The likelihood is parameterised as \(\mathrm{Weibull} (y | a, b) = \frac{a}{b} y ^{a-1} \exp \left( - \frac{x^a}{b} \right)\). The base measure is a Uniform Inverse Gamma Distribution. \(G_0 (a, b | \phi, \alpha _0 , \beta _0) = U(a | 0, \phi ) \mathrm{Inv-Gamma} ( b | \alpha _0, \beta _0)\) \(\phi \sim \mathrm{Pareto}(x_m , k)\) \(\beta \sim \mathrm{Gamma} (\alpha _0 , \beta _0)\) This is a semi-conjugate distribution. The cluster parameter a is updated using the Metropolis Hastings algorithm an analytical posterior exists for b.
DirichletProcessWeibull(
y,
g0Priors,
alphaPriors = c(2, 4),
mhStepSize = c(1, 1),
hyperPriorParameters = c(6, 2, 1, 0.5),
verbose = FALSE,
mhDraws = 250
)Dirichlet process object
Data.
Base Distribution Priors.
Prior for the concentration parameter.
Step size for the new parameter in the Metropolis Hastings algorithm.
Hyper prior parameters.
Set the level of screen output.
Number of Metropolis-Hastings samples to perform for each cluster update.
Kottas, A. (2006). Nonparametric Bayesian survival analysis using mixtures of Weibull distributions. Journal of Statistical Planning and Inference, 136(3), 578-596.