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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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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18 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
12 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 ...
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20 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
20 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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31 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. ...
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69 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
135 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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37 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 $a = [a_1, a_2, ..., a_n]$ ...
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1answer
151 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
30 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, ...
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3answers
77 views

A critical proof or counterexample regarding independence

Does independence of $X^2$ and $Y^2$ imply independence of $X$ and $Y$?
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1answer
41 views

Correlation and dependency of two variables

Lets say I am interested in finding the correlation of the following two metrics. They are aggregations and include the same input A in their formula. Is it possible to talk about correlation of ...
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30 views

When is the determinant of a covariance matrix is 0? [duplicate]

Any covariance matrix $A$ must be non-negative definite or semi-positive definite. This means that its deteraminant should always $|A|\ge0$. In case $|A|=0$, what would happen? or what does this mean ...
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1answer
45 views

When is the IID Assumption too strict for the bootstrap?

The Bootstrap (Efron 1979) assumes that the data are IID. Obviously, if we have time series data then we probably cannot make that assumption unless we have a special case that we a time series of ...
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54 views

Random effects and repeated measures: what would you choose as random effect?

I have a question regarding the use of random effects in order to account for a violation of the assumption independent samples. I have this discussion with my supervisor and we disagree about this ...
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1answer
44 views

confidence intervals for dependent observations

The answer to this question discusses problems associated with calculating P-values for dependent observations. Let's say you have observations from two different groups that are dependent. You ...
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1answer
65 views

DNA: The number of 'AAAAA'-s in a randomly generated DNA sequence that's 1000 base pairs long

Let's say I have a randomly generated sequence consisting of letters A, C, T and G that's 1000 letters long. The probability of each letter occurring is 25%. What is the probability that the sequence ...
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1answer
116 views

required: good and straightforward method to detect change points in dependent univariate time series using r

I know that there are many related threads, packages and papers. Currently I`m reading through many of them. However, I don't plan to dig too deeply into this topic. I need a sound method that works ...
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94 views

Why doesn't correlation of residuals matter when testing for normality?

When $Y = AX + \varepsilon$ (i.e., $Y$ comes from linear regression model), $$\varepsilon \sim \mathcal{N}(0, \sigma^2 I) \hspace{1em} \Rightarrow \hspace{1em} \hat{e} = (I - H) Y \sim \mathcal{N}(0, ...
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2answers
56 views

data representation with nominal, ordinal and continuous variables

Suppose I have data of this format: customer, country, location, unit price, traffic, etc. (more nominal/ordinal variables) I want to know how country affects unit price, how do I go about doing ...
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0answers
44 views

What exactly is a higher-order correlation? [closed]

What exactly is a higher-order correlation? Is the term just a catch-all for all dependencies that are not captured by second-order correlations? Or do people mean something more precise than ...
2
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1answer
52 views

Chi-square test to see if set of dependent correlations are equal

I've got four dependent correlations (i.e., from the same sample) that involve predictor variables $(A,B,C,D)$ and an outcome variable $(E)$. $N=172$. $$\begin{array}{c|cccc}{\rm ...
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24 views

Test which method is better if data is gathered on overlapping time windows (not independent)

I have two methods which are being used to estimate a specific signal. I have a ground truth measurement of this signal and these two methods are using noisy data to estimate this signal. This signal ...
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20 views

Estimating distribution function for dependent observations

Let $X_1,\dots,X_n$ be identically but not necessary independent distributed with distribution function $F$. I'd like to estimate $F$ efficiently. In case, $X_1,\dots,X_n$ are i.i.d., we can estimate ...
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28 views

Correlation between predictor variables and time in Survival Analysis?

I am using survival analysis to model time to an event. I would like to explore the effect of a continuous predictor variable on the hazard rate. The continuous predictor ranges in value from 0-8.5. ...
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89 views

How do I test the difference between two dependent correlation coefficients whilst controlling for other variables?

How do I test the difference between r(X,Y) and r(X,Z) [Williams Test?] whilst controlling for demographic variables that were measured in addition to X and Y and Z [Partial Correlation]? Thanks, ...
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37 views

Neural Network, dependence among outputs?

Is there a way to train a neural network in the following manner: You have $n$ observations in the training set. The neural net will start with random weights, and produce $n$ outputs. I want to ...
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30 views

Is the multivariate Gauss the only pdf incorporating covariances?

I am wondering whether there is another probability density function known to literature which is similar to the multivariate normal distribution in the respect that the pdf incorporates the ...
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1answer
71 views

What are $\rho$-, $\beta$-, and $\alpha$-mixing conditions?

I have seen properties named $\rho$-, $\beta$-, and $\alpha$-mixing conditions in papers related to Copulas and Markov processes like this one: In this paper, we identify conditions on $C$ that ...
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1answer
31 views

Independent vs. Dependent Compound Poisson Distributions

I have an issue with a section of some Actuarial lecture notes that I am reading. Here are the snippets from the notes: "Consider a portfolio consisting of $n$ independent policies. The aggregate ...
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73 views

Estimating variance for identically non independent data

Let $X_{ij}$ with $1\leq i<j\leq n$ (that are $X_{12},\dots, X_{1n},\dots,X_{(n-1)n}$) be ${n \choose 2}$ identically normal distributed $N(0,\sigma^2)$ such that $ \text{corr}(X_{ij},X_{rs})=\rho ...
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37 views

Incorporating the non-independence of 'Date' into a model predicting temperature

I'm trying to analyse some temperature data, collected at 49 sites over a three month period. The data are in the form of a maximum reading at each site on each day. I'm interested in how temperature ...
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94 views

Correlation between independent groups of dependent data

I’m trying to correlate data between an accelerometer and a pedometer (step counts). These are worn simultaneously by 20 people for 7 days. If the two devices give me 1 datum per day at the end of the ...
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39 views

Probability of drawing a cursed coin not from a certain box

There are three boxes of gold coins. In the first box, 1 out of 3 coins are cursed, in the second 2 out of 3 are cursed, and in the third 1 out of 4 are cursed. Furthermore, the first box is ornate, ...
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138 views

A/B Test with factors other than conversion rate

I've read "AB Testing other factors besides conversion rate", but I don't know if it's relevant with my question, even if it seems similar. Here is my problem. Let's assume I am creating a new tools ...
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1answer
75 views

What is the expected value E(X), E(Y), Var (X,Y)

Suppose there are three cards labeled with values 1, 2, and 3, and two of them are chosen at random (without replacement). Let the random variable $X$ be the value on the first card chosen, and let ...
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26 views

Family-wise error of dependent tests?

Say you have a drug of which you want to test wether it increases the number of immune cells in your blood. You divide your sample in two groups where one group receives the treatment and the other ...
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2answers
68 views

Can non-paired data have dependency?

I have two vectors of data of different sample size. Both are the same experiment, but executed in a different environment. Since the sample sizes are different and they don't share any subject, is it ...
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1answer
50 views

Dependency between two independent experiments pointless?

Let's say I have two experiments of the same type, where I measure something x times in one location and y times in another location, is there any point in looking for a dependency in values between ...
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1answer
155 views

Total probability theorem with normal probability density functions

Let $X$ and $Y$ be two continuous random variables. Suppose that: $X$ has normal pdf with mean mu_1 and variance $\sigma_1^2$ $Y|X$ has normal pdf with mean $mu_2=(a+b*X)$ and variance $\sigma_2^2$; ...
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69 views

What is the distribution of an outer product of random values mod P?

I haven't been able to answer this daunting question for days now and I am not able to find the right resource for it, so maybe someone here might help me out. Consider an outer product of two ...
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80 views

dependent samples & correction for multiple testing

I have situation in which I compare many genomic regions between two or more cell lines (CL). Each region is covered by n probes measuring the level of methylation (continuous variable). The coverage ...
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42 views

Order statistics without independence assumption

I want to derive an expression for the cdf of the min of a set of $k$ random variables $X_i$ (with same cdf $f_i(x)$) which are identically distributed but not necessarily independent. So far, I got ...
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1answer
123 views

Understanding tail dependence coefficients

How can I analyze the $\lambda_U$ and $\lambda_L$ results (estimated by non-parametric method)? What does higher or lower coefficients mean? Does $\lambda_U = 0.5$ mean there's some kind of linear ...
2
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0answers
57 views

Naive Bayes with invalid independence assumption

I'm trying to understand the effects of adding non-conditionally independent features to a naive Bayes classifier. Let's say I have the features vector $X = [x_1,x_2,x_3,x_4]$ and that for each value ...
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1answer
456 views

Testing for differences between a sample and a subsample

For reasons I won't go into, I want to test for group differences between an entire sample A ($n=65$) and a subsample B ($n=45$). All of the variables I want use for mean comparisons are continuous. ...
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2answers
311 views

Regression with correlated explanatory variables

I have variables of the following kind (coded in R): ...
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1answer
76 views

Goodness of fit for possibly dependent data

My data consists of about a hundred animal visits to three different feeding zones, and I'm trying to determine if there was a preference for one zone over the others. Each animal visits between one ...
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26 views

Transformation of Martingale Differencce

We know non-zero measurable transformation of a dependent sequence is dependent. I want to ask if a non-zero measurable transformation of a sequence which is not martingale difference is not ...