1. Bayesian II Spring 2010

2. Major Issues in Phylogenetic BI Have we reached convergence? If so, do we have a large enough sample of the posterior?

3. Have we reached convergence? Look at the trace plots of the posterior probability (not reliable) Convergence Diagnostics: – Average Standard Deviation of the Split frequencies: compares the node frequencies between the independent runs (the closer to zero, the better, but it is not clear how small it should be) – Potential Scale Reduction Factor (PSRF): the closer to one, the better

4. Convergence Diagnostics By default performs two independent analyses starting from different random trees (mcmc nruns=2) Average standard deviation of clade frequencies calculated and presented during the run (mcmc mcmcdiagn=yes diagnfreq=1000) and written to file (.mcmc) Standard deviation of each clade frequency and potential scale reduction for branch lengths calculated with sumt Potential scale reduction calculated for all substitution model parameters with sump

5. Have we reached convergence? PSRF (sump command) Model parameter summaries over all 3 runs sampled in files "Ligia16SCOI28SGulfnoADLGGTRGbygene.nex.run1.p", "Ligia16SCOI28SGulfnoADLGGTRGbygene.nex.run2.p" etc: (Summaries are based on a total of 162003 samples from 3 runs) (Each run produced 60001 samples of which 54001 samples were included) 95% Cred. Interval ---------------------- Parameter Mean Variance Lower Upper Median PSRF * ------------------------------------------------------------------------------------------- TL{all} 1.578535 0.008255 1.417000 1.771000 1.573000 1.000 r(A C){1} 0.036558 0.000133 0.016961 0.061987 0.035555 1.000 r(A G){1} 0.405681 0.002305 0.314283 0.502156 0.404811 1.000 r(A T){1} 0.044360 0.000120 0.025482 0.068209 0.043489 1.000 r(C G){1} 0.022006 0.000120 0.004949 0.047283 0.020532 1.000 r(C T){1} 0.472371 0.002269 0.379396 0.565910 0.472279 1.000 r(G T){1} 0.019024 0.000079 0.005074 0.039579 0.017873 1.000 pi(A){1} 0.292047 0.000390 0.254211 0.331575 0.291819 1.000 pi(C){1} 0.204875 0.000278 0.173364 0.238514 0.204491 1.000 pi(G){1} 0.214907 0.000324 0.180784 0.251150 0.214522 1.000 pi(T){1} 0.288171 0.000367 0.251355 0.326301 0.287933 1.000 alpha{1} 0.183087 0.000419 0.146653 0.226929 0.181792 1.000 ------------------------------------------------------------------------------------------- * Convergence diagnostic (PSRF = Potential scale reduction factor [Gelman and Rubin, 1992], uncorrected) should approach 1 as runs converge. The values may be unreliable if you have a small number of samples. PSRF should only be used as a rough guide to convergence since all the assumptions that allow one to interpret it as a scale reduction factor are not met in the phylogenetic context.

6. Copyright restrictions may apply. Nylander, J. A.A. et al. Bioinformatics 2008 24:581-583; doi:10.1093/bioinformatics/btm388 Are We There Yet (AWTY)?

7. Empirical Data: two independent runs 300,000,000 generations: complex model with three partitions (by codon): the bad news Plotted in Tracer

8. Empirical Data: two independent runs 300,000,000 generations: complex model with three partitions (by codon): the good news; splits were highly correlated between the two runs Plotted in AWTY: http://ceb.scs.fsu.edu/awtyhttp://ceb.scs.fsu.edu/awty

9. Empirical Data: two independent runs 300,000,000 generations: complex model with three partitions (by codon): the good news; splits were highly correlated between the two runs Plotted in AWTY: http://ceb.scs.fsu.edu/awtyhttp://ceb.scs.fsu.edu/awty What caused the difference in posterior probabilities? Estimation of particular parameters

10. Yes we have reached convergence: Do we have a large enough sample of the posterior? Long runs are better than short one, but how long? Good mixing: “Examine the acceptance rates of the proposal mechanisms used in your analysis (output at the end of the run) The Metropolis proposals used by MrBayes work best when their acceptance rate is neither too low nor too high. A rough guide is to try to get them within the range of 10 % to 70 %”

11. Acceptance Rates Analysis used 2373953.05 seconds of CPU time on processor 0 Likelihood of best state for "cold" chain of run 1 was -9688.70 Likelihood of best state for "cold" chain of run 2 was -9865.21 Likelihood of best state for "cold" chain of run 3 was -9887.59 Likelihood of best state for "cold" chain of run 4 was -9895.35 Acceptance rates for the moves in the "cold" chain of run 1: With prob. Chain accepted changes to 42.86 % param. 1 (revmat) with Dirichlet proposal 21.42 % param. 2 (revmat) with Dirichlet proposal 55.92 % param. 3 (revmat) with Dirichlet proposal 29.18 % param. 4 (state frequencies) with Dirichlet proposal 12.22 % param. 5 (state frequencies) with Dirichlet proposal 24.61 % param. 6 (state frequencies) with Dirichlet proposal 41.02 % param. 7 (gamma shape) with multiplier 31.74 % param. 8 (gamma shape) with multiplier 79.95 % param. 9 (gamma shape) with multiplier 40.16 % param. 10 (rate multiplier) with Dirichlet proposal 15.80 % param. 11 (topology and branch lengths) with extending TBR 23.62 % param. 11 (topology and branch lengths) with LOCAL

12. tree 1tree 2 tree 3 Posterior probability distribution Parameter space Posterior probability

13. cold chain heated chain Metropolis-coupled Markov chain Monte Carlo a. k. a. MCMCMC a. k. a. (MC) 3

14. cold chain hot chain

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17. unsuccessful swap cold chain hot chain

18. cold chain hot chain

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20. cold chain hot chain successful swap

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23. cold chain hot chain successful swap

24. cold chain hot chain

25. Improving Convergence (Only if convergence diagnostics indicate problem!) Change tuning parameters of proposals to bring acceptance rate into the range 10 % to 70 % Propose changes to ‘difficult’ parameters more often Use different proposal mechanisms Change heating temperature to bring acceptance rate of swaps between adjacent chains into the range 10 % to 70 %. Run the chain longer Increase the number of heated chains Make the model more realistic

26. Sampled value Target distribution Too modest proposals Acceptance rate too high Poor mixing Too bold proposals Acceptance rate too low Poor mixing Moderately bold proposals Acceptance rate intermediate Good mixing