combinationWithRandomEffect_Gauss {ArchaeoChron} R Documentation

## Bayesian modeling for combining Gaussian dates with a random effect

### Description

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.

### Usage

combinationWithRandomEffect_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

### 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)

• theta ~ U(ta, tb)

• sigma ~ UniformShrinkage

### 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.

### Author(s)

Anne Philippe & Marie-Anne Vibet

### References

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

### Examples

  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)


[Package ArchaeoChron version 0.1 Index]