TAMING THE BEAST

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We will be using R to analyze the output of the Birth-Death Skyline plot. RStudio provides a user-friendly graphical user interface to R that makes it easier to edit and run scripts. (It is not necessary to use RStudio for this tutorial).

NS works in theory if and only if the points generated at each iteration are independent. If you already did an MCMC run and know the effective sample size (ESS) for each parameter, to be sure every parameter in every sample is independent you can take the length of the MCMC run divided by the smallest ESS as sub-chain length. This tend to result in quite large sub-chain lengths. This depends on many things, but in general, depends on how accurate the estimates should be. For NS, we get an estimate of the SD, which is not available for PS/SS. If the hypotheses have very large differences in MLs, NS requires very few (maybe just 1) particle, and will be very fast. If differences are smaller, more particles may be required, and the run-time of NS is linear in the number of particles. Marginal likelihood: -12426.207750474812 sqrt(H/N)=(1.8913059067381148)=?=SD=(1.8374367294317693) Information: 114.46521705159945

Bayesian model selection is based on estimating the marginal likelihood: the term forming the denominator in Bayes formula. This is generally a computationally intensive task and there are several ways to estimate them. Here, we concentrate on nested sampling as a way to estimate the marginal likelihood as well as the uncertainty in that estimate. To change the number of segments we have to navigate to the Initialialization panel, which is by default not visible. Navigate to View > Show Initialization Panel to make it visible and navigate to it ( Figure 7).

We can leave the rest of the priors as they are and save the XML file. We want to shorten the chain length and decrease the sampling frequency so the analysis completes in a reasonable time and the output files stay small. (Keep in mind that it will be necessary to run a longer chain for parameters to mix properly). However, the only informative events used by the Coalescent Bayesian Skyline plot are the coalescent events. Thus, using a maximally-flexible parameterization with only one informative event per segment often leads to erratic and noisy estimates of N e N_e N e ​ over time (especially if segments are very short, see Figure 6). Grouping segments together leads to smoother and more robust estimates.

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Marginal likelihood: -12428.557546706481 sqrt(H/N)=(11.22272275528845)=?=SD=(11.252847709777592) Information: 125.94950604206919 The choice of the number of dimensions can also have a direct effect on how fast the MCMC converges ( Figure 14). The slower convergence with increasing dimension can be caused by e.g. less information per interval. To some extent it is simply caused by the need to estimate more parameters though. Figure 14: The ESS value of the posterior after running an MCMC chain with 1 0 7 10 where the argument after N is the particleCount you specified in the XML, and xyz.log the trace log produced by the NS run. Why are some NS runs longer than others? With an estimated 15-25%, Egypt has the highest Hepatits C prevalence in the world. In the mid 20th century, the prevalence of Hepatitis C increased drastically (see Figure 1 for estimates). We will try to infer this increase from sequence data.