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]