental setup?

I've run an experiment where users had to work with 2 systems (one after the other), and grade them on usability. This results in a score 0-100 of both systems. 50% of participants used system 1 first ...
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1answer
17 views

How to describe change in dependent data?

I have observations that were measured before and after an operation, say $X_{before}$ and $X_{after}$. I am interested in the amount of change (either increase or decrease). How could I describe it? ...
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1answer
25 views

how to compare 2 dependent variables [closed]

What is the correct way to compare correlation between 2 dependent variables in R? Thanks Edit: Here is the edited question and apologize for not asking this correctly before: I acquired 2 measures ...
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1answer
55 views

how to plot 3D partial dependence in GBM

I can use the following code to get one-dimensional partial dependence plot. what code can I plot two-variable partial dependence plot, that's the three dimensional figure. Thanks. ...
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0answers
20 views

Choose a Copula for multivariate data

I want to construct a Copula to obtain a PDF that includes the dependence in the variables. Each random variable is uniformly distributed and the covariance/correlation matrix is known. I don't have ...
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12 views

Paired test (non-independent) for rank order data

I have responses from a survey with questions where respondents were asked to rank their top 3 choices from a list of 8 choices. An example of the type of question would be to rank their top 3 methods ...
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14 views

Testing for dependence of unpaired and unequally-sized samples

I've seen several similar questions, but I haven't been able to find an answer. I have two unpaired samples of unequal size and of equal population variance. One concern is that these samples are ...
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23 views

Can longitudinal studies ever be treated as having independent observations?

This may be a dumb questions, but for sake of statistical analyses I'm wondering if the data of a longitudinal study can ever pass the assumption of having independent observations? For example, I am ...
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1answer
83 views

distribution of sample variance of correlated observations

It is well known that if we have n i.i.d. observations of a normal random variable, then Cochran's theorem tells us that: $\frac{(n-1)s^2}{\sigma^2} \widetilde{} χ^2_{n-1}$ But what if the samples ...
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1answer
26 views

Extreme Value Distribution of dependent RV

Let $X_1, \dots, X_n$ be random variables with known identical distribution and covariance matrix $C \in \mathbb{R}^{n\times n}$. How can I model / calculate the extreme value distribution: $$ f(w) = ...
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0answers
18 views

combined significance of consecutive observations with variable variance

I'm facing a statistics question for which I could use some input. I have the following data: ordered observations (along 1 axis, genome coordinates) for 200 samples. For each position, the average ...
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0answers
9 views

Test for variance homogeneity and dependent samples

I have the following question regarding statistical tests for an fMRI phantom (i.e., roughly speaking a standardized object (e.g. cylinder filled with gel) used to make inference e.g. on properties of ...
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1answer
191 views

Does using lagged independent variables makes sense?

While it seems quite common to calculate a lagged version of the dependent variable and to use it on the right hand side of a model (e.g., autoregressive models), I have rarely seen that lagged ...
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38 views

Is the limit of n-wise independent events independent?

Let $(\Omega, \mathscr F, \mathbb P)$ be a probability space. Consider double-indexed events $A_{m,n}$ $ \ \ \ \ \ \ \ \ \ \ \ A_{1,n}, A_{2,n}, A_{3,n} ...$ are n-wise independent. $A_{m,1}: ...
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2answers
659 views

For intuition, what are some real life examples of uncorrelated but dependent random variables?

In explaining why uncorrelated does not imply independent, there are several examples that involve a bunch of random variables, but they all seem so abstract: 1 2 3 4. This answer seems to make ...
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1answer
197 views

Conjecture related to Kolmogorov 0-1 Law (for events)

Let $(\Omega, \mathscr F, \mathbb P)$ be a probability space. Conjecture: Suppose we have events $A_1, A_2, ...$ s.t. $\forall \ A \in \bigcap_n \sigma(A_n, A_{n+1}, ...)$, $P(A) = 0$ or $1$. ...
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64 views

model estimation with feedback loop in variables

I have the following problem regarding fitting of a model where some variables can be biased so that their values are based on knowledge or at good guestimate of $Y$ in the past. In other words: some ...
3
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1answer
62 views

How do we prove these $\sigma$-algebras are not independent?

Given the sequence $(X_n), n=1,2,... $, of iid exponential random variables with parameter $1$, define: $$ M_n := \max \left\{ X_1, \frac{X_1+X_2}{2}, ...,\frac{X_1+\dots+X_n}{n} \right\} $$ I want ...
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1answer
27 views

testing dependent skewed samples

I must compare two distributions of patent data: namely, they are the number of patent applications of companies before vs after an acquisition. I need to perform an hypothesis test to assess if the ...
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22 views

multivariate analysis of dependent data

I have some diet data I am analyzing that was collected in different locations at different times (over 3 years). The nature of the sampling resulted in multiple predators at the same location. The ...
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2answers
156 views

Expectation and Conditional Independence

This question is an aside from another question here on CV. We know that the expectation of the product of two independent random variables is the product of expectations, i.e., ...
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1answer
22 views

How to check if there is a dependency of a numeric variable on other numeric variables?

I need to check if a numeric variable $y$ depends on a set of other numeric variables $(x_1, x_2, ..., x_n)$. I do not know anything about the form of possible dependency (I do not even know if it ...