`'BayLum'`

provides a collection of various
**R** functions for Bayesian analysis of luminescence data.
Amongst others, this includes data import, export, application of age
models and palaeodose modelling.

Data can be processed simultaneously for various samples, including the input of multiple BIN/BINX-files per sample for single grain (SG) or multi-grain (MG) OSL measurements. Stratigraphic constraints and systematic errors can be added to constrain the analysis further.

For those who already know how to use **R**,
`'BayLum'`

won’t be difficult to use, for all others, this
brief introduction may be of help to make the first steps with
**R** and the package `'BayLum'`

as convenient
as possible.

If you read this document before having installed **R**
itself, you should first visit the R
project website and download and install **R**. You may
also consider installing Rstudio, which
provides an excellent desktop working environment for
**R**; however it is not a prerequisite.

You will also need the external software *JAGS* (Just Another
Gibs Sampler). Please visit the JAGS webpage and follow the
installation instructions. Now you are nearly ready to work with
‘BayLum’.

If you have not yet installed `BayLum’, please run the following two
**R** code lines to install ‘BayLum’ on your computer.

```
if(!require("BayLum"))
install.packages("BayLum", dependencies = TRUE)
```

Alternatively, you can load an already installed **R**
package (here ‘BayLum’) into your session by using the following
**R** call.

`library(BayLum)`

Let us consider the sample named *samp1*, which is the example
dataset coming with the package. All information related to this sample
is stored in a subfolder called also *samp1*. To test the package
example, first, we add the path of the example dataset to the object
`path`

.

`<- paste0(system.file("extdata/", package = "BayLum"), "/") path `

Please note that for your own dataset (i.e. not included in the package) you have to replace this call by something like:

`<- "Users/Master_of_luminescence/Documents/MyFamousOSLData" path `

In our example the folder contains the following subfolders and files:

1 | FER1/bin.BIN |

2 | FER1/Disc.csv |

3 | FER1/DoseEnv.csv |

4 | FER1/DoseSource.csv |

5 | FER1/rule.csv |

6 | samp1/bin.BIN |

7 | samp1/DiscPos.csv |

8 | samp1/DoseEnv.csv |

9 | samp1/DoseSource.csv |

10 | samp1/rule.csv |

11 | samp2/bin.BIN |

12 | samp2/DiscPos.csv |

13 | samp2/DoseEnv.csv |

14 | samp2/DoseSource.csv |

15 | samp2/rule.csv |

See *“What are the required files in each subfolder?”* in the
manual of `Generate_DataFile()`

function for the meaning of
these files.

To import your data, simply call the function
`Generate_DataFile()`

:

```
<-
DATA1 Generate_DataFile(
Path = path,
FolderNames = "samp1",
Nb_sample = 1,
verbose = FALSE)
```

The import may take a while, in particular for large BIN/BINX-files. This can become annoying if you want to play with the data. In such situations, it makes sense to save your imported data somewhere else before continuing.

To save the obove imported data on your hardrive use

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

To load the data use

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

To see the overall structure of the data generated from the BIN/BINX-file and the associated CSV-files, the following call can be used:

`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
```

It reveals that `DATA1`

is basically a list with 9
elements:

Element | Content |
---|---|

`DATA1$LT` |
Lx/Tx values from each sample |

`DATA1$sLT` |
Lx/Tx error values from each sample |

`DATA1$ITimes` |
Irradiation times |

`DATA1$dLab` |
The lab dose rate |

`DATA1$ddot_env` |
The environmental dose rate and its variance |

`DATA1$regDose` |
The regenarated dose points |

`DATA1$J` |
The number of aliquots selected for each BIN-file |

`DATA1$K` |
The number of regenarted dose points |

`DATA1$Nb_measurement` |
The number of measurements per BIN-file |

To get an impression on how your data look like, you can visualise
them by using the function `LT_RegenDose()`

:

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

Note that here we consider only one sample, and the name of the
folder is the name of the sample. For that reason the argumetns were set
to `FolderNames = samp1`

and
`SampleNames = samp1`

.

For a multi-grain OSL measurements, instead of
`Generate_DataFile()`

, the function
`Generate_DataFile_MG()`

should be used with similar
parameters. The functions differ by their expectations:
*Disc.csv* instead of *DiscPos.csv* file for Single-grain
OSL Measurements. Please check type `?Generate_DataFile_MG`

for further information.

To compute the age of the sample *samp1*, you can run the
following code:

```
<- Age_Computation(
Age DATA = DATA1,
SampleName = "samp1",
PriorAge = c(10, 100),
distribution = "cauchy",
LIN_fit = TRUE,
Origin_fit = FALSE,
Iter = 10000
)
```

```
Compiling model graph
Resolving undeclared variables
Allocating nodes
Graph information:
Observed stochastic nodes: 6
Unobserved stochastic nodes: 9
Total graph size: 139
Initializing model
```

```
>> Sample name <<
----------------------------------------------
samp1
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Point estimate Uppers confidence interval
A 1.026 1.05
D 1.027 1.053
sD 1.091 1.105
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
---------------------------------------------------------------------------------------------------
parameter Bayes estimate Credible interval
----------------------------------------------
A 23.1
lower bound upper bound
at level 95% 10 50.094
at level 68% 10 20.619
----------------------------------------------
D 57.535
lower bound upper bound
at level 95% 21.362 124.947
at level 68% 21.794 51.767
----------------------------------------------
sD 38.076
lower bound upper bound
at level 95% 0.116 136.59
at level 68% 1.109 28.869
```

This also works if `DATA1`

is the output of
`Generate_DataFile_MG()`

.

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`

. If it is not desirable to re-run the model from scratch, read theTo 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.

`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.

`distribution`

, equivalent dose dispersion
optionBy 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 log-normal distribution with mean or average equal to the palaeodose for the first model
- a log-normal distribution with median equal to the palaeodose for the second model.

`SavePdf`

and `SaveEstimates`

optionThese 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 convergence of the parameters`A`

,`D`

,`sD`

. For the export the arguments`OutputTableName`

and`OutputTablePath`

have to be specified.

`PriorAge`

optionBy 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.**

In the previous example we considered only the simplest case: one
sample, and one BIN/BINX-file. However, ‘BayLum’ allows to process
multiple BIN/BINX-files for one sample. To work with multiple
BIN/BINX-files, the names of the subfolders need to beset in argument
`Names`

and both files need to be located unter the same
`Path`

.

For the case

`<- c("samp1", "samp2") Names `

the call `Generate_DataFile()`

(or
`Generate_DataFile_MG()`

) becomes as follows:

```
##argument setting
<- 1
nbsample <- length(Names)
nbbinfile <- c(length(Names))
Binpersample
##call data file generator
<- Generate_DataFile(
DATA_BF Path = path,
FolderNames = Names,
Nb_sample = nbsample,
Nb_binfile = nbbinfile,
BinPerSample = Binpersample,
verbose = FALSE
)
##calculate the age
<- Age_Computation(
Age DATA = DATA_BF,
SampleName = Names,
BinPerSample = Binpersample
)
```

```
Compiling model graph
Resolving undeclared variables
Allocating nodes
Graph information:
Observed stochastic nodes: 12
Unobserved stochastic nodes: 15
Total graph size: 221
Initializing model
```

```
>> Sample name <<
----------------------------------------------
samp1 samp2
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Point estimate Uppers confidence interval
A 1.054 1.09
D 1.057 1.095
sD 1.008 1.01
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
---------------------------------------------------------------------------------------------------
parameter Bayes estimate Credible interval
----------------------------------------------
A 2.383
lower bound upper bound
at level 95% 1.22 3.449
at level 68% 1.79 2.79
----------------------------------------------
D 5.933
lower bound upper bound
at level 95% 3.392 8.431
at level 68% 4.431 6.7
----------------------------------------------
sD 0.861
lower bound upper bound
at level 95% 0.001 2.657
at level 68% 0.002 0.76
```

The function `Generate_DataFile()`

(or
`Generate_DataFile_MF()`

) can process multiple files
simultaneously including multiple BIN/BINX-files per sample.

We assume that we are interested in two samples named:
*sample1* and *sample2*. In addition, we have two
BIN/BINX-files for the first sample named: *sample1-1* and
*sample1-2*, and one BIN-file for the 2nd sample named
*sample2-1*. In such case, we need three subfolders named
*sample1-1*, *sample1-2* and *sample2-1*; which
each subfolder containing only one BIN-file named
**bin.BIN**, and its associated files
**DiscPos.csv**, **DoseEnv.csv**,
**DoseSourve.csv** and **rule.csv**. All of
these 3 subfolders must be located in *path*.

To fill the argument corectly `BinPerSample`

: \(binpersample=c(\underbrace{2}_{\text{sample 1: 2
bin files}},\underbrace{1}_{\text{sample 2: 1 bin file}})\)

```
<-
Names c("sample1-1", "sample1-2", "sample2-1") # give the name of the folder datat
<- 2 # give the number of samples
nbsample <- 3 # give the number of bin files
nbbinfile <- Generate_DataFile(
DATA Path = path,
FolderNames = Names,
Nb_sample = nbsample,
Nb_binfile = nbbinfile,
BinPerSample = binpersample
)
```

`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())
<- combine_DataFiles(L1 = DATA2, L2 = DATA1)
DATA3 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
`list`

s (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
`integer`

s (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 by the user. Please see the function manual for further
details.*

If no stratigraphic constraints were set, the following code can be
used to analyse the age of the sample *GDB5* and *GDB3*
simultaneously.

```
= c(1, 10, 10, 100)
priorage <- AgeS_Computation(
Age DATA = DATA3,
Nb_sample = 2,
SampleNames = c("GDB5", "GDB3"),
PriorAge = priorage,
distribution = "cauchy",
LIN_fit = TRUE,
Origin_fit = FALSE,
Iter = 1000,
jags_method = "rjags"
)
```

`Warning: No initial values were provided - JAGS will use the same initial values for all chains`

```
Compiling rjags model...
Calling the simulation using the rjags method...
Adapting the model for 1000 iterations...
Burning in the model for 4000 iterations...
Running the model for 5000 iterations...
Simulation complete
Calculating summary statistics...
Calculating the Gelman-Rubin statistic for 6 variables....
Finished running the simulation
```

```
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Sample name: GDB5
---------------------
Point estimate Uppers confidence interval
A_GDB5 1.005 1.017
D_GDB5 1.048 1.157
sD_GDB5 1.003 1.012
----------------------------------------------
Sample name: GDB3
---------------------
Point estimate Uppers confidence interval
A_GDB3 1.001 1.004
D_GDB3 1.008 1.03
sD_GDB3 1.012 1.043
---------------------------------------------------------------------------------------------------
*** 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: GDB5
---------------------
Parameter Bayes estimate Credible interval
A_GDB5 7.122
lower bound upper bound
at level 95% 5.785 8.521
at level 68% 6.299 7.673
Parameter Bayes estimate Credible interval
D_GDB5 17.818
lower bound upper bound
at level 95% 16.618 18.909
at level 68% 17.232 18.38
Parameter Bayes estimate Credible interval
sD_GDB5 4.448
lower bound upper bound
at level 95% 3.402 5.444
at level 68% 3.914 4.945
----------------------------------------------
Sample name: GDB3
---------------------
Parameter Bayes estimate Credible interval
A_GDB3 47.164
lower bound upper bound
at level 95% 36.607 57.864
at level 68% 40.845 51.644
Parameter Bayes estimate Credible interval
D_GDB3 104.87
lower bound upper bound
at level 95% 97.176 112.142
at level 68% 101.201 108.674
Parameter Bayes estimate Credible interval
sD_GDB3 16.087
lower bound upper bound
at level 95% 10.605 22.227
at level 68% 12.909 19.039
----------------------------------------------
```

**Note:** For an automated parallel processing you can
set the argument `jags_method = "rjags"`

to
`jags_method = "rjparallel"`

.

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, \[PriorAge=c(\underbrace{0.01,10}_{GDB5\ prior\
age},\underbrace{10,100}_{GDB3\ prior\ age})\]

With the function `AgeS_Computation()`

it is possible to
take the stratigraphic relations between samples into account and define
constraints.

For example, we know that *GDB5* is in a higher
stratigraphical position, hence it likely has a younger age than sample
*GDB3*.

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
<- c("samp1", "samp2")
Names <- 2
nbsample <- Generate_DataFile(
DATA3 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
<- combine_DataFiles(L1 = DATA1, L2 = DATA2) DATA3
```

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 accountsample 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:

```
<- SCMatrix(Nb_sample = 2,
SC 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:

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

```
<-
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,
jags_method = 'rjags')
```

`Warning: No initial values were provided - JAGS will use the same initial values for all chains`

```
Compiling rjags model...
Calling the simulation using the rjags method...
Adapting the model for 1000 iterations...
Burning in the model for 4000 iterations...
Running the model for 5000 iterations...
Simulation complete
Calculating summary statistics...
Calculating the Gelman-Rubin statistic for 6 variables....
Finished running the simulation
```

```
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Sample name: samp1
---------------------
Point estimate Uppers confidence interval
A_samp1 1.005 1.01
D_samp1 1 1.001
sD_samp1 1.001 1.004
----------------------------------------------
Sample name: samp2
---------------------
Point estimate Uppers confidence interval
A_samp2 1.003 1.008
D_samp2 1.003 1.014
sD_samp2 1.002 1.004
---------------------------------------------------------------------------------------------------
*** 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 9.729
lower bound upper bound
at level 95% 9.148 10
at level 68% 9.703 9.999
Parameter Bayes estimate Credible interval
D_samp1 29.413
lower bound upper bound
at level 95% 23.754 34.346
at level 68% 26.92 32.178
Parameter Bayes estimate Credible interval
sD_samp1 67.554
lower bound upper bound
at level 95% 50.785 85.744
at level 68% 58.233 75.135
----------------------------------------------
Sample name: samp2
---------------------
Parameter Bayes estimate Credible interval
A_samp2 10.411
lower bound upper bound
at level 95% 10 11.216
at level 68% 10 10.482
Parameter Bayes estimate Credible interval
D_samp2 18.306
lower bound upper bound
at level 95% 17.184 19.547
at level 68% 17.698 18.848
Parameter Bayes estimate Credible interval
sD_samp2 4.602
lower bound upper bound
at level 95% 3.49 5.611
at level 68% 3.971 5.062
----------------------------------------------
```

Thee results can be also be used for an alternative graphical representation:

`plot_Ages(Age, plot_mode = "density")`

```
SAMPLE AGE HPD68.MIN HPD68.MAX HPD95.MIN HPD95.MAX ALT_SAMPLE_NAME AT
1 samp1 9.729 9.703 9.999 9.148 10.000 NA 2
2 samp2 10.411 10.000 10.482 10.000 11.216 NA 1
```

If MCMC trajectories did not converge, it means we should run
additional MCMC iterations.

For `AgeS_computation()`

and `Age_OSLC14()`

models
we can run additional iterations by supplying the function output back
into the parent function. In the following, notice we are using the
output of the previous `AgeS_computation()`

example, namely
`Age`

. The key argument to set/change is
`DATA`

.

```
<- AgeS_Computation(
Age DATA = Age,
Nb_sample = 2,
SampleNames = c("GDB5", "GDB3"),
PriorAge = priorage,
distribution = "cauchy",
LIN_fit = TRUE,
Origin_fit = FALSE,
Iter = 1000,
jags_method = "rjags"
)
```

```
Calling the simulation using the rjags method...
Note: the model did not require adaptation
Burning in the model for 4000 iterations...
Running the model for 5000 iterations...
Simulation complete
Calculating summary statistics...
Calculating the Gelman-Rubin statistic for 6 variables....
Finished running the simulation
```

```
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Sample name: GDB5
---------------------
Point estimate Uppers confidence interval
A_GDB5 1.001 1.003
D_GDB5 1.001 1.002
sD_GDB5 1.005 1.02
----------------------------------------------
Sample name: GDB3
---------------------
Point estimate Uppers confidence interval
A_GDB3 1.002 1.004
D_GDB3 1.011 1.037
sD_GDB3 1.008 1.027
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
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>> Bayes estimates of Age, Palaeodose and its dispersion for each sample and credible interval <<
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Sample name: GDB5
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Parameter Bayes estimate Credible interval
A_GDB5 9.721
lower bound upper bound
at level 95% 9.141 10
at level 68% 9.69 10
Parameter Bayes estimate Credible interval
D_GDB5 29.278
lower bound upper bound
at level 95% 23.74 34.531
at level 68% 26.935 32.33
Parameter Bayes estimate Credible interval
sD_GDB5 67.645
lower bound upper bound
at level 95% 50.695 84.768
at level 68% 58.756 75.809
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Sample name: GDB3
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Parameter Bayes estimate Credible interval
A_GDB3 10.417
lower bound upper bound
at level 95% 10 11.231
at level 68% 10 10.485
Parameter Bayes estimate Credible interval
D_GDB3 18.291
lower bound upper bound
at level 95% 17.022 19.483
at level 68% 17.645 18.85
Parameter Bayes estimate Credible interval
sD_GDB3 4.617
lower bound upper bound
at level 95% 3.544 5.692
at level 68% 3.984 5.086
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```