[ExI] kepler study says 8.8e9 earthlike planets

[Anders Sandberg]

On 2013-11-09 11:24, Eugen Leitl wrote:
> On Wed, Nov 06, 2013 at 11:34:00PM +0000, Anders Sandberg wrote:
>> Actually, it is. It is just a single data point, but it can skew 
>> things surprisingly strongly: 
>> http://www.nickbostrom.com/papers/anthropicshadow.pdf 
> Why are you using probability in a perfectly biased case
> of one sample? It isn't applicable. The first sample only
> gives you the information that it's possible. Only the
> second unbiased sample gives you a lot of information.
>
> The first sample is almost pefectly useless.

The "almost" is the relevant thing here.

What is the probability of an existential threat wiping out humanity 
this century? It makes sense to talk about this probability, yet there 
is *no* data point for it. (And if there were ever one data point, there 
would never be another one - frequentism fails. )

One can reason under conditions of high uncertainty, and that does 
include having no or one data points. Sure, the dispersion of your 
probability estimates is going to be huge, but one can still apply 
rigorous thinking.

If I flip a coin and get heads, I have very little evidence for how 
biased the coin is. I know the probability of heads cannot be 0, but it 
could be that it actually is 10^-100 and I was lucky. What I can do is 
estimate a posterior probability distribution (in this case it ends up a 
triangular beta distribution) and use that as my best guess. Obviously 
getting more data will quickly improve the estimate, but that is not 
always possible. Saying "I don't know" and refusing to reason about 
anything dependent on the probability might not be on the table, nor 
rational - I actually do know a little.

>> Actually, they know the probability is nonzero. That is in itself a
> Cogito, ergo sum is a trivial result. We know we exist, we care
> to know how many of others like us are there.
Depending on whether you buy the self-sampling assumption or the 
self-indication assumption you get some weak evidence for this (or not).


Reasoning under extreme uncertainty is very different from reasoning 
under normal uncertainty. Normal uncertainty can afford to shy away from 
tainted data; extreme uncertainty has to squeeze every drop of rational 
evidence out of even the (non)existence of data.

-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University