Parameter Priors

## Introduction

BEAST offers a wide range of prior distributions that can be used for the parameters used in its models. This page provides a description of and the rationale behind the default priors on each parameter of those standard models in BEAUti, with the goal of providing every parameter with a proper and reasonable prior.

Complementing the parameter priors described here, we also provide a page on coalescent priors, which offers possible choices to put a prior on the underlying tree and its branch lengths.

### Relative rate parameters in BEAST v1.10

As of version 1.10, BEAST makes use of a re-parameterisation of the between partition relative rates parameter. The old parameterisation - default in versions before 1.10 - is called mu, the new parameterisation is called nu.

The reason for this change is to allow the use of a Dirichlet prior on the relative rates. This, in turn, is to provide a proper prior so that the marginal likelihood estimation (MLE) can work on these models (previously, with mu, an improper uniform prior [0,Inf[ was used).

The difference between mu and nu is that mu is weighted by partition size so it is a per-site relative rate and if multiplied by the clock rate, will give the absolute rate of a site in that partition. nu is a per-partition rate; this allows the delta exchange transition kernel to maintain a mean of 1 and thus be suitable for the Dirichlet prior.

As of BEAST 1.10, the nu parameters are what are operated on and they have the Dirichlet prior in the priors table in BEAUti. To make things more comparable with older versions of BEAST, the mu values are also calculated and logged. In future versions we will keep logging both nu and mu` for completeness.

You can switch this to the old formulation (i.e. BEAST v1.8.4 and older) by checking the “Use classic priors/operators” at the top of the Priors table in BEAUti.

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