## Posts

Out-of-body reasoning (OOBR) 2021-01-09T16:10:34.665Z
A short talk on SB and friends 2020-11-29T21:07:40.653Z

Comment by jon-zero on Beautiful Probability · 2021-01-28T10:17:05.046Z · LW · GW

No-one's going to read this reply, as I'm 13 years too late, but -- oh dear me -- MacKay makes hard work of the medical example.

A straightforward Frequentist solution follows.  There are 4 positive cases among the 30 subjects in class A and 10 subjects in class B.  We'll believe that treatment A is better if it's very unlikely that, were the treatments identical, there would be so relatively few positive cases among the A's.  There are 91390 ways of picking 4 from 40, with only 3810 ~= 4.17% having 0 or 1 in class A.  So, unless we were unlucky (4.17% chance) with the data, we can conclude that treatment A is better.

Comment by jon-zero on What's the big deal about Bayes' Theorem? · 2021-01-28T08:44:02.899Z · LW · GW

You might find this reference useful: Bayesian Epistemology.

Personal view: if you think you're capable of forming reasonable priors, you're "probably" a Bayesian.

Comment by jon-zero on Dissolving Sleeping Beauty · 2021-01-24T22:13:48.255Z · LW · GW

I think my argument is more stark: I'm saying that there are fundamentally two types of credence, (A) and (B) in the comment above, and only one of them is relevant to rational decision-making.

I agree with intuition being the thing that separates Halfers and Thirders, but I'm saying that they're fighting over irrelevant Type (B) credence -- "inner" credence in the OOBR post I linked to.

Comment by jon-zero on Dissolving Sleeping Beauty · 2021-01-24T17:56:31.668Z · LW · GW

I've added the Sleeping Beauty tag for you.

Since the rational agent in SBP has full knowledge of the experimental set-up, she has no need of any subjective credence: any bet she takes can be made solely on the facts of the experiment.

Paradoxes like SBP seem to evaporate if you distinguish two types of credence: (A) credence for the experiment that the agent is a part of, vs. (B) credence for the outcomes encountered within the experiment.  Type (A) credence for the experimental protocol is all you need for decision-making.  Type (B) credence is implied by the experimental protocol and adds nothing to the agent's decision-making capabilities, so you're free to define that however you wish.

See https://www.lesswrong.com/posts/8ecgHXWQBiuY97B2X/ for more detail.

Comment by jon-zero on A Simplified Version of Perspective Solution to the Sleeping Beauty Problem · 2021-01-12T22:42:23.544Z · LW · GW

Thank you for the quick reply.

I would agree that having a clear decision objective is important.  I would go further: without an objective, why should anyone care how the agent (who, by definition, takes action) feels about their circumstances?  I note in your final sentence that you see things differently, but I don't have a killer argument to the contrary.

I can see the need for subjective probability, but only in model selection.  Thereafter, you're working to find a strategy maximising the expected value of an objective function.  I recorded my thoughts here.

Comment by jon-zero on A Simplified Version of Perspective Solution to the Sleeping Beauty Problem · 2021-01-12T09:24:06.935Z · LW · GW

Being new to this, I have no problem asking naïve questions, so: why does Sleeping Beauty need to have any "credence" at all?  She's armed with the facts of the experiment and can make decisions based solely on those; why does anyone suppose that she forms some "credence" as a proxy for the facts?

Just like to add that I found your website very clear and, in parts, quite compelling.  Thank you.