mcmc: Obtain posterior samples for all model parameters

Description

This is the function to actually run the MCMC machinery to produce posterior samples from all model parameters and required derived values. It is a generic function, so that customized versions may be conveniently defined for specific subclasses of GeneralData, GeneralModel, and McmcOptions input.

Usage

mcmc(data, model, options, ...)
# S4 method for GeneralData,GeneralModel,McmcOptions
mcmc(
  data,
  model,
  options,
  program = c("JAGS"),
  verbose = FALSE,
  fromPrior = data@nObs == 0L,
  ...
)
# S4 method for DataMixture,GeneralModel,McmcOptions
mcmc(
  data,
  model,
  options,
  fromPrior = data@nObs == 0L & data@nObsshare == 0L,
  ...
)
# S4 method for Data,LogisticIndepBeta,McmcOptions
mcmc(data, model, options, ...)
# S4 method for DataDual,Effloglog,McmcOptions
mcmc(data, model, options, ...)
# S4 method for DataDual,EffFlexi,McmcOptions
mcmc(data, model, options, ...)

Value

The posterior samples, an object of class Samples.

Arguments

data: The data input, an object of class GeneralData
model: The model input, an object of class GeneralModel
options: MCMC options, an object of class McmcOptions
...: unused
program: the program which shall be used: currently only “JAGS” is supported
verbose: shall progress bar and messages be printed? (not default)
fromPrior: sample from the prior only? Defaults to checking if nObs is 0. For some models it might be necessary to specify it manually here though.

Functions

mcmc(data = GeneralData, model = GeneralModel, options = McmcOptions): Standard method which uses JAGS
mcmc(data = DataMixture, model = GeneralModel, options = McmcOptions): Method for DataMixture with different fromPrior default
mcmc(data = Data, model = LogisticIndepBeta, options = McmcOptions): Obtain posterior samples for the model parameters based on the pseudo 'LogisticsIndepBeta' DLE model. The joint prior and posterior probability density function of the intercept $ϕ_{1}$ (phi1) and the slope $ϕ_{2}$ (phi2) are given in Whitehead and Williamson (1998) and TsuTakawa (1975). However, since asymptotically, the joint posterior probability density will be bivariate normal and we will use the bivariate normal distribution to generate posterior samples of the intercept and the slope parameters. For the prior samples of of the intercept and the slope a bivariate normal distribution with mean and the covariance matrix given in Whitehead and Williamson (1998) is used.
mcmc(data = DataDual, model = Effloglog, options = McmcOptions): Obtain the posterior samples for the model parameters in the Efficacy log log model. Given the value of $ν$ , the precision of the efficacy responses, the joint prior or the posterior probability of the intercept $θ_{1}$ (theta1) and the slope $θ_{2}$ (theta2) is a bivariate normal distribtuion. The $ν$ (nu), the precision of the efficacy responses is either a fixed value or has a gamma distribution. If a gamma distribution is used, the samples of nu will be first generated. Then the mean of the of the nu samples will be used the generate samples of the intercept and slope parameters of the model
mcmc(data = DataDual, model = EffFlexi, options = McmcOptions): Obtain the posterior samples for the estimates in the Efficacy Flexible form. This is the mcmc procedure based on what is described in Lang and Brezger (2004) such that samples of the mean efficacy responses at all dose levels, samples of sigma2 $s i g m a^{2}$ , the variance of the efficacy response and samples of sigma2betaW $s i g m a_{b e t a_{W}}^{2}$ , the variance of the random walk model will be generated. Please refer to Lang and Brezger (2004) for the procedures and the form of the joint prior and posterior probability density for the mean efficay responses. In addition, both sigma2 and sigma2betaW acan be fixed or having an inverse-gamma prior and posterior distribution. Therefore, if the inverse gamma distribution(s) are used, the parameters in the distribution will be first updated and then samples of sigma2 and sigma2betaW will be generated using the updated parameters.

Details

Reproducible samples can be obtained by setting the seed via set.seed before in the user code as usual. However, note that because the RNG sampler used is external to R, running this MCMC function will not change the seed position -- that is, the repeated call to this function will then result in exactly the same output.

Examples

Run this code


# create some data from the class 'Data'
myData <- Data(x=c(0.1,0.5,1.5,3,6,10,10,10),
               y=c(0,0,0,0,0,0,1,0),
               doseGrid=c(0.1,0.5,1.5,3,6,
                          seq(from=10,to=80,by=2)))

# Initialize the CRM model 
model <- LogisticLogNormal(mean=c(-0.85, 1),
                           cov=
                             matrix(c(1, -0.5, -0.5, 1),
                                    nrow=2),
                           refDose=56)


# Sample from the posterior distribution
options <- McmcOptions(burnin=100,
                       step=2,
                       samples=1000)

samples <- mcmc(data = myData, model = model, options=options)


##obtain mcmc DLE samples given the data, LogisticIndepBeta (DLE model) and mcmc simulations options
## data must be of 'Data' class
data<-Data(x=c(25,50,50,75,100,100,225,300),y=c(0,0,0,0,1,1,1,1),
           doseGrid=seq(25,300,25))
## model must be of 'LogisticIndepBeta' class
model<-LogisticIndepBeta(binDLE=c(1.05,1.8),DLEweights=c(3,3),DLEdose=c(25,300),data=data)
## options must be ''McmcOptions' class
options<-McmcOptions(burnin=100,step=2,samples=200)
set.seed(94)
samples<-mcmc(data=data,model=model,options=options)
##obtain mcmc efficacy samples given the data, 'Effloglog' model (efficacy model) and
## mcmc simulations options data must be of 'DataDual' class
data<-DataDual(x=c(25,50,25,50,75,300,250,150),
              y=c(0,0,0,0,0,1,1,0),
              w=c(0.31,0.42,0.59,0.45,0.6,0.7,0.6,0.52),
              doseGrid=seq(25,300,25),placebo=FALSE)
## model must be of 'Effloglog' class
Effmodel<-Effloglog(Eff=c(1.223,2.513),Effdose=c(25,300),nu=c(a=1,b=0.025),data=data,c=0)

## options must be ''McmcOptions' class
options<-McmcOptions(burnin=100,step=2,samples=200)
set.seed(94)
samples<-mcmc(data=data,model=Effmodel,options=options)
##obtain mcmc efficacy samples given the data, 'EffFlexi' model (efficacy model) and 
## mcmc simulations options
## data must be of 'DataDual' class
data<-DataDual(x=c(25,50,25,50,75,300,250,150),
               y=c(0,0,0,0,0,1,1,0),
               w=c(0.31,0.42,0.59,0.45,0.6,0.7,0.6,0.52),
               doseGrid=seq(25,300,25))
## model must be of 'EffFlexi' class

Effmodel<- EffFlexi(Eff=c(1.223, 2.513),Effdose=c(25,300),
                    sigma2=c(a=0.1,b=0.1),sigma2betaW=c(a=20,b=50),smooth="RW2",data=data)

## options must be ''McmcOptions' class
options<-McmcOptions(burnin=100,step=2,samples=200)
set.seed(94)
samples<-mcmc(data=data,model=Effmodel,options=options)

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