Does anyone know anything about this field?

http://en.wikipedia.org/wiki/Bayesian_probability

It seems that it's a way of quantizing probabilities that also includes some subjective priors. For example

One criticism levelled at the Bayesian probability interpretation has been that a single probability assignment cannot convey how well grounded the belief is—i.e., how much evidence one has. Consider the following situations:

1. You have a box with white and black balls, but no knowledge as to the quantities
2. You have a box from which you have drawn n balls, half black and the rest white
3. You have a box and you know that there are the same number of white and black balls

The Bayesian probability of the next ball drawn being black is 0.5 in all three cases.

Mathematicians probably pull their hair out at this. The first case seems a bit of a stretch, but the second point at least seems reasonable.

The reason I ask is that a lot of physicists apply this reasoning to particle physics, to try and predict what the LHC will see.

http://ite.gmu.edu/~klaskey/SYST664/Bayes_Unit9.pdf


LHC=Large Hadron Collider

application of Baye's rule to LHC
http://www.lepp.cornell.edu/~eotcor07/budapest_plehn_07.pdf

Ben...make me interested in this subject...talk to me

Ben...make me interested in this subject...talk to me

Bayesian analysis as applied to LHC physics? I don't know very much about it, other than they are trying to assess likelyhoods of certain models being discovered, before taking any data!

Bayesian analysis is extremely powerful. I have used it to pull many a rabbit out of a hat. My best rabbit was determining whether a failure has occurred despite having not a just a low signal-to-noise ratio but a scenario where noise dominated the signal (signal-to-noise ratio less than one). By accumulating evidence over time, I was able to let the signal rise above the noise.

The Kalman filters used to guide missiles and spacecraft are inherently Bayesian. These couple prior estimates of some state with measurements that are somehow indicative of the state to come up with a new estimate of the state.

DH---

Can you tell me anything about the ``likely-hood function''?

Can you tell me anything about the ``likely-hood function''?
Spell it correctly and you will have better luck searching. Its likelihood, not likelyhood. This wikipedia article (http://en.wikipedia.org/wiki/Likelihood_function) is fairly good. Let me know if you have any questions.

I think the third situation is an ordinary probability problem, not a Bayesian one.

I think the third situation is an ordinary probability problem, not a Bayesian one.

But Bayesian statistics has to reduce to regular statistics when everything is known, I'd assume. In other words, a ``frequentist'' approach and a Bayesian approach can give different answers if the ``true'' answer isn't known, but if the true answer IS known, they have to give the same number.

Bayesian analysis is extremely powerful. I have used it to pull many a rabbit out of a hat. My best rabbit was determining whether a failure has occurred despite having not a just a low signal-to-noise ratio but a scenario where noise dominated the signal (signal-to-noise ratio less than one). By accumulating evidence over time, I was able to let the signal rise above the noise.

The Kalman filters used to guide missiles and spacecraft are inherently Bayesian. These couple prior estimates of some state with measurements that are somehow indicative of the state to come up with a new estimate of the state.

Not sure if this will help, but as an EE I can pull a signal out of 120 db of noise [that is a negative S/N ratio !] if I know what signal [have prior information] I am looking for. Then I build a matching filter and it will spike even if it is drowned in noise. Most communication has no prior information, like radio, tv or cellular telephony.

The Bayes formula says in part [loosley] .... P[A] given that B has occurred.
Those last 5 words are very powerful information. Certainty in fact.

Don't know if this helps but maybe insight from another angle.

Ben
This subject is covered under the heading of Conditional Probability.
Have some fun and look over the Monty Hall Problem at Wiki.
Highly counter-intuitive.

Another well known application is the issue of false positives and negatives and a doctor's estimation of the liklihood that you have a disease given the test results.

Bayesean calculations can solve these problems.

Note that p[B/A] = probability that B occurs given that A has occurred.
and p[B/A] = p[ A implies B] = p[A => B]


Finally, with regard to physics experimentation .....
It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence.

It can be seen as a way of understanding how the probability that a theory is true is affected by a new piece of evidence.

This is how people have been using it lately. i think that some in the community are still skeptical of the analyses.

This is how people have been using it lately. i think that some in the community are still skeptical of the analyses.

It's really easy to fool yourself in some situations, say by missing hidden correlations created in the act of recording the new piece of evidence, or by making an apparently minor change in the wording or logic of the hypothesis that have major effects on the independence of the conditioning events etc.

For example, in paulfr's noted use of Bayesian statistics to estimate the odds of having a disease given a positive test result, it's easily possible that something about the doctor's criteria for ordering the test influences the odds of a false positive.

It's the ease of being led astray in practice, rather than any questions about the soundness of the basic theory, that I would guess create valid suspicion.

Silly example (in different words) I recall creating an actual discussion in technical papers:

Propose that all badgers on Guam have green fur. "Equivalently" (truth table sense), if an animal on Guam does not have green fur, it is not a badger. Go to Guam, observe that all visible animals do not have green fur, and are not badgers. Does your research increase the Bayesian probability that the original proposition is correct ?