Re: how to interpret a conditional probability


"David Jones" <dajxxx@xxxxxxxxx> wrote in message
news:44fc55d4$1@xxxxxxxxxxxxxxxxx
Takashi Yamauchi wrote:
I wonder if you could help me and point me to somewhere.

this is a simple question (I think), but not for me.

Say, you estimated a conditional probability

P(theta_1 | x) = 0.54,

THETA = {theta_1, theta_2}, wehre P(theta_1)=P(theta_2)=0.5.

So, Theta is dichotomous (yes, no), x is data/observation, and the
prior

probabilities are 0.5. This conditional probability means that after

observation x, the probability of P(theta_1 | x) improved only
slightly

(compared to the prior P(theta_1) = 0.5).

How do you evaluate this conditional probability? Any index to say

something statistically? For example, you can caculate the posterior
odds for theta_1;

0.54/(1-0.54) or take the logorithm of the odds. Then, how do you
evaluate

these statistically? Is there any way to evluate how much 0.54 is

informative (statistically)? where should I look?

Thank you

takashi

One approach would be to extend the discussion to a fully defined
decision problem. The "optimal" decision depends on the probability
distribution, as does the expected cost. Thus you could measure how
useful the observation x is, by comparing the expected costs before
and after the observation. This is on the basis that "money" is easier
to understand/compare than probabilities or odds.

David Jones


Thank you. Can I use the Bayes factor? such that
P(x | theta_1) / P(x | theta_2) = Bayes factor

If so, how do I interpret the Bayes factor? Do you know of a good
paper/book that discusses the interpretation of Bayes factor?

takashi yamauchi


.

Relevant Pages
Loading