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First method: The principle You can always transform one distribution to another through a transformation of the independent variable, so we get if $p:\mathbb{R}^N\to(\mathbb{R}^+\bigcup\{0\})^N$ is a probability density function of $N$ variables and we transform the independent variables $\mathbb{R}^N\to\mathbb{R}^N$ by some differentiable transformation ...


Several things spring to mind here. The "brain dead" way to estimate things would be to take the mean of all the samples and divide by the standard deviation. But as you point out, that gives you a rather large standard deviation and it does not take advantage of everything you know. In general, such an approach would suffer very badly from aliasing: if you ...

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