Likelihood of OSL samples for JAGS models use in Age_OSLC14

A list of models for OSL data to define likelyhood in JAGS models.

data("ModelOSL")

Format

This list contains:

AgesMultiCS2_EXPLIN

a list of 4 models that all consider a saturating exponential plus linear growth. These 4 models have different distribution to describe equivalent dose values around the palaeodose.

AgesMultiCS2_EXP

a list of 4 models that all consider a saturating exponential growth. These 4 models have different distribution to describe equivalent dose values around the palaeodose.

AgesMultiCS2_EXPZO

a list of 4 models that all consider a saturating exponential plus linear growth and fitting through the origin. These 4 models have different distribution to describe equivalent dose values around the palaeodose.

AgesMultiCS2_EXPLINZO

a list of 4 models that all consider a saturating exponential growth and fitting through the origin. These 4 models have different distribution to describe equivalent dose values around the palaeodose.

Details

The different distibutions to describe equivalent dose values around the palaeodose are:

cauchy

a Cauchy distribution with postition parameter equal to the palaeodose of the sample

gaussian

a Gaussian distribution with mean equal to the palaeodose of the sample

lognormal_A

a log-normal distribution with mean or Average equal to the palaeodose of the sample

lognormal_M

a log-normal distribution with Median equal to the palaeodose of the sample

For more information we refer to the function AgeS_Computation, section Details.

References

Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd international workshop on distributed statistical computing, volume 124, page 125. Technische Universit at Wien, Austria.

Plummer, M. (2015). JAGS Version 4.0. 0 user manual.

Examples

data(ModelOSL)
## The JAGS model of the likelyhood for a saturating exponential plus linear growth
## (a function of the type \code{f(x)=a(1-exp(-x/b))+cx+d})
## and a gaussian distribution of equivalent doses around the palaeodose:
writeLines(ModelOSL$AgesMultiOSL_EXPLIN$gaussian)
#> D~dmnorm(mu,omega)
#> for(i1 in ind_OSL){
#>   sD[CS_OSL[i1]]~dt(0,pow(0.16*D[CS_OSL[i1]],-2),1)T(0,)
#>   pD[CS_OSL[i1]]<-pow(sD[CS_OSL[i1]],-2)
#>   mu[CS_OSL[i1]]<-A[i1]*ddot[CS_OSL[i1]]
#>   for(i2 in ind_OSL){
#>     Sigma[CS_OSL[i1],CS_OSL[i2]]=A[i1]*A[i2]*Gamma[CS_OSL[i1],CS_OSL[i2]]
#>   }
#> }
#> omega<-inverse(Sigma)
#> 
#> # Likelihood:
#> for(i in ind_OSL){
#>   for(bf in (CSBinPerSample[CS_OSL[i]]-BinPerSample[CS_OSL[i]]+1):(CSBinPerSample[CS_OSL[i]])){
#>     for(j in 1:J[bf]){
#>       # prior on growth function
#>       xa[(index[bf]+j)]~dnorm(6.5,1/(9.2^2))T(0,)
#>       xb[(index[bf]+j)]~dnorm(50,1/(1000^2))T(0,)
#>       xc[(index[bf]+j)]~dnorm(0.002,1/(0.01^2))T(0,)
#>       xd[(index[bf]+j)]~dnorm(0.5,1/(2.5^2))T(-xa[(index[bf]+j)],)
#>       sigmaf[(index[bf]+j)]~dexp(20)
#>       
#>       De[(index[bf]+j),1]~dnorm(D[CS_OSL[i]],pD[CS_OSL[i]])
#>       #
#>       xprecision[(index[bf]+j),1]<-1/(sigmaf[(index[bf]+j)]^2+sN[(index[bf]+j),1]^2) ##<-- ???? sN[j,1]^2 ????
#>       N[(index[bf]+j),1]~dnorm(xQ[(index[bf]+j),1],xprecision[(index[bf]+j),1])
#>       xQ[(index[bf]+j),1]<-xa[(index[bf]+j)]*(1-exp(-De[(index[bf]+j),1]/xb[(index[bf]+j)]))+xc[(index[bf]+j)]*De[(index[bf]+j),1]+xd[(index[bf]+j)]
#>       
#>       for(k in 2:K[bf]){
#>         xprecision[(index[bf]+j),k]<-1/(sigmaf[(index[bf]+j)]^2+sN[(index[bf]+j),k]^2)
#>         N[(index[bf]+j),k]~dnorm(xQ[(index[bf]+j),k],xprecision[(index[bf]+j),k])
#>         xQ[(index[bf]+j),k]<-xa[(index[bf]+j)]*(1-exp(-De[(index[bf]+j),k]/xb[(index[bf]+j)]))+xc[(index[bf]+j)]*De[(index[bf]+j),k]+xd[(index[bf]+j)]
#>         De[(index[bf]+j),k]<-IT[(index[bf]+j),(k-1)]*sDlab[bf]
#>       }
#>     }
#>   }
#> }