ArchaeoChron (version 0.1)

eventModel_Gauss: Bayesian modeling for combining Gaussian dates using the Event Model

Description

Bayesian modeling for combining Gaussian dates. These dates are assumed to be contemporaneous of the event date. The posterior distribution of the event date is sampled by MCMC algorithm as well as those of all parameters of the Bayesian model as described in Lanos & Philippe (2017).

Usage

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

Arguments

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

Value

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.

Details

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)

  • sigmai ~ UniformShrinkage

• theta ~ U(ta, tb)

References

P. Lanos and A. Philippe. Hierarchical Bayesian Modeling for Combining Dates in Archaeological Context. Journal de la SFdS, Vol. 158 (2) pp 72-88 2017.

Examples

# NOT RUN {
  data(sunspot)
  MCMC = eventModel_Gauss(M=sunspot$Age[1:10], s= sunspot$Error[1:10], refYear=rep(2016,10), 
  studyPeriodMin=900, studyPeriodMax=1500, variable.names = c('theta'))
  plot(MCMC)
  gelman.diag(MCMC)
# }