Changes made in Version 1.2

25 May 2001: Changing the way MCMC steps are counted

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Changes made
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prog.cc
The function DoSampling has been rewritten. Care has been taken to get the acceptance ratio for Metropolis-Hastings steps right. Note that the sequences of hidden states as well as the recombination parameter lambda are updated with Gibbs sampling. Gibbs steps are always accepted and are therefore not included in computing the acceptance ratio.

4 July 2001: Changing the sampling of lambda

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Changes made in class ChangeLambda, file treemanip2.cc
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• ChangeLambda
  New constructor. Specifying the prior parameters of the beta distribution in the constructor is meant to be a temporary solution until they can be read in from the program interface. The default prior is chosen to be reasonably flat to reflect the absence of prior information.
• MHaccept
  Left out, because MH (Metropolis-Hastings) sampling has been replaced by Gibbs sampling. The function MHaccept has been replaced by the new function SampleNewLambda.
• SampleNewLambda
  New function. Samples new lambda from the posterior distribution according to equation (2.3) in C.P. Robert et al., Statistics & Probability Letters 16 (1), 77-83, 1993.
• UpdatePosteriorBeta
  New function. Updates the posterior parameters of the Beta distribution according to equation (2.3) in C.P. Robert et al., Statistics & Probability Letters 16 (1), 77-83, 1993.
• GenNewLambda and AdjustDelta
  Left out.
• UpdateTPprobs
  Updates the transition probabilities with the current value of lambda. New version: The functional dependence of the transition probabilities between tree topologies on lambda has been redefined. Rather than using Grainne's original definition, where lambda denotes the probability that no recombination occurs, lambda is now defined as the probability that no recombination is observed. Define S0 and S1 to be the topologies in two adjacent sites, 0 and 1. These topologies are the same with probability lambda. The probability of a transition from S0 to S1 is equal to (1-lambda)*P(S1)/[1-P(S0)], so the total transition probability is P(S1|S0)= lambda*delta(S0,S1)+ (1-lambda)*P(S1)/[1-P(S0)][1-delta(S0,S1)]. For equal prior probabilities P(Si)=1/3, this reduces to equation (5) in Husmeier, Neural Network World 4 (10), 589-595, 2000. The advantage of this definition is that lambda can now be given a conjugate prior of a standard form, namely the beta distribution. Note that tp[i][k] is the log probability for a transition from topology i into topology k.

New variables:

• alphaPrior, betaPrior
  Parameters of the prior distribution.
• alphaPosterior, betaPosterior
  Parameters of the posterior distribution.

Function ProposeLambda has been rewritten to accommodate the changes described above. Note that in the new scheme, lambda is updated with Gibbs sampling. This implies that all sampled values will be accepted; so there is no longer a need to determine the acceptance ratio.

6 July 2001

• File treemanip.h, class TreeCalc: New function UpdateLambda().
• File treemanip.h, class TreeCalc: New Bool variable updateLambda.
• File ChooseOptions.h: New char[4] variable updateLambda.
• File ChooseOptions.cc: Changes in ChangeOptions().
• File prog.cc: Set function UpdateLambda().

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