run.bayesian.vam: Compute the Bayesian method for a virtual age model

In rcqls/VAM: Virtual Age Models

Compute the Bayesian method for a virtual age model

Description

For bayesian.vam object, the method run.bayesian.vam produces a sample from the posterior distribution of the parameters using a Gibbs sampling algorithm with a Metropolis Hasting step. The generated sample is memorized in the bayesian.vam object and can be used in particular by the coef.bayesian.vam and summary.bayesian.vam to produce Bayesian estimators of the parameters.

Usage

run.bayesian.vam(obj,par0,fixed,sigma.proposal,nb=100000,burn=10000,profile.alpha=FALSE,method=NULL,verbose=FALSE,history=FALSE,proposal='norm',...)

Arguments

obj	an object of class bayesian.vam specifying the virtual age model considered, the prior distribution of the parameters and the data set of observations.
par0	an optional argument specifying the initial parameter values for the Gibbs sampling method. par0 is a vector whose length is equal to the total number of parameters in the formula used for defining the object obj. The successive values of par0 respectively refer to the parameters of time to failure distribution of the new unmaintained system, of the CM effect model and finally of the PM effect models (if defined and in the same order as they appear in the obj formula). If par0 is not specified, the Gibbs sampling method is initialized at the maximum likelihood estimators parameters values (see mle.vam). In order to compute this maximum likelihood estimators, the optimization method is initialized at the means of the prior distributions.
fixed	an optional argument specifying the parameters for which the value is fixed to initialization. fixed can be a vector of logical whose length is equal the total number of parameters in the formula used for defining the object obj. The successive values of fixed respectively refer to the parameters of time to failure distribution of the new unmaintained system, of the CM effect model and finally of the PM effect models (if defined and in the same order as they appear in the obj formula). Otherwise fixed can be equivalently a vector of integers corresponding to the indexes of the true values in the previous fixed version.
sigma.proposal	an optional argument specifying the standard deviation of the instrumental distribution of the Metropolis Hasting step of the Gibbs sampling algorithm. That can be a seldom value and then this standard distribution will be the same for all the parameters. Otherwise, it can be vector whose length is equal to the total number of parameters.
nb	an optional argument specifying when to stop the Gibbs sampling algorithm. If history=FALSE, nb represents the number of iterations of the Gibbs sampling algorithm. Otherwise, it represents the number of accepted simulated values for the different marginal posterior distributions of the parameters in the Metropolis Hasting step.
burn	an optional argument specifying the number of burn in iterations of the Gibbs sampling algorithm.
profile.alpha	an optional argument specifying if the likelihood is profiled in \alpha (the log likelihood is replaced by the contrast function, see contrast.mle.vam). If the likelihood is profiled the prior distribution of parameter \alpha is not used. However it must have been specified in the bayesian.vam object even if it is not used.
method	an optional argument to be used by the maximum likelihood method for computing the initialization of the Gibbs algorithm (see run.mle.vam).
verbose	an optional argument to be used by the maximum likelihood method for computing the initialization of the Gibbs algorithm (see run.mle.vam).
history	an optional argument defining how to stop the Gibbs sampling method and how to memorized its result. The plotting method plot.bayesian.vam needs to run the Bayesian method with history=TRUE, but that takes more computing time.
proposal	an optional argument specifying the instrumental distribution of the Metropolis Hasting step of the Gibbs sampling algorithm. Possible distributions are 'norm' for normal distribution and 'lnorm' for log-normal distribution. That can be a seldom value and then the used distribution will be the same for all the parameters. Otherwise, it can be vector whose length is equal to the total number of parameters.
...	some supplementary arguments for the maximum likelihood method used to compute the initialization of the Gibbs algorithm (see run.mle.vam).

Details

The standard deviation of the instrumental distribution of the Metropolis Hasting play an important part. It can be specified with the sigma.proposal argument. If it is too big or too small regarding to the parameter value space, the sampling method can be very long to converge. In fact the standard deviations, sigma.proposal, specifies how the marginal parameters spaces are explored. If the standard deviation is too small, only a little part of the parameter space is explored. If it is too big, the simulated parameters values would be ever rejected in the Metropolis Hasting step.

Value

The function produces an sample of the posterior parameter value which is memorized in mle.vam object. If history=FALSE, the method produces a list whose length is equal to the total number of parameters. Each element of this list corresponds to the sampled values for a parameter (in the same order as they appears in par0. If history=TRUE, the method produces a data frame. Each accepted marginal sampled value of a parameter is alliteratively memorizes in this data frame. The column ind specifies the index of the corresponding parameter (starting from 0). The sampled values is in the column estimate. If profile.alpha=TRUE, a third column called alpha provides the corresponding estimate of \alpha.

Author(s)

R. Drouilhet et L. Doyen

See Also

bayesian.vam to define the Bayesian object. coef.bayesian.vam to extract the parameters estimation values of the Bayesian method. summary.bayesian.vam to produce a result summary of the Bayesian method. hist.bayesian.vam for plotting the histogram of the posterior distribution of the parameters. plot.bayesian.vam for plotting estimating characteristics of the model.

Examples

simARAInf<-sim.vam(  ~ (ARAInf(.4) | Weibull(.001,2.5)))
simData<-simulate(simARAInf,30)
bayesARAInf <- bayesian.vam(Time & Type ~ (ARAInf(~Unif(0,1)) | Weibull(~Unif(0,1),~Unif(2,4))),data=simData)
run(bayesARAInf,profile.alpha=TRUE)
coef(bayesARAInf)
coef(bayesARAInf,par0=c(1e-2,2.5,0.5),fixed=2)

rcqls/VAM documentation built on Jan. 14, 2024, 9:07 p.m.