Re: Is it possible for a probability to be unknown?


Randy Poe wrote:
tjb wrote:
Randy Poe <poespam-trap@xxxxxxxxx> wrote:
Bayesian probability is an estimate of our degree of belief in
different outcomes. A Bayesian would say you can assign
probabilities to events about which you have no knowledge
whatsoever, such as the existence of life on Mars.

Ah. I take it then that Bayesian probability would put the probability at
50% in the example in the original post in this thread.

In Bayesian language, the initial belief is called the "a priori"
or "prior" distribution. There isn't one "Bayesian probability".
I think you could make a case for distributions with p(red) = 50%,
p(red) = 100%, or p(red) = any nonzero value.

This may well be what I'm thinking of. Well, maybe I should give some
context by stating why I made this thread in the first place.

Basically, a book I'm reading quotes a definition of agnosticism (lack of
belief in God, but also lack of disbelief; i.e., fence-sitting), and the
book suggests that this quoted definition implies that God's existence and
non-existence are equiprobable. However, it's not actually stated within
the quotation that they are equiprobable, and I couldn't quite determine
how it was *implied* within it either.

You are correct that the author has made a mistake, thinking
that two possibilities implies two equally-likely possibilities.

He doesn't mention what the book is, but a (wild) guess might be that
it is "The Probability of God" by Stephen Unwin. This book explicitly
brings a Bayesian approach to the question of religious belief. The
book (though not the cover - curse those marketing types) is fairly
modest in that its main point seems to be that Bayesian methods have
the potential to clarify a person's subjective beliefs and it doesn't
claim to have once and for all settled the existence (or nonexistence)
of God. His conclusion is that it is more likely than not that God
exists, though like a true Bayesian he acknowledges that other people
with other prior beliefs might come to different conclusions. At once
place he writes (since you need a prior probability to get off the
ground) "Bayesian analysts would generally agree that the choice of
prior probabilties must be considered and justified on a case by case
basis ... Here, I think that the expression of complete ignorance [of
whether or not God exists] is a good case for the 50-50 argument" (pg
57). In the next couple of pages he tries to give some argumentation to
back this up, so he is not simply unaware of the issue or naively
assuming that uncertainty implies probability 50%. Somewhat humorously,
he has an appendix for setting up an Excel spread*** to play around
with his calculations in which the initial prior probability is a
parameter that anyone could modify if they see fit. If this isn't the
book, I would be interested in hearing from the OP what it was.

I think a Bayesian agnostic could again put the a priori p(God)
as any value between 0 and 100%, exclusive. (If he/she chose
0 or 100%, that would indicate firm atheism or firm theism).

My theory was that by implying that there is no evidence either way, the
quoted definition also implied that the probability was 50-50 (with the
author using the logic that if there is no evidence, it is 50-50). I
wonder if the author was using Bayesian probability then. Hmm.

I think the author is following a common misconception about
probability.

- Randy

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