Create a Dirichlet Mixture of the Weibull distribution
Create a Dirichlet Mixture of the Weibull distribution
The likelihood is parameterised as Weibull(y∣a,b)=baya−1exp(−bxa). The base measure is a Uniform Inverse Gamma Distribution. G0(a,b∣ϕ,α0,β0)=U(a∣0,ϕ)Inv−Gamma(b∣α0,β0)
ϕ∼Pareto(xm,k)
β∼Gamma(α0,β0)
This is a semi-conjugate distribution. The cluster parameter a is updated using the Metropolis Hastings algorithm an analytical posterior exists for b.
alphaPriors: Prior for the concentration parameter.
mhStepSize: Step size for the new parameter in the Metropolis Hastings algorithm.
hyperPriorParameters: Hyper prior parameters.
verbose: Set the level of screen output.
mhDraws: Number of Metropolis-Hastings samples to perform for each cluster update.
Returns
Dirichlet process object
References
Kottas, A. (2006). Nonparametric Bayesian survival analysis using mixtures of Weibull distributions. Journal of Statistical Planning and Inference, 136(3), 578-596.