more random than random!

A revealing question on X validated the past week was asking for a random generator that is “more random” than the outcome of a specific random generator, à la Oliver Twist:The question is revealing of a quite common misunderstanding of the nature of random variables (as deterministic measurable transforms of a fundamental alea) and of their maybe paradoxical ability to enjoy stability or predictable properties. And much less that it relates to the long-lasting debate about the very [elusive] nature of randomness. The title of the question is equally striking: “Random numbers without pre-specified distribution” which could be given some modicum of meaning in a non-parametric setting, still depending on the choices made at the different levels of the model…

normal variates in Metropolis step

A definitely puzzled participant on X validated, confusing the Normal variate or variable used in the random walk Metropolis-Hastings step with its Normal density… It took some cumulated efforts to point out the distinction. Especially as the originator of the question had a rather strong a priori about his or her background:

“I take issue with your assumption that advice on the Metropolis Algorithm is useless to me because of my ignorance of variates. I am currently taking an experimental course on Bayesian data inference and I’m enjoying it very much, i believe i have a relatively good understanding of the algorithm, but i was unclear about this specific.”

despite pondering the meaning of the call to rnorm(1)… I will keep this question in store to use in class when I teach Metropolis-Hastings in a couple of weeks.

all those ε’s…

A revealing [and interesting] question on X validated about ε’s… The question was about the apparent contradiction in writing Normal random variates as the sum of their mean and of a random noise ε in the context of the bivariate Normal variate (x,y), since using the marginal x conditional decomposition led to two different sets of ε’s. Which did not seem to agree. I replied about these ε’s having to live in different σ-algebras, but this reminded me of some paradoxes found in fiducial analysis through this incautious manipulation of ε’s…