Similar to dic.fit but uses MCMC instead of a direct likelihood optimization routine to fit the model. Currently, four distributions are supported: log-normal, gamma, Weibull, and Erlang. See Details for prior specification.
dic.fit.mcmc(
dat,
prior.par1 = NULL,
prior.par2 = NULL,
init.pars = c(1, 1),
ptiles = c(0.05, 0.95, 0.99),
verbose = 1000,
burnin = 3000,
n.samples = 5000,
dist = "L",
seed = NULL,
...
)a cd.fit.mcmc S4 object
the data
vector of first prior parameters for each model parameter. If NULL then default parameters are used (as described in Details section).
vector of second prior parameters for each model parameter. If NULL then default parameters are used (as described in Details section).
the initial parameter values (vector length = 2 )
returned percentiles of the survival survival distribution
how often do you want a print out from MCMCpack on iteration number and M-H acceptance rate
number of burnin samples
number of samples to draw from the posterior (after the burnin)
distribution to be used (L for log-normal,W for weibull, G for Gamma, and E for erlang, off1G for 1 day right shifted gamma)
seed for the random number generator for MCMC
additional parameters to MCMCmetrop1R
The following models are used: $$Log-normal model: f(x) = \frac{1}{x*\sigma \sqrt{2 * \pi}} exp\{-\frac{(\log x - \mu)^2}{2 * \sigma^2}\}$$ $$Log-normal Default Prior: \mu ~ N(0, 1000), log(\sigma) ~ N(0,1000)$$ $$Weibull model: f(x) = \frac{\alpha}{\beta}(\frac{x}{\beta})^{\alpha-1} exp\{-(\frac{x}{\beta})^{\alpha}\}$$ $$Weibull Default Prior Specification: log(\alpha) ~ N( 0, 1000), \beta ~ Gamma(0.001,0.001)$$ $$Gamma model: f(x) = \frac{1}{\theta^k \Gamma(k)} x^{k-1} exp\{-\frac{x}{\theta}\}$$
$$Gamma Default Prior Specification: p(k,\theta) \propto \frac{1}{\theta} * \sqrt{k*TriGamma(k)-1}$$ (Note: this is Jeffery's Prior when both parameters are unknown), and $$Trigamma(x) = \frac{\partial}{\partial x^2} ln(\Gamma(x))$$.) $$Erlang model: f(x) = \frac{1}{\theta^k (k-1)!} x^{k-1} exp\{-\frac{x}{\theta}\}$$ $$Erlang Default Prior Specification: k \sim NBinom(100,1), log(\theta) \sim N(0,1000)$$ (Note: parameters in the negative binomial distribution above represent mean and size, respectively)