Might help to distinguish (uncertainty of) actualities from potentialities (CS Peirce vocabulary) as for instance actualities are (must be) discrete and finite (e.g. non-random parameters driving a random phenomena in _this_ universe) while potentialities must be any logically allowed possibly continuous quantity (exactly).

I would agree that statistical problems and estimates should be about (uncertainty of) actualities, but the real importance of vocabulary is that the community can agree on it. Hopefully people might agree that there should be such a distinction (actualities from potentialities) if only to avoid a lot of confusion.

Yes, this is an example I used in my public lecture in Australia (and that my daughter also learned in secondary school). However, this is not a statistical problem, in my opinion, rather a stochastic approximation to this unique and known number.

]]>When I am using simulation, or Monte Carlo methods, I rely on the law of large numbers and the stabilisation of frequencies. So Monte Carlo is a ‘frequentist” method, granted, but it is not connected with a statistical issue, which is why I find the debate “frequentist vs. Bayesian” rather vacuous here…

]]>Well, we can “estimate” pi by generating data in a square and counting the proportion of points that fall inside the circle inside the square http://yichuanshen.de/blog/2012/01/06/monte-carlo-pi/ We could do this in a Bayesian way as well by putting a prior on pi. The Binomial likelihood here is defined for every value of pi (which is not true in Larry’s example), even though there is only one true value.

]]>I don’t know why you keep calling it “known.”

Known means: you know it. But you don’t know it!

To estimate the normalizing constant of a posterior from

simulated values, what method do you use?

Frequentist or Bayes? If bayes, how do you do it?

By the way, credit where credit is due: the example is

due to Ed!

Best wishes

Larry

Indeed, I think that, in both cases, we should not use the wording *estimate*, but instead the wording *approximation*.

Hi, Larry! The constant c is known in this case, which makes all the difference with an unknown parameter driving the distribution of an observed sample. For instance, I cannot make observations about c, I cannot build a likelihood on c, &tc… At a more subtle level, we should get back to what Persi suggested as Bayesian numerical analysis (in the 1992 Purdue Symposium?).

]]>You never know what the next strangest thing on the internet can be..! As a Bayesian I do not say that everything is random, rather that using a probability distribution (or a measure) is the optimal way to represent my uncertainty about things, like non-random parameters driving a random phenomena. In the current case, my prior distribution is a Dirac mass.

]]>If you only consider the 100th digit of π, I would indeed say it is a similar issue: using a series representation of π eventually leads to this 100th digit. And there is no clear “observation” I can gather about this 100th digit… If now you are interested in the distribution of the digits of , this is another issue: I have observations and I can put a prior of the distribution. (Not that it will answer the on-going mathematical question about the randomness of the digits of π, obviously!)

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