2. Bayesian statistics named after the Reverend Mr Bayes based on the concept that you can estimate the statistical properties of a system after measuting its behaviour in a large number of trials, and compare measured behaviour with some null hypothesis The support for the hypothesis is termed “posterior probability”

3. Bayesian statistics so if you have a die (six sides) you can measure its bias by rolling it a thousand times, and counting the number of 1’s, 2’s, etc. Your “prior” hypothesis is of unbiased representation of the six numbers. If you have an over/under representation of a particular score, the probability that the die is biased can be estimated from the posterior probability of getting that pattern in 1000 trials, given a biased die.

4. Bayesian phylogenetics is based on assessing, using maximum likelihood optimality criteria. lots of trees model parameters (all of which fall in the optimal zone) and summarising the resultant best trees as a consensus, where the proportional support for each retained node is the Bayesian posterior probability of that node being correct

5. Bayesian phylogenetics in practice, four tricks are used to make this possible Markov chains these are “models” of complex behaviours of systems, where the output of one state of the system is independent of the previous experience of the system, and can be described by a series of “emission” probabilities (per aligned site rates of change, relative rates of base substitution) - used for estimating likelihoods

6. Bayesian phylogenetics in practice, four tricks are used to make this possible Markov chains Monte Carlo sampling This describes the concept of casino-style gambling (as in Monte Carlo casinios) where the sum of all trials yields a result (profit for the house) even if indivisual trials go against this. - so we can try out different trees, and ALSO different model parameters (rates of change, invariant %, gamma distribution alpha value)

7. use the Markov Chain Monte Carlo process to sample treespace and modelspace

8. Bayesian phylogenetics in practice, four tricks are used to make this possible Markov chains Monte Carlo sampling Metropolis algorithm “if the tree/model combination just tested is better than the old one, keep it, but.... if it is worse than the old one, reject it most of the time, but randomly keep suboptimal tree/model combinations” (so the process never stops)

9. as the number of generations of the MCMCMC process increases, the trees & models found converge on an optimum

10. Bayesian phylogenetics in practice, four tricks are used to make this possible Markov chains Monte Carlo sampling Metropolis algorithm coupled run more than one Markov Chain, and allow them to swap parameters, so that local optima for, eg, substitution models, get tested on different trees, etc

11. Bayesian phylogenetics MCMCMC collect all the trees after the models have reached effective stationarity. compute the consensus of these trees, and calculate the proportional support for each node this is the Bayesian posterior probability or pp

12. Bayesian phylogenetics NOTE... that empirical tests using “synthetic” data suggest that Bayesian methods tend to overestimate the support for a node support >90% (also given as 0.9) is OK support >95% is good looking for >99%...