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Bioinformatics Lecture 7, part 4 of 4 
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Bayesian methods represent a
fundamental intellectual breakthrough to solving problems
in almost any field. Bayesian methods attack problems by
asking the question, "Would
we recognize the best answer if we saw it?". If we know how to answer that question, the most straightforward solution would be to test all possible answers (trees), and see which one was the most likely one to be generated by the observed data. To illustrate, imagine the set of all probabilities as a surface, each point on the surface representing the probability that a given tree would generate the alignment we see. The best trees, and their variants, will appear as peaks on the surface, and the worst trees and their variants will appear as valleys. 
from http://artedi.ebc.uu.se/course/X32004/Phylogeny/PhylogenyTreeSearch/PhylogenySearch.html 
P(model

data)

ie. what is the
probability that the model would generate the data we actually see? 
Bayes Theorem: 
where P(ModelData)
is the posterior probability of the model, given the
data
P(DataModel) is the probability of the data, given the model P(Model) is the prior probability of the model (without any knowledge of the data). eg, if all models are equally valid, P(model) = 1/the number of possible models P(Data) is the prior probability of the data (without any knowledge of the model) 
prior probability
 the probability calculated on theoretical grounds,
with no knowledge of the experimental data posterior probability  the probability of seeing a particular result, calculated from the experimental data. 
numerator  one tree denominator  all trees 
For
an unrooted tree with s branches, 
For
a rooted tree, 
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