Sentence examples for chance function from inspiring English sources

This measure is not the standard Lebesgue measure, but rather a measure defined by the chance function in question.

The expertise of the chance function in the original Principal Principle is unconditional rational initial credences should simply adopt values equal to the chances.

That is, where C is the agent's credence function, and P is the chance function, and the agent has no inadmissible evidence, it should be that C(A | H ∧ T) = P(A | T).

Other authors claim priority for other "oughts": Mason (2013) favors the probability function that is most reasonable for the agent to adopt in response to her evidence, given her epistemic limitations, while Oddie and Menzies (1992) favor the objective chance function as a measure of objective rightness.

As Hájek notes, if \(c\) is defined on propositions concerning ethical matters, or mathematical matters, or aesthetic matters, or facts about the current time or the agent's current location, it is not clear that it could possibly be the chance function of any world, since chances cannot attach to these sorts of proposition.

In general, assuming the agent has no inadmissible evidence, the rational credence in A given E is the expected value, given E, of the chance of A given H ∧ T. That is, where C is the agent's credence function, and P is the chance function, it should be the sum across all possible combinations of H and T of C(H ∧ T | E P(A | H ∧ T).

Objection 1: Not all probabilistic credence functions could be chance functions.

In particular, the probability functions that feature in radioactive decay and quantum mechanics have some claim to being chance functions.

One way of doing this would be to argue that proper chance functions are such that sequences with the same frequencies should have the same measure.

In particular, he applies it to views according to which chances vary with time, even though Milne makes no explicit reference to any temporal parameter on the chance functions he uses in his argument.

But such a principle seems open to the objection that two different but close chance functions could easily result in the same pattern of outcomes, particularly if there were relatively few relevant outcomes.