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Isn't it just like sampling in general? You ideally want to sample IID from the target distribution, so that sample mean looks like population mean. If you don't sample IID, you have a sampling bias and you have to correct for that, which costs you samples in the sense that only a subset of your samples are independent (because autocorrelation decays).


Compared to the difficulty of getting confidence intervals for quantiles in the frequentist setting, Bayes handles this most elegantly. It is easiest to do by taking a few thousand draws of the bivariate posterior distribution of $\mu$ and $\sigma$, computing the quantile, e.g., $\mu + \sigma \Phi^{-1}(q)$, and analyzing the distribution of these derived ...


I stumbled on this while looking for an answer to my own misunderstanding of the step size algorithm, so your mileage my vary on this answer... With that said, the idea is that the slice sampler is there because we can't solve the dynamical system exactly, but with a discrete system. Because it's going to have an error, we use the slice sampler to compensate ...

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