The tree prior and mutation model parameter priors used for the real data analyses are the same as the ones for analyses of the simulation data.
To accommodate augmented mutation model parameter space for a model-specific pseudoprior, the new function for ψ becomes (13) ψ κ = { φ I (k, δ ) δ k = 1 0 δ k = 0, where the mapping function I k, δ) returns the index of the element in φ according to k, which indicates the type of parameter, and δ, which specifies the currently active model.
Additional file 8: Model specification, prior distributions for demographic parameters and locus-specific mutation model parameters used for the diyABC analyses.
We took Carlin and Chib's suggestion and obtained preliminary posterior distributions of mutation model parameters by running a short MCMC (of 40,000,000 steps) with each microsatellite model.
The mutation model parameters for the microsatellite loci were the mean mutation rate (μ mic), the parameter determining the shape of the gamma distribution of individual loci mutation rate (P ), and the Single Insertion Nucleotide rate (SNI ).
This means the dimensions of φ and δ, and hence the model parameter dimension, are not changed even though mutation model parameters are effectively included and excluded in the likelihood during the MCMC.
Moolgavkar et al. [ 114] partially overcome the problem posed by this instantaneous rise in the hazard after perturbation of the two-mutation model parameters in their analysis of the Colorado uranium miners data by assuming a fixed period (3.5 years) between the appearance of the first malignant cell and the clinical detection of malignancy.
We parameterize the mutation model with a single parameter, the AT bias, which represents the equilibrium content of adenine and thymine after a very long evolution under mutation alone (the complementary variable GC bias, expressing the equilibrium content of guanine and cytosine under mutation alone, is sometimes alternatively used).
The mean correlation coefficient between predicted and observed site-specific amino acid distributions is larger than < r> = 0.70 for a mutation model with no free parameters and no genetic code.
The default model parameters were used, specifically mutation model prior: (0.50, 0.50, 0.00), max number of trees to consider per location: 1 and beta risk prior parameters: (5.00, 5.00).
We further assume π(A) = π(T) and π(C) = π(G) (Chargaff second parity rule), so that the only parameter of the mutation model is the stationary AT frequency, AT = π(A) + π(T).
