chronoOutliers_Gauss {ArchaeoChron} R Documentation

## Bayesian chronologies of Gaussian dates using the outlier modelling of Oxcal software

### Description

Bayesian modeling for combining Gaussian dates. These dates are assumed to be contemporaneous of the event date. The posterior distribution is sampled by a MCMC algorithm as well as those of all parameters of the Bayesian model.

### Usage

```chronoOutliers_Gauss(M, s, refYear=NULL, outliersIndivVariance, outliersBernouilliProba,
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 for coversion into calendar dates `outliersIndivVariance` vector of individual variance for delta[i] `outliersBernouilliProba` vector of Bernouilli probability for each date. Reflects a prior assumption that the date is an outlier. `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.

### Author(s)

Anne Philippe & Marie-Anne Vibet

### References

Bronk Ramsey C., Dealing with outliers and offsets in Radiocarbon dating, Radiocarbon, 2009, 51:1023-45.

### Examples

```  ### simulated data (see examples(chronoEvent_Gauss))

# Number of event
Nevt  = 3
# number of dates by events
measurementsPerEvent = c(2,3,2)
# positions
pos = 1 + c(0, cumsum(measurementsPerEvent) )

# simulation of data
theta.evt = seq(1,10, length.out= Nevt)
theta.evt[3] <- theta.evt[3] - 3 # stratigraphic inversion

theta = NULL
for(i in 1:Nevt ){
theta = c(theta, rep(theta.evt[i],measurementsPerEvent[i]))
}

s = seq(1,1, length.out= sum(measurementsPerEvent))

M=NULL
for( i in 1:sum(measurementsPerEvent)){
M= c(M, rnorm(1, theta[i], s[i] ))
}

MCMCSample = chronoOutliers_Gauss(M, s, outliersIndivVariance = rep(5,7),
outliersBernouilliProba=rep(0.2,7), studyPeriodMin=-10, studyPeriodMax=30,
numberAdapt = 1000, numberUpdate = 1000, numberSample = 5000)
plot(MCMCSample)
```

[Package ArchaeoChron version 0.1 Index]