# Tagged Questions

Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies.

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### Correlation and Causation. When can we believe correlation (reasonably, at least) imply causation

We always hear, when reading on correlation, that "correlation does not imply causation." Still, I have never seen any source that tries to answer the question of when can we reasonably conclude a ...
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### randomness in nature [closed]

What is the explanation of the apparent randomness of high-level phenomena in nature? For example the distribution of females vs. males in a population (I am referring to randomness in terms of the ...
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### Conjugate prior of the Dirichlet distribution?

What is the conjugate prior distribution of the Dirichlet distribution?
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### Error to sum of Euler phi-functions

The number theory identity $\phi(1) + \phi(2) + \dots + \phi(n) \approx \frac{3n^2}{\pi^2}$ can be interpreted as counting relatively prime pairs of numbers $0 \leq \{ x,y \} \leq n$ . Has anyone ...
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### Concentration inequalities for the maximum of the rescaled/normalized sum of iid random variables

I am interested in concentration inequalities for the maximum of the rescaled/normalized sum of iid random variables. Let $X_1,..., X_n$ be i.i.d random variables, $S_n$ their centered sum and $M_n$ ...
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### Distance metric between two sample distributions (histograms)

Context: I want to compare the sample probability distributions (PDFs) of two datasets (generated from a dynamical system). These datasets depend on a set of parameters, and I want a concise way to ...
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Let $X_1,X_2,\ldots,X_n$ be i.i.d. random variables in $\mathbb{R}$ with common cumulative distribution function (CDF) $F(x)$. The empirical approximation to $F(x)$ is defined as follows: $$\hat{F}... 0answers 193 views ### How far away is the maximum of n i.i.d. chi-squared random variables from the rest of the sequence as n gets large? Suppose that I have a sequence of n i.i.d. chi-squared random variables with k degrees of freedom X_1, X_2, \ldots, X_n, and denote X_{\max}=\max(X_1, X_2, \ldots, X_n). Let k be increasing ... 1answer 205 views ### Mean -> Frechet mean, Standard deviation ->? Given a finite set A of points of a metric space (X, d), I would like to find its mean. A Frechet mean seems appropriate here: \arg \min_{x \in X} \sum_{a \in A} d(x, a)^2. I also would like ... 1answer 137 views ### Estimating the variance of error in empirical approximation to a distribution Let X_1,X_2,\ldots,X_n be i.i.d. random variables in \mathbb{R} with common cumulative distribution function (CDF) F(x). The empirical approximation to F(x) is defined as follows:$$\hat{F}...
Let $X_1,X_2,\ldots,X_n$ be a sequence of $n$ i.i.d. chi-squared random variables with $k$ degrees of freedom, and denote by $X_\max$ the maximum of this sequence. Furthermore, let $k=\omega(1)$ ...