129k views

### What is the difference between a consistent estimator and an unbiased estimator?

I'm really surprised that nobody appears to have asked this already... When discussing estimators, two terms frequently used are "consistent" and "unbiased". My question is simple: what's the ...
48k views

### Why is sample standard deviation a biased estimator of $\sigma$?

According to the Wikipedia article on unbiased estimation of standard deviation the sample SD $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$ is a biased estimator of the SD of the ...
46k views

### What is the difference between ZCA whitening and PCA whitening?

I am confused about ZCA whitening and normal whitening (which is obtained by dividing principal components by the square roots of PCA eigenvalues). As far as I know, \mathbf x_\mathrm{ZCAwhite} = \...
3k views

### Is it true that Bayesian methods don't overfit?

Is it true that Bayesian methods don't overfit? (I saw some papers and tutorials making this claim) For example, if we apply a Gaussian Process to MNIST (handwritten digit classification), but only ...
4k views

### How can I find the standard deviation of the sample standard deviation from a normal distribution?

Forgive me if I've missed something rather obvious. I'm a physicist with what is essentially a (histogram) distribution centered about a mean value that approximates to a Normal distribution. The ...
1k views

### Why does this excerpt say that unbiased estimation of standard deviation usually isn't relevant?

I was reading on the computation of the unbiased estimation of standard deviation and the source I read stated (...) except in some important situations, the task has little relevance to ...
294 views

### Square-root transform dependent variable to gaussian for ML problem

I have a ML problem with dependent y-variables that are skew-symmetric to the right. I perform the transformation $\sqrt y$ on my dependent variable before running the ML algorithm, and then make a ...
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### Precision of bone density measurement

I just did a precision study scanning 30 patients twice. The calculator presented the least significant change score, but how do I calculate my precision? For instance, the ISCD states that the ...
Assume you have a random variable $X$ for which you want to compute a $1/4$-approximate $\sigma'$ of $\sigma = \sqrt{\operatorname{Var}(X)}$ (i.e. $|\sigma - \sigma'| \leq \sigma/4$). You can only get ...