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Yeah there was a glitch during publishing and now Cloudflare is breaking my access to the database to fix. I'll work on it later today.Dale said:@Greg Bernhardt it looks like you are still listed as the author here in the forums even though it is fixed on the Insights page
Yes, that was a problem, but there has been some well recognized work on that by Harold Jeffreys. He came up with a non-informative prior which is invariant under a coordinate transformation. But even with Jeffreys’ prior you can still have cases where it cannot be normalized.atyy said:I think another problem with non-informative priors is that it is not well-defined for continuous variables, since a smooth change of variables may take a "non-informative" prior into an "informative" prior.
atyy said:I think another problem with non-informative priors is that it is not well-defined for continuous variables, since a smooth change of variables may take a "non-informative" prior into an "informative" prior.
One of the nice features of Bayesian methods that I did not address is related to this.Stephen Tashi said:Under a smooth change of variables in frequentist statistics, important things may not go smoothly.
If you have random samples of the posterior distribution of the variance then the square root of those samples are random samples of the posterior distribution of the standard deviation. Similarly with any function of the posterior samples.Stephen Tashi said:if f(x1,x2,...xn) is a formula for an unbiased estimate of the variance of a random variable, then f(x1,x2,...xn) need not be an unbiased estimator for the standard deviation of the same random variable.
That seems like a good use of the technique. Most of my papers with a Bayesian analysis also had a frequentist analysis. But recently I have had a couple that just went pure Bayesian.atyy said:This paper uses both Frequentist and Bayesian error analysis - IIRC they use 2 different priors: https://arxiv.org/abs/astro-ph/9812133
I must admit that I felt a little embarrassed to write so much philosophy. But in the end I went ahead and did it anyway.atyy said:I like the huge amount of philosophy in these posts despite @Dale's aversion to interpretive issues![]()
Yes, I thought it was a very good video. Well done and largely accurate.Swamp Thing said:It would be great if you could take a look at it and share your thoughts:
I tried to post a comment on the article, but it said "You must be logged in to post a comment". I was already logged in, but I clicked on the link anyway, and it just took me back to the article.Dale said:
This is not a pure calculation. Earlier I had defined ##X\in[0.49,0.51]## as being practically equivalent to a fair coin. This is a concept known as a ROPE (region of practical equivalence). So in this case a coin that is unfair by less than 0.01 is practically fair. That is a judgement call.haruspex said:We could calculate P(X∈[0,1]|E)=1 and argue any observed frequency is fair.