Re: practical reasoning and strong SSA

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 1 Jun 1999 23:18:52 -0700

On Tue, Jun 01, 1999 at 10:07:05PM -0700, hal.domain.name.hidden wrote:
> I don't follow where the dependence on SSSA comes from. This is the
> assumption that each observer-moment should be considered as a random
> selection from all observer-moments in the universe (broadly defined).
>
> Your example would seem to be classical Bayesian reasoning. A priori
> you don't know whether the sixth digit of pi is a 9, so you give that
> 1/10 probability. After seeing Mathematica's output, you estimate the
> probability that it would say it is a 9 when the actual digit is not a 9
> (i.e. make a mistake), which is very small. You feed that into the Bayes
> formula and end up with a strong probability that the sixth digit is 9.
>
> Are you saying that Bayesian analysis depends on the Strong SSA? Could
> you elaborate on this?

Bayesian analysis in general does not depend on the Strong SSA, but any
Bayesian analysis where you try to compute P(X | I observe Y) does because
you need the Strong SSA to compute P(I observe Y | X) and P(I observe Y |
not X).

My example is one of classical Bayesian reasoning, but it is slightly
different from the way you put it, because I don't have direct knowledge
that Mathematica outputs a 9 for the sixth digit of Pi. I do know that I
am reading "N[Pi]=3.14159", and Strong SSA is needed to derive the
probability that I am reading "N[Pi]=3.14159" if Pi doesn't begin with
3.14159.
Received on Tue Jun 01 1999 - 23:22:36 PDT