Under the Bayesian paradigm, the posterior density of the unknown quantities is given by (4) where θ refers to the vector of unknown parameters.
For compactness, we encapsulate the aforementioned parameters in a vector ξ = (α, β, μ111,…, μTIC, w0, p01,…, p0 J ). Unknown parameters, i.e. θ, in our model are estimated in an MCMC fashion, which means we first must devise a sampling scheme under which samples from the posterior density of our parameters, given data and fixed parameters, f ∝ f f, are drawn.
The random samples are then used in approximating the posterior density functions of the parameters.
Under the sequential Monte Carlo Bayesian framework, an adaptive RBPF method is developed, which uses an analytical method to estimate the mobile state while applying the particle filter to estimate the posterior density of sight conditions and the unknown static parameters.
Typically Markov Chain Monte Carlo is used to compute the posterior density; however, this process is computationally intensive.
Posterior probabilities for each split were calculated from the posterior density of trees.
The extra column stores the posterior density.
Truncation ensures normalization of the posterior density.
Posterior probabilities for internal node were calculated from the posterior density of trees.
Posterior probabilities for each split and a phylogram with mean branch lengths were calculated from the posterior density of trees.
