Remarks

save(DATA1, file = "YourPath/DATA1.RData")

load(DATA1, file = "YourPath/DATA1.RData")

str(DATA1)

List of 9
 $ LT            :List of 1
  ..$ : num [1, 1:7] 2.042 0.842 1.678 3.826 4.258 ...
 $ sLT           :List of 1
  ..$ : num [1, 1:7] 0.344 0.162 0.328 0.803 0.941 ...
 $ ITimes        :List of 1
  ..$ : num [1, 1:6] 15 30 60 100 0 15
 $ dLab          : num [1:2, 1] 1.53e-01 5.89e-05
 $ ddot_env      : num [1:2, 1] 2.512 0.0563
 $ regDose       :List of 1
  ..$ : num [1, 1:6] 2.3 4.6 9.21 15.35 0 ...
 $ J             : num 1
 $ K             : num 6
 $ Nb_measurement: num 16

LT_RegenDose(
  DATA = DATA1,
  Path = path,
  FolderNames = "samp1",
  SampleNames = "samp1",
  Nb_sample = 1,
  nrow = NULL
  )

Remark 1: MCMC trajectories

• If MCMC trajectories did not converge, you can add more iteration with the parameter Iter in the function Age_Computation(), for example Iter = 20000 or Iter = 50000.

• To increase the precision of prior distribution, if not specified before you can use the argument PriorAge. For example: PriorAge= c(0.01,10) for a young sample and PriorAge = c(10,100) for an old sample.

• If the trajectories are still not convergering, you should whether the choice you made with the argument distribution and dose-response curves are meaningful.

Remark 2: LIN_fit and Origin_fit, dose-response curves option

• By default, a saturating exponential plus linear dose response curve is expected. However, you choose other formula by changing arguments LIN_fit and Origin_fit in the function.

Remark 3: distribution, equivalent dose dispersion option

By default, a cauchy distribution is assumed, but you can choose another distribution by replacing the word cauchy by gaussian, lognormal_A or lognormal_M for the argument distribution.

The difference between the models: lognormal_A and lognormal_M is that the equivalent dose dispersion are distributed according to:

• a lognormal distribution with mean or average equal to the palaeodose for the first model
• a lognormal distribution with median equal to the palaeodose for the second model.

Remark 4: SavePdf and SaveEstimates option

These two arguments allow to save the results to files.

• SavePdf = TRUE create a PDF-file with MCMC trajectories of parameters A (age), D (palaeodose), sD (equivalent doses dispersion). You have to specify OutputFileName and OutputFilePath to define name and path of the PDF-file.

• SaveEstimates = TRUE saves a CSV-file containing the Bayes estimates, the credible interval at 68% and 95% and the Gelman and Rudin test of convergency of the parameters A, D, sD. For the export the arugments OutputTableName and OutputTablePath have to be specified.

Remark 4: PriorAge option

By default, an age between 0.01 ka and 100 ka is expected. If the user has more informations on the sample, PriorAge should be modified accordingly.

For example, if you know that the sample is an older, you can set PriorAge=c(10,120). In contrast, if you know that the sample is younger, you may want to set PriorAge=c(0.001,10). Ages of \(<=0\) are not possible. The minimum bound is 0.001.

Please note that the setting of PriorAge is not trivial, wrongly set boundaries are likely biasing your results.

Combine files using the function combine_DataFiles()

If the user has already saved informations imported with Generate_DataFile() function (or Generate_DataFile_MG() function) these data can be concatenate with the function combine_DataFiles().

For example, if DATA1 is the output of sample named “GDB3”, and DATA2 is the output of sample “GDB5”, both data can be merged with the following call:

data("DATA1", envir = environment())
data("DATA2", envir = environment())
DATA3 <- combine_DataFiles(L1 = DATA2, L2 = DATA1)
str(DATA3)

List of 9
 $ LT            :List of 2
  ..$ : num [1:188, 1:6] 4.54 2.73 2.54 2.27 1.48 ...
  ..$ : num [1:101, 1:6] 5.66 6.9 4.05 3.43 4.97 ...
 $ sLT           :List of 2
  ..$ : num [1:188, 1:6] 0.333 0.386 0.128 0.171 0.145 ...
  ..$ : num [1:101, 1:6] 0.373 0.315 0.245 0.181 0.246 ...
 $ ITimes        :List of 2
  ..$ : num [1:188, 1:5] 40 40 40 40 40 40 40 40 40 40 ...
  ..$ : num [1:101, 1:5] 160 160 160 160 160 160 160 160 160 160 ...
 $ dLab          : num [1:2, 1:2] 1.53e-01 5.89e-05 1.53e-01 5.89e-05
 $ ddot_env      : num [1:2, 1:2] 2.512 0.0563 2.26 0.0617
 $ regDose       :List of 2
  ..$ : num [1:188, 1:5] 6.14 6.14 6.14 6.14 6.14 6.14 6.14 6.14 6.14 6.14 ...
  ..$ : num [1:101, 1:5] 24.6 24.6 24.6 24.6 24.6 ...
 $ J             : num [1:2] 188 101
 $ K             : num [1:2] 5 5
 $ Nb_measurement: num [1:2] 14 14

The data structure should become as follows

• 2 lists (1 list per sample) for DATA$LT, DATA$sLT, DATA1$ITimes and DATA1$regDose
• A matrix with 2 columns (1 line per sample) for DATA1$dLab, DATA1$ddot_env
• 2 integers (1 integer per BIN files here we have 1 BIN-file per sample) for DATA1$J, DATA1$K, DATA1$Nb_measurement.

Single-grain and multiple-grain OSL measurements can be merged in the same way. To plot the \(L/T\) as a function of the regenerative dose the function LT_RegenDose() can be used again:

LT_RegenDose(
  DATA = DATA3,
  Path = path,
  FolderNames = Names,
  Nb_sample = nbsample,
  SG = rep(TRUE, nbsample)
)

Note: In the example DATA3 contains information from the samples ‘GDB3’ and ‘GDB5’, which are single-grain OSL measurements. For a correct treatment the argument SG has to be manually set be the user. Please see the function manual for further details.

Remarks

If the MCMC trajectories did not converge, we refer to the comments above.

As for the function Age_computation(), the age for each sample is set by default between 0.01 ka and 100 ka. If you have more informations on your samples it is possible to change PriorAge parameters. PriorAge is a vector of size = 2*$Nb_sample, the two first values of PriorAge concern the 1st sample, the next two values the 2nd sample and so on.

For example, if you know that sample named GDB5 is a young sample whose its age is between 0.01 ka and 10 ka, and GDB3 is an old sample whose age is between 10 ka and 100 ka, \[PriorAge=c(\underbrace{0.01,10}_{GDB5\ prior\ age},\underbrace{10,100}_{GDB3\ prior\ age})\]

Ordering samples

To take into account stratigraphic constraints, the information on the samples need to be ordered. Either you enter a sample name (corresponding to subfolder names) in Names parameter of the function Generate_DataFile(), ordered by order of increasing ages or you enter saved .RData informations of each sample in combine_DataFiles(), ordered by increasing ages.

# using Generate_DataFile function
Names <- c("samp1", "samp2")
nbsample <- 2
DATA3 <- Generate_DataFile(
  Path = path,
  FolderNames = Names,
  Nb_sample = nbsample,
  verbose = FALSE
)

# using the function combine_DataFiles()
data(DATA1, envir = environment()) # .RData on sample GDB3
data(DATA2, envir = environment()) # .RData on sample GDB5
DATA3 <- combine_DataFiles(L1 = DATA1, L2 = DATA2)

Define matrix to set stratigraphic constraints

Let SC be the matrix containing all information on stratigraphic relations for this two samples. This matrix is defined as follows:

• matrix dimensions: the row number of StratiConstraints matrix is equal to Nb_sample+1, and column number is equal to \(Nb\_sample\).

• first matrix row: for all \(i\) in \(\{1,...,Nb\_Sample\}\), StratiConstraints[1,i] <- 1, means that the lower bound of the sample age given in PriorAge[2i-1] for the sample whose number ID is equal to \(i\) is taken into account

• sample relations: for all \(j\) in ${2,…,Nb_Sample+1}$ and all \(i\) in \(\{j,...,Nb\_Sample\}\), StratiConstraints[j,i] <- 1 if the sample age whose ID is equal to \(j-1\) is lower than the sample age whose ID is equal to \(i\). Otherwise, StratiConstraints[j,i] <- 0.

To the define such matrix the function SCMatrix() can be used:

SC <- SCMatrix(Nb_sample = 2,
               SampleNames = c("samp1", "samp2"))

In our case: 2 samples, SC is a matrix with 3 rows and 2 columns. The first row contains c(1,1) (because we take into account the prior ages), the second line contains c(0,1) (sample 2, named samp2 is supposed to be older than sample 1, named samp1) and the third line contains c(0,0) (sample 2, named samp2 is not younger than the sample 1, here named samp1). We can also fill the matrix with the stratigraphic relations as follow:

SC <- matrix(
  data = c(1, 1, 0, 1, 0, 0),
  ncol = 2,
  nrow = (2 + 1),
  byrow = T
  )

Age computation

Age <-
  AgeS_Computation(
  DATA = DATA3,
  Nb_sample = 2,
  SampleNames = c("samp1", "samp2"),
  PriorAge = priorage,
  distribution = "cauchy",
  LIN_fit = TRUE,
  Origin_fit = FALSE,
  StratiConstraints = SC,
  Iter = 1000
  )

Compiling model graph
   Resolving undeclared variables
   Allocating nodes
Graph information:
   Observed stochastic nodes: 1445
   Unobserved stochastic nodes: 1739
   Total graph size: 20624

Initializing model

Warning: [plot_MCMC()] 'n.iter' out of range, reset to number of observations

>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
 Sample name:  samp1 
---------------------
         Point estimate Uppers confidence interval
A_samp1      1.02        1.04 
D_samp1      1.01        1.03 
sD_samp1     1       1.02 
----------------------------------------------
 Sample name:  samp2 
---------------------
         Point estimate Uppers confidence interval
A_samp2      1.02        1.03 
D_samp2      1       1 
sD_samp2     1.03        1.09 


---------------------------------------------------------------------------------------------------
 *** WARNING: The following information are only valid if the MCMC chains have converged  ***
---------------------------------------------------------------------------------------------------



>> Bayes estimates of Age, Palaeodose and its dispersion for each sample and credible interval <<
----------------------------------------------
 Sample name:  samp1 
---------------------
Parameter    Bayes estimate       Credible interval 
 A_samp1     9.709 
                         lower bound     upper bound
                 at level 95%    9.14        10 
                 at level 68%    9.67        10 

Parameter    Bayes estimate       Credible interval 
 D_samp1     29.14 
                         lower bound     upper bound
                 at level 95%    24.15       33.88 
                 at level 68%    27.04       31.98 

Parameter    Bayes estimate       Credible interval 
sD_samp1     68.34 
                         lower bound     upper bound
                 at level 95%    51.4        87.58 
                 at level 68%    59.34       78 
----------------------------------------------
 Sample name:  samp2 
---------------------
Parameter    Bayes estimate       Credible interval 
 A_samp2     10.39 
                         lower bound     upper bound
                 at level 95%    10          11.24 
                 at level 68%    10          10.43 

Parameter    Bayes estimate       Credible interval 
 D_samp2     18.26 
                         lower bound     upper bound
                 at level 95%    17.11       19.3 
                 at level 68%    17.56       18.78 

Parameter    Bayes estimate       Credible interval 
sD_samp2     4.595 
                         lower bound     upper bound
                 at level 95%    3.49        5.5 
                 at level 68%    3.96        4.92 

----------------------------------------------