Sunrise Problem - One Day, Many Suns

One Day, Many Suns

Alternatively, one could say that a sun is selected from all the possible stars every day, being the star that one sees in the morning. The plausibility of the "sun will rise tomorrow" (i.e., the probability of that being true) will then be the proportion of stars that do not "die", e.g., by becoming novae, and so failing to "rise" on their planets (those that still exist, irrespective of the probability that there may then be none, or that there may then be no observers).

One faces a similar reference class problem: which sample of stars should one use. All the stars? The stars with the same age as the sun? The same size?

Mankind's knowledge of star formations will naturally lead one to select the stars of same age and size, and so on, to resolve this problem. In other cases, one's lack of knowledge of the underlying random process then makes the use of Bayesian reasoning less useful. Less accurate, if the knowledge of the possibilities is very unstructured, thereby necessarily having more nearly uniform prior probabilities (by the principle of indifference). Less certain too, if there are effectively few subjective prior observations, and thereby a more nearly minimal total of pseudocounts, giving fewer effective observations, and so a greater estimated variance in expected value, and probably a less accurate estimate of that value.