Coalescent Tree Prior ; frequent Size ; Jeffreys past on people Size

The first-run I will make use of a coalescent tree past that assumes a (*unknown*) continual inhabitants size right back through energy. This tree prior was the best for trees explaining the connections between individuals in the same population/species. This prior has a parameter (constant.popSize) that will be tested by MCMC. As the parameter is also part of the MCMC condition it needs to likewise have a prior circulation specified for this. The default previous submission was uniform with a very high higher bound. Within setting the posterior circulation in the price appears like:

As you can see the posterior hateful was 2.3 +/- 0.144, whereas the last mean speed was actually 5.05. Why performed the tree prior have an effect on the speed estimate? The solution is somewhat intricate in easy terms and conditions, a continuing dimensions coalescent prior (with consistent before on constant.popSize) likes big trees. They prefers big woods since when the constant.popSize parameter are big, the coalescent previous favors huge woods and because the last on constant.popSize was uniform with a very high bound, the constant.popSize can become big. The model can achieve big trees without altering the department lengths (regarding level of genetic change) by decreasing the evolutionary speed consequently. Thus consequently this forest previous favors decreased rates. This result is expressed inside earliest papers about MCMC strategy root BEAST (Drummond et al, 2002) and it’s really easy to correct. All we need to would is actually change the prior on constant.popSize to avoid they from prefering big trees.

As it happens that a tremendously all-natural previous the constant.popSize factor could be the Jeffreys prior (discover Drummond et al, 2002 for precisely why its natural and a few simulations that demonstrate it). This is actually the rear submission of price when utilizing a Jeffreys previous in the constant.popSize parameter for the Primates example:

As you can tell the posterior indicate are 5.2 +/- 0.125 additionally the distribution seems rather uniform (if I ran it longer it could have a look better yet). Recollection that earlier mean rates was actually 5.05. This means that, there’s absolutely no factor involving the marginal rear distribution on rates plus the limited previous submission. Even as we expect the posterior only reflects the prior. This can be a lot nicer actions. Moral regarding the story: utilize the Jeffreys prior while using the constant-size coalescent (unless you may have an informative past circulation on constant.popSize). Later forms of BEAST will probably have the Jeffreys before as the standard option for this parameter.

Yule Tree Before ; Uniform Prior on Delivery Price

When it comes to 3rd run I will make use of a Yule tree prior that thinks a (unknown) continuous lineage birth price for every part in the forest. This forest before are most suitable for woods explaining the relations between individuals from various variety. The yule prior parameter (yule.birthRate) is frequently thought of as explaining the web rates of speciation. This past parameter (yule.birthRate) are tested by MCMC. As the factor can part of the MCMC county it should also have a prior distribution specified because of it. The standard prior distribution try uniform. Using this forest previous the rear circulation associated with rate seems like:

As you can see the posterior indicate was 4.9 +/- 0.16. This is not somewhat unlike all of our prior circulation and so was behaving perfectly how we expect they to.

Why tthe guy differences in behaviour for different tree priors?

So why will be the consistent prior on yule.birthRate functioning the way we count on after consistent previous on constant.popSize was not? The answer is in the way in which the many designs is parameterized. If coalescent prior was basically parameterized with a parameter which was add up to 1/constant.popSize, then a uniform prior could have behaved nicely (in place the Jeffreys before was performing this re-parameterization). Conversely if Yule tree product were parameterized with a parameter corresponding to 1/yule.birthRate (which would portray the mean department size) it can posses behaved *badly* in the same way to coalescent prior with a uniform before on constant.popSize.