Difference between Bayesian & Modern Probability

[woundedtiger4]

Hi all,

What is the difference between Bayesian Probability
http://en.wikipedia.org/wiki/Bayesian_probability

and the normal probability that we study at University, isn't Bayesian Probability simply the conditional probability that we study in Probability & Measure or in any other text of probability?

Thanks in advance.

 

[Stephen Tashi]

I suggest you consult other sources. That article is isn't well written.

You have to distinguish between at least 3 different subjects. There are

1) The Mathematical theory of probability

2) Different ways of posing real life problems as problems of mathematicas - e.g. "Bayesian" vs "Frequentist" statistics

3) Philosophical ideas about what probability means.

The Wikipedia article appears to be about 3), the philosophical or metaphysical interpretation of probability. According to E.T. Jaynes, there are thousands of different Bayesian interpretations of probability.

The major philosophical interpretations of probability don't disagree on the mathematical laws of probability. There have been other sets of axioms proposed for theories of probability and there are "theories of evidence" (such as Dempster-Schafer) that are more general ideas than probability. But when you say a mathematician is a "Bayesian", it usually refers to subject 2) - i.e. to a style of approaching statistical problems.

The probability theory you learn in introductory university courses isn't contradicted by Bayesian methods introduced in more advanced courses. Whether it is contradicted by anything taught in the Philosophy Department, who's to say? You'll have to ask philosophers.

 

[woundedtiger4]

I suggest you consult other sources. That article is isn't well written.

You have to distinguish between at least 3 different subjects. There are

1) The Mathematical theory of probability

2) Different ways of posing real life problems as problems of mathematicas - e.g. "Bayesian" vs "Frequentist" statistics

3) Philosophical ideas about what probability means.

The Wikipedia article appears to be about 3), the philosophical or metaphysical interpretation of probability. According to E.T. Jaynes, there are thousands of different Bayesian interpretations of probability.

The major philosophical interpretations of probability don't disagree on the mathematical laws of probability. There have been other sets of axioms proposed for theories of probability and there are "theories of evidence" (such as Dempster-Schafer) that are more general ideas than probability. But when you say a mathematician is a "Bayesian", it usually refers to subject 2) - i.e. to a style of approaching statistical problems.

The probability theory you learn in introductory university courses isn't contradicted by Bayesian methods introduced in more advanced courses. Whether it is contradicted by anything taught in the Philosophy Department, who's to say? You'll have to ask philosophers.

OKKKKKKK

Sir, thank you very much.