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Intuition has to be trained through arduous application to become other than misleading. There are too many implied questions here for a single post. However, addressing those here does provide a series of links summarizing some of the properties of the gamma distribution, so the implied questions posited may have some value to the potential reader. Q1 Chi-...


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One of the ways to compute PCA is by using eigen-decomposition of the covariance matrix of the data matrix $\underset{N \times n}{X}$, which is $\underset{n\times n}{X^TX}$ if $X$ is mean-centralized. Since we generally have $n \ll N$, it's computationally much faster to compute the eigenvectors of the covariance matrix $X^TX$. It outputs $n$ eigenvalues and ...


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I guess there are several questions in your posts. So I'll make several small answers. You can't say that $Var(F(X)+F(−X)) = Var(2F(X))$. You must be carefull not two mix distribution and random variables: $F(X)$ and $F(-X)$ may have the same distribution but they are still two distinct random variables: they won't take the same values at the same times, ...


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To add to David Robinson's answer, the initial $\alpha$ and $\beta$ parameters of the Beta distribution can be computed from a desired mean ($\mu$) and standard deviation ($\sigma$) using the following formulae: $\alpha = \frac{-\mu(\mu^2-\mu+\sigma^2)}{\sigma^2}$ $\beta = \frac{(\mu-1)(\mu^2-\mu+\sigma^2)}{\sigma^2}$ For example, if the desired mean = 0.27 ...


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It is rather odd that you would need to explain the concept of unbiasedness to a lay audience at all. If they are not already familiar with the idea of an "expected value", and some other general ideas in sampling theory, then what exactly is the necessity in distinguishing a biased from an unbiased estimator? Will you also explain consistency of ...


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LDA is a special case of a n̶a̶i̶v̶e̶ Bayes classifier. It is assuming Gaussian distributions For different classes, the distributions have the same variance (the same covariance matrix for their distribution with respect to the variables $X$). Gaussian Naive Bayes classifier is a special case of LDA If you consider the naive Bayes classifier with the ...


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Here's my intuition: The LDA classifier assumes that across all classes, the $p$ predictors $\boldsymbol{X}_k$ (for $k=1, \dots,p$) all share some covariance matrix ${\boldsymbol \Sigma}$, but may have different means $\boldsymbol{\mu}_k$. Thus, if you define the alternate set of predictors $\boldsymbol{Z}$ to be $p$ independent normal random variables with ...


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The term 'sufficient statistic' is pretty theoretical (i.e., it would not typically be taught in applied stats classes) and I am not sure you are hoping for a theoretical answer. But, what you have above (about normal and binomial) is a bit off. Although it is a theoretical term, the general idea of it is not that complicated (actually way simpler probably ...


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Actually, without some further assumptions on the form of the transfer function in the Wold representation, I don't think it is actually true that it can always be well approximated by a ratio of finite-order polynomials. There are classes of time-series models for covariance-stationary processes where this approximation is not considered adequate --- e.g., ...


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