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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9 views

Analysis of clustered data

I have records of $multiple$ visits from many different patients in several different clinics (i.e. visits nested within patients nested within clinic) and plan to perform an analysis that takes into ...
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21 views

Comparing two correlated dependent variables

I have two dependent variables that I want to predict. One is a normally-distributed continuous variable, and the other is a binary categorical variable (0 or 1). They're moderately correlated so that ...
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1answer
58 views

Asymmetric measure of non-linear dependence/correlation?

I am definitely not a statistician/mathematician so feel free to tell me I'm an idiot if I am. As far as I can tell from my Wikipediaing all of the main measures of dependence are symmetric and ...
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1answer
24 views

Differences between reviewers and people being reviewed in terms of learning achievement

An experiment about the review process was made. Participants were students visiting a course. One group had to solve some exercises and the other group had to review their work and give feedback. At ...
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13 views

Non idependence within groups

I have to train a machine learning model for classifying two groups. Unfortunately, my positive group has a small number and many cases are not independent from each other (observations taken in ...
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45 views

Best machine learning methtod for classificating datasets with non-independent cases within the groups

I have to perform binary classification of my data with supervised machine learning, but I have some difficulties working with my data set. It consists many genetic mutations that have parameters ...
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1answer
37 views

Example of dependence with zero covariance

This is a constructivist question. Please provide a bi-variate distribution or density/mass function of two absolutely continuous/discrete (but not mixed-type) random variables, which (may) have ...
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9 views

Flow of influence in a v-structure for Probabilistic Graphical Models

I'm not very sure I understand why an observed v-structure have different flow of influence behaviour for a directed and an undirected graph. What is the intuition behind the actual definition for ...
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31 views

ANOVA of pairwise (non-independent) data in R

I am trying to do a one-way ANOVA of data that is generated from pairwise comparisons, and am having difficulty resolving the problem of non-independence. I have 12 populations, and for each pairwise ...
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28 views

Expected value of product of squares of two dependent random variables

Given two random dependent variables, $X_1$ and $X_2$, and expected value and variance of each of these variables. How would one go about calculating the expected value of the product of the squares ...
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1answer
113 views

Why is independence required for two- sample proportions z test?

I read in several books as well as in different posts (e.g. here) that independence is required for two-sample proportions z tests. But so far I could not find an explanation why this is the case and ...
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2answers
95 views

How does one find the mean of a sum of dependent variables?

I know that the mean of the sum of independent variables is the sum of the means of each independent variable. Does this apply to dependent variables as well? Thanks.
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1answer
37 views

Resources to understand why dependence is a problem [duplicate]

For many statistical procedures, it seems the observations must be independent. For example the observations within each group in a two-sample t-test must be independent for the standard error/P-value ...
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14 views

Method to analyze data which has no repetitional measurement

I am trying to find a good method to analyze my data, and I am really lost. My data is only from one riverstretch, no repetitional measurement. I look at three stretches of the river, near ...
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1answer
31 views

multi stage binomial “process”

I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution $$ X_1 \sim \text B(K,p) $$ , p is the ...
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17 views

Logistic regression and cluster ID

The dataset consists of all prescriptions classified as on or off-label (0 or 1), meaning possible more than one prescription per child (pnr-number) I want to know the off-label rates per year for ...
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2answers
45 views

how to deal with dependence/interaction among covariates in a cox regression model

In case of a linear regression, if we are to account for interaction between two regressors x1 and x2, we write a model like ...
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17 views

How can I make use of correlations between datasets for building multiple models?

I'm building models for a bunch of spatial points. Linear regressions models, for now, but I will have expand to more complex ones (non-linear, time-series models, etc.). So far, I've looked at the ...
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13 views

Is analysis of variance here a correct test?

Suppose I have measurements: $f(x_i, y_i)$ $f(v_i, w_i)$ $f(x_i, v_i)$ $f(y_i, w_i)$ If I put these into groups $(xy), (vw)$ and $(xv, yw)$ and do a single-factor ANOVA with the previous three ...
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1answer
30 views

Are identical samples independent?

Are results of two different tests performed on exact same sample independent or dependent? For example, if the same group of rats were injected some drug A, results collected, then long enough time ...
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78 views

Compare differences in dependent frequencies

I would like to compare two error rates (proportion of incorrect answers in questions with dichotomous response-format) for two different items, and I am looking for some advice on how to do that. ...
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1answer
62 views

Assume (x,y) are drawn from independent & identical distribution when y=f(x)

Sometimes we say the following: $X$ is some training data given by $X:=\{(x_1,y_1),...,(x_l,y_l)\}\subset R^d \text{x}R$. Assume that the training data had been drawn from independent and identical ...
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55 views

joint distribution, probability, calculating probabilities under false independent assumption, when the random variables are actually dependent

Suppose I have random variables $X,Y,Z$ and I would like to compute the probability that random variable $X$ is smaller than $Y$ and $Z$: $$ \pi_X \overset{def}{=} Pr(X < Y, X < Z) = \int Pr(x ...
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1answer
61 views

Using random forest for survival analysis with time varying covariates

I've been trying to train a model that predicts an individual's survival time. My training set is an unbalanced panel; it has multiple observations per individual and thus time varying covariates. ...
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3answers
74 views

Cox Models treatments depending on time until event

I'm trying to get the "productivity" of treatments like sending an email, calling or sending an SMS and their combinations in the paying debtor's probability. I couldn't find one model that satisfies ...
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1answer
69 views

How can I evaluate the probability density function of $Z=X+Y$,if $X$ and $Y$ are not independent?

If $Z=X+Y$, and the PDFs of $X$ and $Y$ are both functions of a deterministic variable $d$, how can I evaluate the PDF of $z$ while the convolution cannot be used here (due to lack of independence)?
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1answer
64 views

What are the implications of estimating a covariance matrix from a correlated sample?

Given a sample of $n$ independent observations $x_1,...,x_n$ (where $x_i$ are $p$-dimensional column vectors), the $p \times p$ sample covariance matrix is defined as ...
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1answer
62 views

Estimation based on observing sum of two variables

Let $X_1,\dots,X_n$ are i.i.d normal $N(\mu,\sigma^2).$ Suppose that we only observe $$ X_1+X_2,\dots,X_1+X_n,\dots,X_{n-1}+X_n, $$ i.e, $X_i+X_j$ for all $i<j.$ I wish to find the best estimator ...
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37 views

Estimating of variance of dependent normal distribution

Let $X_1,\dots,X_n$ are independent and identically unobservable variable on $\Omega$. Suppose that $f:\Omega\times\Omega\mapsto \mathbb R$ be unknown function such that we know the value of ...
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35 views

Expected value non-independent random variables

Let $X$ be a set of costumers, {$x_1, ..., x_N$}, each $x_i \in X$ have a discount $p_i$ in the interval $[0,1]$, it means if $p_i$ is 0.3, $x_i$ will pay only 0.3 of the entire value. I want to know ...
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33 views

Expected value of a function that is not sampled uniformly

How can I calculate the expected value of a random variable $R(\Omega)$, when the samples are not i.i.d? In my specific case, I have more samples at lower values of the parameter of the function, ...
2
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1answer
45 views

1-Way ANOVA with single independent/repeated (within/between) factor

I want to perform an ANOVA on data with a single factor with three levels. The difficulty for me is that two of the levels are repeated measures (within subjects) and the third level is independent ...
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15 views

Expectation of ratio of functions of Bernoullis: a concentration question

Consider the following $n \times n$ symmetric matrix of i.i.d. Bernoulli random variables, $X_{ij}$. For $i=1,...,n$ and $i<j\le n$. Let $X_{ij} \sim \text{Bernoulli}(p)$ when $i \ne j$, and let ...
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1answer
41 views

Does $P(B|A) \neq P(B| A^c)$ prove dependence?

Does P(B|A)!=P(B|!A) prove dependence? != means 'is not equal to' !A means 'not A' or 'the complement of A' Thanks. Edit: I believe I may have proved that inequality shows dependence. Proof: ...
2
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1answer
22 views

Dependent chi-squares vector: how to calculate cdf of $X_{(n)}$?

Consider a vector of central&1-degree Chi square distributed variable $(X_1, X_2,...,X_n)$, it is simple to calculate the cdf of $X_{(n)}$ (maximum of order statistics), when they are independent. ...
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1answer
97 views

chi-squared test when variables dependent

For a square matrix, is it appropriate to use a chi-squared distribution when each level of the variables are assumed to have the same overall frequency? Specifically, I'm analyzing a dataset of the ...
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36 views

Correlation between non-independent variables

I want to conduct correlation between two variables, that have common term (difference scores). Originally there are three variables X, Y, Z. I want to conduct correlation between two variables that ...
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41 views

Are these distributions independent?

I'm trying to compare the medians of two non-normal distributions: $A$ and $B$. $A$ is the distribution of completion durations for one type of task $B$ is the distribution of completion durations ...
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20 views

How to eliminate dependent inputs?

There are a lot of statistical methods that rely on the assumption of input independence. For example, Naive Bayes text classifiers operate under the assumption that occurrences of different words are ...
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29 views

ANOVA and dependence WITHIN a group

I have three different methods that I would like to compare using ANOVA. The variable to compare is method accuracy that I get trough cross-validation. This means that the same data set (N=60 ...
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1answer
18 views

Integrating multiple tests Bayes factors

I have been using an Bayesian-centric R package for some genomics analysis to detect mutations in 3 individuals from the same family. I have to do each analysis for each individual separately due to ...
2
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40 views

Variance-covariance matrix as the sum of variance covariance matrices

I have a variance-covariance matrix, $\mathrm{V}$. This allows me to take a vector, $x$ of independent random variables drawn from a known distribution, and induce a required variance-covariance ...
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2answers
33 views

GLMM for SNA and non-independency data

I contact you because my case is particular and I don’t know much about GLMM. I have data of social networks (network metrics) of a nonhuman primate species. These data are by nature non independent ...
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51 views

Extremal serial dependence

As part of my analysis of heavy-tailed time series of company returns, I would like to check whether extreme returns exhibit serial dependence, i.e. if extreme events are followed by extreme events. ...
2
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0answers
76 views

Analysis for cross-subjects correlation

Suppose that an investigator has collected some longitudinal data from each of the $n$ subjects, and that a correlation coefficient is computed on the data between any pair of subjects, leading to ...
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3answers
224 views

Best method to predict binary outcome with multiple records per subject

I am interested in building a model to predict the binary outcome, retention (1 - retained; 0 - not retained) with various potential predictor variables (either continuous or categorical). With that ...
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42 views

Probability of vector similarity wrt dimensionality

I'm trying to show that the probability that two vectors are similar to each other increases as the number of dimensions decreases. I define similarity between two vectors $a = [a_1, a_2, ..., a_n]$ ...
2
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1answer
198 views

Statistical Power of ROC/AUC Test with non-IID Samples :: To how many IID Samples are my non-IID Samples Equivalent?

I've been assigned to solve the following problem as part of a serious, biological research project. I think I have a tentative solution, but I'm wondering whether the approach I've picked is the ...
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1answer
210 views

Sum of Dependent Poisson Random Variables

I am working with the distribution of the sum of two dependent random variables. In my problem, there are two unobserved events, X and Y, where X precedes Y and Y is a function of the outcome of X, ...
4
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3answers
85 views

A critical proof or counterexample regarding independence

Does independence of $X^2$ and $Y^2$ imply independence of $X$ and $Y$?