On 2/5/2025 5:53 AM, John Clark wrote:
On Wed, Feb 5, 2025 at 5:48 AM Bruce Kellett <bhkellet...@gmail.com>
wrote:
/> The sequence of N repetitions gives you an estimate of the
probability distribution/.
*OK, but even if N=1, such as when I flip a coin just once, I can
still obtain a probability of it coming up headsthat makes sense.*
But Quentin is asserting that if it comes up heads then the probability
of heads was 1 and the probability of tails was 0. Thus completely
misapplying the concept of probability.
*And the long-run relative frequency of an event occurring in repeated
trials is just one way to define probability, you could also say it's
the ratio of all possible favorable outcomes to all possible outcomes,
or as a degree of belief based on available evidence that can be
updated when new evidence becomes available.*
That's right. It's a common confusion that probability is a */thing/*
and we must correctly grasp what it is. But probability is more like
energy or value. It means different things that only have in common
that they obey the mathematical rules of probability. And that fact is
the strength of the theory. Relative frequency in one context can be
interpreted as rational degree of belief in a another. It can be
inferred from symmetries and applied to bets.
Brent
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