Archive for random variates

twenty-four to nil

Posted in Books, Kids, Statistics with tags , , , on September 16, 2022 by xi'an

Another puzzling question on X validated, where the expectation of a random sum of deterministic vectors is to be computed. (That is, the sum involves a random number of terms.) Without enough detail to understand why this proves a difficulty, given that each deterministic vector is to be invoked at most once. Nonetheless, my (straightforward) answer there

Y_1\underbrace{\mathbb P(\tau\ge 1)}_{=1}+Y_2\mathbb P(\tau\ge 2)+\cdots+Y_N\underbrace{\mathbb P(\tau=N)}_{=0}

proved much more popular (in terms of votes) that many of my much more involved answers there. Possibly because both question and answer are straightforward.

more random than random!

Posted in Books, Kids, pictures, Statistics with tags , , , , , , on December 8, 2017 by xi'an

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

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , , , on November 14, 2017 by xi'an

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…

Posted in Kids, pictures, Statistics, University life with tags , , , , , , on October 25, 2017 by xi'an

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…

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