Bayesian Phylogeny

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Bayesian Phylogeny
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• Bayes Rule
• Probability Likelihood X Prior Information
• Some normalising factors

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• Important Terms
• Prior probability the probability of the event
  before considering some additional data
• Posterior probability the probability of the
  event after taking into consideration some
  observed data

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• In molecular phylogenetics the prior is usually
  flat

Why bother?
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• 1. Because we get the answer as a probability

A coin is known to be biased The coin is tossed
three times two heads and one tail
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• 2. Because this formulation allows us to use
  another approach to get to the best tree (MCMC
  see later)

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• 3. Integrates over parameters instead of
  optimising over parameters

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• MCMC
• Produces a long chain of trees/parameters sampled
  according to their probability
• The number of times the chain visits tree X is
  proportional to the probability of tree X

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Burnin

• Typically the chain will take some time before
  trees are sampled according to their probability
• Initially probability of trees increases with
  time
• Programmes need to be allowed to run until the
  probabilities are fluctuating randomly about a
  constant mean
• Data generated before the chain reaches a
  steadystate are discarded

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• Chain is sampled every x steps

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• Multiple chains may be used (Metropolis coupled
  MCMC MC3)
• - Only one chain is sampled
• - The other chains are heated (i.e. they can take
  bigger steps)
• Chains can swap states
• Allows crossing of valleys

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• Likelihood
• maximise
• Bayes Rule
• maximise

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• Bayesian methods can be
• - relatively fast
• - easily interpretable
• - often very accurate

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• But
• - sometimes overestimate confidence
• - difficult to be sure of convergence
• - difficult to decide how long to run the chain
  for

e.g. MrBayes