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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3
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30 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
39 views

Dependent/Conditional Probability over time [closed]

I deal with statistics to quantify and describe time series all the time, however, I was asked by a friend to help provide a solution to his problem. The scenario is essentially this: 100 empty ...
0
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0answers
34 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
13 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 ...
2
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1answer
44 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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16 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
41 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 ...
0
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0answers
11 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
23 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 ...
2
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1answer
13 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 ...
4
votes
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 ...
1
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0answers
21 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
26 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 ...
0
votes
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 ...
0
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0answers
21 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 ...
0
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1answer
17 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 ...
0
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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? ...
0
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1answer
23 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 ...
0
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1answer
40 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. ...
0
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0answers
19 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 ...
0
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0answers
10 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 ...
0
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0answers
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 ...
0
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0answers
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 ...
1
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1answer
62 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 ...
1
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1answer
25 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) = ...
0
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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 ...
0
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0answers
7 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 ...
3
votes
1answer
187 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 ...
0
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0answers
36 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
637 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 ...
7
votes
1answer
194 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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0answers
62 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
votes
1answer
59 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 ...
1
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1answer
25 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 ...
1
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0answers
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 ...
2
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2answers
142 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., ...
3
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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 ...
1
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0answers
27 views

Estimation of the mean when data points are not independent

When we estimate the mean with 95% confidence, this formula is used: $\hat{\mu}=\overline{\mu}\pm1.95\times\frac{\overline{\sigma}}{\sqrt{N}}$, where $\overline{\mu}$ is the sample mean, ...
0
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0answers
25 views

How to prove dependency?

I am a beginner. I have two variables X and Y. How can I prove that the values of Y are dependent on the values of X? I can show whether the relationship is weak or strong using Pearson's ...
0
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1answer
32 views

Hosmer Lemeshow for correlated data

Is it OK to use HL to judge the goodness-of-fit of a Logistic Regression when the data is a time series correlated from one period to another? I know that HL assumes independence of events, but I ...
0
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0answers
9 views

Calculating the error on a variable, given the error on a dependant variable

I have a variable which is given by the equation: M = M(a) * (N/20) Now if M(a) has an error of let's say 10%, how do I ...
3
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0answers
27 views

Comparing non-independent discrete distributions of animals

My team made some experiments how animals choose their location in different environmental conditions (to check the hypothesis of ideal free distribution). The animals were placed in the experimental ...
0
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0answers
41 views

Comparing R-squared across regression equations with a dependent sample

I was able to find information on how to compare R-squared values across regression equations with independent samples by creating confidence intervals around the estimates. However, the sample used ...
1
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1answer
43 views

Can a joint second moment exist if the joint distribution cannot be derived?

I am struggling with writing down a relationship between two variables and I am happy for each and every comment that points out, how I can overcome this problem: Let $x\sim N(\mu,\Sigma), x ...
2
votes
1answer
21 views

Correlation of exam notes, the students school and their technological knowledge

I have a set of data about some students and I want to check if their success in exams is determined by their level of technological knowledge, or their school. So, I have a table with those values ...
0
votes
0answers
19 views

Analyzing dependency in multiple quantitative and qualitative variables

I'm analizing a tiny dataset with data about 30 consumers. I have columns representing gender (QL), age (QN), nationality (QL), technological knowledge (QN), achieved operations (QL), and so on. QL ...
4
votes
3answers
973 views

If two events are not mutually exclusive, does that mean they're independent?

Suppose we have two events, $A$ and $B$. I want to find out if $A$ and $B^c$ are which one of mutually exclusive or independent. I have figured out that they are not mutually exclusive.. does that ...
3
votes
2answers
179 views

Dependent identically distributed random variables

If $X_1$ and $X_2$ are dependent identically distributed, can we show that $Pr(X_1>X_2) = Pr(X_2>X_1)$? For i.i.d, it is obvious, but what if they are dependent?
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0answers
9 views

Comparing dependent anonymous samples

I have data collected each year from 2010-2015. In this data I have demographic information and a self-reported score on a 5 pt Likert scale. The surveys were anonymous but I know that many of the ...
2
votes
1answer
29 views

KDD 15 paper: scoring bigrams

I am by no mean into Statistics nor NLP. And I am reading the following paper, trying to learn something new: ...