combinationWithRandomEffect: Bayesian modeling for combining Gaussian dates with a random...
In ArchaeoChron: Bayesian Modeling of Archaeological Chronologies

Description Usage Arguments Details Value Author(s) References Examples

Bayesian modeling for combining Gaussian dates with known variance and with the addition of a random effect. These dates are assumed to be contemporaneous of the target date and have non identical distributions as the variance may be different for each date. In addition, a random effect is introduced in the modelling by a shrinkage distribution as defined by Congdom (2010). The posterior distribution of the modeling is sampled by a MCMC algorithm implemented in JAGS.

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combinationWithRandomEffect_Gauss(M, s, refYear=NULL, studyPeriodMin, studyPeriodMax, 
        numberChains = 2, numberAdapt = 10000, numberUpdate = 10000, 
        variable.names = c("theta"), numberSample = 50000, thin = 10)

`M`	vector of measurement
`s`	vector of measurement errors
`refYear`	vector of year of reference for ages
`studyPeriodMin`	numerical value corresponding to the start of the study period in BC/AD format
`studyPeriodMax`	numerical value corresponding to the end of the study period in BC/AD format
`numberChains`	number of Markov chains simulated
`numberAdapt`	number of iterations in the Adapt period of the MCMC algorithm
`numberUpdate`	number of iterations in the Update period of the MCMC algorithm
`variable.names`	names of the variables whose Markov chains are kept
`numberSample`	number of iterations in the Acquire period of the MCMC algorithm
`thin`	step between consecutive iterations finally kept

If there are Nbobs measurements M associated with their error s, the model is the following one :

for j in (1:Nbobs)
- Mj ~ N(muj, sj^2)
- muj ~ N(theta, sigmai^2)
theta ~ U(ta, tb)
sigma ~ UniformShrinkage

This function returns a Markov chain of the posterior distribution. The MCMC chain is in date format BC/AD, that is the reference year is 0. Only values for the variables defined by 'variable.names' are given.

Anne Philippe & Marie-Anne Vibet

Congdom P. D., Bayesian Random Effect and Other Hierarchical Models: An Applied Perspective,Chapman and Hall/CRC, 2010

  data(sunspot)
  MCMC = combinationWithRandomEffect_Gauss(M=sunspot$Age[1:10], s= sunspot$Error[1:10], 
  refYear=rep(2016,10), studyPeriodMin=0, studyPeriodMax=1500, variable.names = c('theta'))
  plot(MCMC)
  gelman.diag(MCMC)