Sunrise problem

The sunrise problem illustrates the difficulty of using probability theory when evaluating the plausibility of statements or beliefs.

The sunrise problem was first introduced publicly in 1763 by Richard Price in his famous coverage of Thomas Bayes' foundational work in Bayesianism.

Laplace inferred the number of days by saying that the universe was created about 6000 years ago, based on a young-earth creationist reading of the Bible.

To find the conditional probability distribution of p given the data, one uses Bayes' theorem, which some call the Bayes–Laplace rule.

However, Laplace recognized this to be a misapplication of the rule of succession through not taking into account all the prior information available immediately after deriving the result: But this number [the probability of the sun coming up tomorrow] is far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at present moment can arrest the course of it.E.T.

[4] A reference class problem arises: the plausibility inferred will depend on whether we take the past experience of one person, of humanity, or of the earth.