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cousin_it comments on Bayesian Flame - Less Wrong
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http://www.xuru.org/st/DS.asp
50% confidence interval for mean: 4.07 to 6.46, stddev: 2.15 to 4.74
90% confidence interval for mean: 0.98 to 9.55, stddev: 1.46 to 11.20
If there's only one sample, the calculation fails due to division by n-1, so the frequentist says "no answer". The Bayesian says the same if he used the improper prior Cyan mentioned.
Hm, should I understand it that the frequentist assumes normal distribution of the mean value with peak at the estimated 5.26?
If so, then frequentism = bayes + flat prior.
Improper priors are however quite tricky, they may lead to paradoxes such as the two-envelope paradox.
The prior for variance that matches the frequentist conclusion isn't flat. And even if it were, a flat prior for variance implies a non-flat prior for standard deviation and vice versa. :-)
Of course, I meant flat distribution of the mean. The variance cannot be negative at least.
Using the flat improper prior I was talking about before, when there's only one data point the posterior distribution is improper, so the Bayesian answer is the same as the frequentist's.