One — LessWrong

The public dataset is approximately symmetrical, so it is very likely that the distribution of the Bernoulli rate is also symmetrical (probability at p is equal to probability at 1-p). Let the probabilities of getting k Rs over all 5 trials for k=0...5 be $(a, b, c, c, b, a)$ . Then, from the public dataset, we have $a + b / 5 \approx 0.252854, 4 b / 5 + 2 c / 5 \approx 0.166231, 6 c / 5 \approx 0.161832$ . These have standard deviation $\approx 0.0004,$ which is negligible, so we can treat these as linear equations. Solving, we get $a = 0.224781, b = 0.140359, c = 0.13486$ , and we can then solve for the marginal frequencies $\frac{b / 5}{a + b / 5} = 0.111020, \frac{2 c / 5}{4 b / 5 + 2 c / 5} = 0.324512,$ etc.

Not sure if this (experiment set?) is a good test of priors, since I got an exact answer without having to consider priors, other than

One4mo*

Experiment: Test your priors on Bernoulli processes.

Answer:

[0.111020, 0.324512, 0.5, 0.675488, 0.888980]

I will provide my solution when the market is resolved.

Replying toExperiment: Test your priors on Bernoulli processes.

One4mo

Experiment: Test your priors on Bernoulli processes.

No; your distribution gives probabilities [0.253247, 0.168831, 0.155844, 0.168831, 0.253247] for the number of Rs in the first four trials. This predicts that the number of experiments with two Rs is binomially (i.e. approximately normally) distributed with mean ~155844 and standard deviation ~363, but the actual number is 161832, around 16 standard deviations away from the mean.

Replying toThe Rising Sea

One5mo

The Rising Sea

Was this written by AI? The self-altering of consistency makes no sense and I can't think of a reason that just discovering an inconsistency in the universe would cause a vacuum decay. Even if the universe was a simulation, discovering a bug doesn't mean exploiting it, though maybe the simulators would end the simulation (which wouldn't create any propagation, it'd just end it at once.)