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I am trying to learn something about Bayesian Analysis by doing an example.

I have a series of 10 matches played between A and B, where each match is the first to 3 points. With an example data set that looks like this:

ABBAA

BAAA

AABBA

BBB

BABB

AAA

AABA

BAAA

AABBB

AAA

I would like to calculate the probability that A wins any given point, based on this data set and using a Bayesian approach.

I have read some information on Bayesian Analysis and I believe that in order to start I need to have something called a prior probability distribution (please correct me at any point if I am wrong). This distribution I was thinking I would construct from the mean number of points won by A across all 40 points played along with the standard deviation.

Next I need to calculate the likelihood function and there is something called a posterior function too. To be honest I am starting to get a little lost by this point and I am slightly confused as I already have my data and this seems to be trying to predict what I already have.

Help?

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# A simple Bayesian example

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