# Tagged Questions

Events (or random variables) are independent when information on some of them tells you nothing about the probability of occurrence (/ distribution) of the others. Please DO NOT use this tag for independent variable use [predictor] instead.

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### Why is dependence a problem?

I'm interested in why dependent observations are a problem in statistics. Let's say you want to know if there is a difference in mean exam scores between two schools. You collect 50 observations in ...
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### test independence between quantitative and categorical predictors

Is there any universal statistical test to test the independence between quantitative and categorical predictors? For two quantitative variables I know I could use correlation tests, and for two ...
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### Does the central limit theorem hold for the prediction error over different samples?

Given an (infinite) data population from which you repeatedly draw samples of a fixed size. On each sample you learn a classifier which you then evaluate by computing the prediction error on a large ...
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### Implications and interpretation of conditional independence assumption

I am currently studying Treatment Effect Analysis and I am reading about the Conditional Independence Assumption (CIA): \begin{align} (Y_1,Y_0)\perp D|X \end{align} So the outcomes are independent of ...
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### Testing independence hypothesis in logistic regression

One of the primary hypotheses in logistic regression theory is the independence of observations. Once the model is fitted to the data (using likelihood maximization procedure for example), I am ...
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### Parallelization of an iterative model

What I have: An iterative process based on the application of a very simple algebra to represent a rate, with total dependence among any iteration and its predecessor (one input parameter for (n)th ...
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### Independence of samples

Recently I started doing verification on daily temperature forecasts by different providers. I calculated the absolute forecast errors for each of the providers, and I am planning on performing ANOVA ...
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### How to prove independentness of marginal/conditional (?) posterior distributions?

This is a question about exercises 4.2 and 4.3 of Jim Albert’s “Bayesian Comptutation With R” (p. 82). Note that while this might be homework, in my case it is not. We are to prove that, given two ...
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### Optimal approach to independence check

I want to see if a vendor is biased against one type of vehicle compared to another. I have two categories of vehicles: OWN and T/C. The vendor sells fuel to these vehicles. The process is as ...