Konrad Scheffler wrote:
I strongly disagree with this. The ("true") relative frequency is not the
same thing as the correct posterior. One can imagine a situation where the
correct posterior (calculated from the available information) is very far
from the relative frequency which one would obt
ai-boun...@engr.orst.edu] On Behalf Of
Lehner, Paul E.
Sent: Thursday, February 19, 2009 4:06 PM
To: Jean-Louis GOLMARD; Austin Parker; Konrad Scheffler; Peter Szolovits
Cc: uai@ENGR.ORST.EDU
Subject: Re: [UAI] A perplexing problem - Last Version
Austin, Jean-Lous, Konrad, Peter
Thank you for your r
On Mon, 23 Feb 2009, Francisco Javier Diez wrote:
> Konrad Scheffler wrote:
> > I agree this is problematic - the notion of calibration (i.e. that you can
> > say P(S|"70%") = .7) does not really make sense in the subjective Bayesian
> > framework where different individuals are working with diffe
librated. This is just like the
> TWC problem only more complex.
>
> So if Bayesian inference is inappropriate for the TWC problem, is it also
> inappropriate here? Is my advice bad?
>
> Paul
>
>
> From: uai-boun...@engr.orst.edu [mailto:uai-boun...@engr.orst.
Konrad Scheffler wrote:
I agree this is problematic - the notion of calibration (i.e. that you can
say P(S|"70%") = .7) does not really make sense in the subjective Bayesian
framework where different individuals are working with different priors,
because different individuals will have differen
ures.
Tod
_
From: uai-boun...@engr.orst.edu [mailto:uai-boun...@engr.orst.edu] On Behalf
Of Lehner, Paul E.
Sent: Thursday, February 19, 2009 4:06 PM
To: Jean-Louis GOLMARD; Austin Parker; Konrad Scheffler; PeterSzolovits
Cc: uai@ENGR.ORST.EDU
Subject: Re: [UAI] A perplexing problem - Last Version
Au
This time, the probabilistic model is underspecified, since it has 2
probabilities,
but it is not important for answering the question since the answer to
question 1 is is propositions 3 et 4:
if TWC forecasts are calibrated then P(S/70%) = 70%, and prior 2 plays
no role.
You find this si
Consider the following revised version.
The TWC problem
1. Question: What is the chance that it will snow next Monday?
2. My subjective prior: 5%
3. Evidence: The Weather Channel (TWC) says there is a “70%
chance of snow” on Monday.
4. TWC forecasts of snow are calibrate
em only more complex.
So if Bayesian inference is inappropriate for the TWC problem, is it also
inappropriate here? Is my advice bad?
Paul
From: uai-boun...@engr.orst.edu [mailto:uai-boun...@engr.orst.edu] On Behalf Of
Lehner, Paul E.
Sent: Monday, February 16, 2009 11:40 AM
To: uai@ENG
Paul, your restated problem reminds me of one I encountered in
medicine in the 1980's. When an internist sends a patient's sample to
a pathologist and the pathologist says "90% chance of cancer", how is
the internist supposed to interpret that answer in light of his own
priors? Empiricall
I agree this is problematic - the notion of calibration (i.e. that you can
say P(S|"70%") = .7) does not really make sense in the subjective Bayesian
framework where different individuals are working with different priors,
because different individuals will have different posteriors and they
ca
o if Bayesian inference is inappropriate for the TWC problem, is it
also inappropriate here? Is my advice bad?
Paul
From: uai-boun...@engr.orst.edu [mailto:uai-boun...@engr.orst.edu]
On Behalf Of Lehner, Paul E.
Sent: Monday, February 16, 2009 11:40 AM
To: uai@ENGR.ORST.EDU
Subject: Re: [
Paul Snow
Sent: Monday, February 16, 2009 3:24 AM
To: uai@engr.orst.edu
Subject: Re: [UAI] A perplexing problem
Dear Paul,
If the Weather Channel is Bayesian, then say they used that empricial
prior that you did (5%), and they observed evidence E to arrive at
their 70% for the snow S given E.
Their
Peter Szolovits wrote:
If TWC is really calibrated, then your conditions 5 and 6 are false, no?
I agree with Peter's solution. If I build a model for this problem, it
must contain at least two variables: Snow and TWC_report. According with
my model, the TWC forecasts are calibrated if and onl
rst.edu
Subject: Re: [UAI] A perplexing problem
Dear Paul,
If the Weather Channel is Bayesian, then say they used that empricial
prior that you did (5%), and they observed evidence E to arrive at
their 70% for the snow S given E.
Their Bayes' ratio is 44.3. Yours, effectively, is 10 (assuming
UAI members
Thank you for your many responses. You've provided at least 5 distinct answers
which I summarize below.
(Answer 5 below is clearly correct, but leads me to a new quandary.)
Answer 1: "70% chance of snow" is just a label and conceptually should be
treated as "XYZ". In other word
Dear Paul,
if you consider TWC prediction as a part of the probabilistic model,
you get 4 probabilities for modelling a model which needs 3
probabilities to be specified.
(the model is given by the 2-way table given by (Snow/not snow and
snow prediction of 70%/not snow prediction of 70%).
Dear Paul,
If the Weather Channel is Bayesian, then say they used that empricial
prior that you did (5%), and they observed evidence E to arrive at
their 70% for the snow S given E.
Their Bayes' ratio is 44.3. Yours, effectively, is 10 (assuming that
the event "They say 70%" coincides with "They
Hi Paul,
Your calculations are correct (although I note you really mean
P("70%"|not S) = 0.01 in the calc below).
^^^
Sometimes it helps to think about what the numbers actually
mean. First 0.05 prob of snow is quite a low prior.
You need to have quite "certain" evidence to move that up
If TWC is really calibrated, then your conditions 5 and 6 are false, no?
On Feb 13, 2009, at 4:28 PM, Lehner, Paul E. wrote:
I was working on a set of instructions to teach simple two-
hypothesis/one-evidence Bayesian updating. I came across a problem
that perplexed me. This can’t be a new
Hi Paul,
Your calculation is correct, but the numbers in the example are odd. If
TWC really only manage to predict snow 10% of the time (90% false negative
rate), you would be right not to assign much value to their predictions
(you do assign _some_, hence the seven-fold increase from your prio
1. Note that you haven't really used the "70%" at all. You could
restate the problem with any other statement you liked in there.
2. Your basic reasoning is correct. However, your modelling choice
seems poor. I would try replacing "TWC forecasts 70% chance of
snow" with "TWC fore
Paul,
I'm not aware of this being discussed anywhere but my observation is
that the information given makes TWC quite lousy -- the probability of
the forecast "70% chance of snow" is much too high when there is no
snow. It is a very specific piece of forecast and I would expect this
probabil
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