Sunrise problem
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The sunrise problem can be expressed as follows: "What is the probability that the sun will rise tomorrow?" The sunrise problem illustrates the difficulty of using probability theory when evaluating the plausibility of statements or beliefs. According to the Bayesian interpretation of probability, probability theory can be used to evaluate the plausibility of the statement, "The sun will rise tomorrow." The sunrise problem was first introduced publicly in 1763 by Richard Price in his famous coverage of Thomas Bayes' foundational work in Bayesianism.
The sunrise problem can be expressed as follows: "What is the probability that the sun will rise tomorrow?" The sunrise problem illustrates the difficulty of using probability theory when evaluating the plausibility of statements or beliefs. According to the Bayesian interpretation of probability, probability theory can be used to evaluate the plausibility of the statement, "The sun will rise tomorrow." The sunrise problem was first introduced publicly in 1763 by Richard Price in his famous coverage of Thomas Bayes' foundational work in Bayesianism. \Pr(\text{Sun rises tomorrow} \mid \text{It has risen } k \text{ times previously}) = \frac{\int_0^1 p^{k+1}\,dp}{\int_0^1 p^k \,dp}= \frac{k+1}{k+2}. By this formula, if one has observed the sun rising 10000 times previously, the probability it rises the next day is 10001/10002 \approx 0.99990002 . Expressed as a percentage, this is approximately a 99.990002 \% chance. 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: E.T. Jaynes noted that Laplace's warning had gone unheeded by workers in the field. 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. A consequence is that each referent would hold different plausibility of the statement. In Bayesianism, any probability is a conditional probability given what one knows. That varies from one person to another.
References
Further reading
Howie, David. (2002). Interpreting probability: controversies and developments in the early twentieth century. Cambridge University Press. pp. 24.
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