This function allows the application of Bayesian models on luminescence data, measured with the single-aliquot regenerative-dose (SAR, Murray and Wintle, 2000) protocol. In particular, it follows the idea proposed by Combes et al., 2015 of using an hierarchical model for estimating a central equivalent dose from a set of luminescence measurements. This function is (I) the adaption of this approach for the R environment and (II) an extension and a technical refinement of the published code.

```
analyse_baSAR(object, XLS_file = NULL, aliquot_range = NULL,
source_doserate = NULL, signal.integral, signal.integral.Tx = NULL,
background.integral, background.integral.Tx = NULL,
irradiation_times = NULL, sigmab = 0, sig0 = 0.025,
distribution = "cauchy", baSAR_model = NULL, n.MCMC = 1e+05,
fit.method = "EXP", fit.force_through_origin = TRUE,
fit.includingRepeatedRegPoints = TRUE, method_control = list(),
digits = 3L, distribution_plot = "kde", plot = TRUE,
plot_reduced = TRUE, plot.single = FALSE, verbose = TRUE, ...)
```

object

'>Risoe.BINfileData, '>RLum.Results, '>RLum.Analysis character or list (**required**):
input object used for the Bayesian analysis. If a `character`

is provided the function
assumes a file connection and tries to import a BIN-file using the provided path. If a `list`

is
provided the list can only contain either `Risoe.BINfileData`

objects or `character`

s
providing a file connection. Mixing of both types is not allowed. If an '>RLum.Results
is provided the function directly starts with the Bayesian Analysis (see details)

XLS_file

character (*optional*):
XLS_file with data for the analysis. This file must contain 3 columns:
the name of the file, the disc position and the grain position
(the last being 0 for multi-grain measurements).
Alternatively a `data.frame`

of similar structure can be provided.

aliquot_range

numeric (*optional*):
allows to limit the range of the aliquots used for the analysis.
This argument has only an effect if the argument `XLS_file`

is used or
the input is the previous output (i.e. is '>RLum.Results). In this case the
new selection will add the aliquots to the removed aliquots table.

source_doserate

numeric **(required)**:
source dose rate of beta-source used for the measuremnt and its uncertainty
in Gy/s, e.g., `source_doserate = c(0.12, 0.04)`

. Paramater can be provided
as `list`

, for the case that more than one BIN-file is provided, e.g.,
`source_doserate = list(c(0.04, 0.004), c(0.05, 0.004))`

.

signal.integral

vector (**required**):
vector with the limits for the signal integral used for the calculation,
e.g., `signal.integral = c(1:5)`

. Ignored if `object`

is an '>RLum.Results object.
The parameter can be provided as `list`

, see `source_doserate`

.

signal.integral.Tx

vector (*optional*):
vector with the limits for the signal integral for the Tx curve. I
f nothing is provided the value from `signal.integral`

is used and it is ignored
if `object`

is an '>RLum.Results object.
The parameter can be provided as `list`

, see `source_doserate`

.

background.integral

vector (**required**):
vector with the bounds for the background integral.
Ignored if `object`

is an '>RLum.Results object.
The parameter can be provided as `list`

, see `source_doserate`

.

background.integral.Tx

vector (*optional*):
vector with the limits for the background integral for the Tx curve.
If nothing is provided the value from `background.integral`

is used.
Ignored if `object`

is an '>RLum.Results object.
The parameter can be provided as `list`

, see `source_doserate`

.

irradiation_times

numeric (*optional*): if set this vector replaces all irradiation
times for one aliquot and one cycle (Lx and Tx curves) and recycles it for all others cycles and aliquots.
Plesae note that if this argument is used, for every(!) single curve
in the dataset an irradiation time needs to be set.

sigmab

numeric (*with default*):
option to set a manual value for the overdispersion (for LnTx and TnTx),
used for the Lx/Tx error calculation. The value should be provided as
absolute squared count values, cf. calc_OSLLxTxRatio.
The parameter can be provided as `list`

, see `source_doserate`

.

sig0

numeric (*with default*):
allow adding an extra component of error to the final Lx/Tx error value
(e.g., instrumental errror, see details is calc_OSLLxTxRatio).
The parameter can be provided as `list`

, see `source_doserate`

.

distribution

character (*with default*):
type of distribution that is used during Bayesian calculations for
determining the Central dose and overdispersion values.
Allowed inputs are `"cauchy"`

, `"normal"`

and `"log_normal"`

.

baSAR_model

character (*optional*):
option to provide an own modified or new model for the Bayesian calculation
(see details). If an own model is provided the argument `distribution`

is
ignored and set to `'user_defined'`

n.MCMC

integer (*with default*):
number of iterations for the Markov chain Monte Carlo (MCMC) simulations

fit.method

character (*with default*):
fit method used for fitting the growth curve using the function
plot_GrowthCurve. Here supported methods: `EXP`

, `EXP+LIN`

and `LIN`

fit.force_through_origin

logical (*with default*):
force fitting through origin

fit.includingRepeatedRegPoints

logical (*with default*):
includes the recycling point (assumed to be measured during the last cycle)

method_control

list (*optional*):
named list of control parameters that can be directly
passed to the Bayesian analysis, e.g., `method_control = list(n.chains = 4)`

.
See details for further information

digits

integer (*with default*):
round output to the number of given digits

distribution_plot

character (*with default*): sets the final distribution plot that
shows equivalent doses obtained using the frequentist approach and sets in the central dose
as comparison obtained using baSAR. Allowed input is `'abanico'`

or `'kde'`

. If set to `NULL`

nothing is plotted.

plot

logical (*with default*):
enables or disables plot output

plot_reduced

logical (*with default*):
enables or disables the advanced plot output

plot.single

logical (*with default*):
enables or disables single plots or plots arranged by `analyse_baSAR`

verbose

logical (*with default*):
enables or disables verbose mode

...

parameters that can be passed to the function calc_OSLLxTxRatio
(almost full support), readxl::read_excel (full support), read_BIN2R (`n.records`

,
`position`

, `duplicated.rm`

), see details.

Function returns results numerically and graphically:

-----------------------------------
`[ NUMERICAL OUTPUT ]`

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

** RLum.Results**-object

**slot:** `@data`

Element |
Type |
Description |

`$summary` |
`data.frame` |
statistical summary, including the central dose |

`$mcmc` |
`mcmc` |
coda::mcmc.list object including raw output |

`$models` |
`character` |
implemented models used in the baSAR-model core |

`$input_object` |
`data.frame` |
summarising table (same format as the XLS-file) including, e.g., Lx/Tx values |

**slot:** `@info`

The original function call

------------------------
`[ PLOT OUTPUT ]`

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

(A) Ln/Tn curves with set integration limits,

(B) trace plots are returned by the baSAR-model, showing the convergence of the parameters (trace) and the resulting kernel density plots. If

`plot_reduced = FALSE`

for every(!) dose a trace and a density plot is returned (this may take a long time),(C) dose plots showing the dose for every aliquot as boxplots and the marked HPD in within. If boxes are coloured 'orange' or 'red' the aliquot itself should be checked,

(D) the dose response curve resulting from the monitoring of the Bayesian modelling are provided along with the Lx/Tx values and the HPD. Note: The amount for curves displayed is limited to 1000 (random choice) for performance reasons,

(E) the final plot is the De distribution as calculated using the conventional (frequentist) approach and the central dose with the HPDs marked within. This figure is only provided for a comparison, no further statistical conclusion should be drawn from it.

**Please note: If distribution was set to log_normal the central dose is given as geometric mean!**

0.1.33 (2018-06-06 14:45:55)

Mercier, N., Kreutzer, S. (2018). analyse_baSAR(): Bayesian models (baSAR) applied on luminescence data. Function version 0.1.33. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J. (2018). Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.8.6. https://CRAN.R-project.org/package=Luminescence

Internally the function consists of two parts: (I) The Bayesian core for the Bayesian calculations and applying the hierchical model and (II) a data pre-processing part. The Bayesian core can be run independently, if the input data are sufficient (see below). The data pre-processing part was implemented to simplify the analysis for the user as all needed data pre-processing is done by the function, i.e. in theory it is enough to provide a BIN/BINX-file with the SAR measurement data. For the Bayesian analysis for each aliquot the following information are needed from the SAR analysis. LxTx, the LxTx error and the dose values for all regeneration points.

**How the systematic error contribution is calculated?**

Standard errors (so far) provided with the source dose rate are considered as systematic uncertainties and added to final central dose by:

$$systematic.error = 1/n \sum SE(source.doserate)$$

$$SE(central.dose.final) = \sqrt{SE(central.dose)^2 + systematic.error^2}$$

Please note that this approach is rather rough and can only be valid if the source dose rate errors, in case different readers had been used, are similar. In cases where more than one source dose rate is provided a warning is given.

**Input / output scenarios**

Various inputs are allowed for this function. Unfortunately this makes the function handling rather complex, but at the same time very powerful. Available scenarios:

**(1) - object is BIN-file or link to a BIN-file**

Finally it does not matter how the information of the BIN/BINX file are provided. The function
supports **(a)** either a path to a file or directory or a `list`

of file names or paths or
**(b)** a '>Risoe.BINfileData object or a list of these objects. The latter one can
be produced by using the function read_BIN2R, but this function is called automatically
if only a filename and/or a path is provided. In both cases it will become the data that can be
used for the analysis.

`[XLS_file = NULL]`

If no XLS file (or data frame with the same format) is provided the functions runs an automatic process that consists of the following steps:

Select all valid aliquots using the function verify_SingleGrainData

Calculate Lx/Tx values using the function calc_OSLLxTxRatio

Calculate De values using the function plot_GrowthCurve

These proceeded data are subsequently used in for the Bayesian analysis

`[XLS_file != NULL]`

If an XLS-file is provided or a `data.frame`

providing similar information the pre-processing
steps consists of the following steps:

Calculate Lx/Tx values using the function calc_OSLLxTxRatio

Calculate De values using the function plot_GrowthCurve

Means, the XLS file should contain a selection of the BIN-file names and the aliquots selected for the further analysis. This allows a manual selection of input data, as the automatic selection by verify_SingleGrainData might be not totally sufficient.

**(2) - object RLum.Results object**

If an '>RLum.Results object is provided as input and(!) this object was
previously created by the function `analyse_baSAR()`

itself, the pre-processing part
is skipped and the function starts directly the Bayesian analysis. This option is very powerful
as it allows to change parameters for the Bayesian analysis without the need to repeat
the data pre-processing. If furthermore the argument `aliquot_range`

is set, aliquots
can be manually excluded based on previous runs.

`method_control`

These are arguments that can be passed directly to the Bayesian calculation core, supported arguments are:

Parameter |
Type |
Descritpion |

`lower_centralD` |
numeric | sets the lower bound for the expected De range. Change it only if you know what you are doing! |

`upper_centralD` |
numeric | sets the upper bound for the expected De range. Change it only if you know what you are doing! |

`n.chains` |
integer | sets number of parallel chains for the model (default = 3) (cf. rjags::jags.model) |

`inits` |
list | option to set initialisation values (cf. rjags::jags.model) |

`thin` |
numeric | thinning interval for monitoring the Bayesian process (cf. rjags::jags.model) |

**User defined models**

The function provides the option to modify and to define own models that can be used for
the Bayesian calculation. In the case the user wants to modify a model, a new model
can be piped into the funtion via the argument `baSAR_model`

as `character`

.
The model has to be provided in the JAGS dialect of the BUGS language (cf. rjags::jags.model)
and parameter names given with the pre-defined names have to be respected, otherwise the function
will break.

**FAQ**

Q: How can I set the seed for the random number generator (RNG)?

A: Use the argument `method_control`

, e.g., for three MCMC chains
(as it is the default):

method_control = list( inits = list( list(.RNG.name = "base::Wichmann-Hill", .RNG.seed = 1), list(.RNG.name = "base::Wichmann-Hill", .RNG.seed = 2), list(.RNG.name = "base::Wichmann-Hill", .RNG.seed = 3) ))

This sets a reproducible set for every chain separately.

Q: How can I modify the output plots?

A: You can't, but you can use the function output to create own, modified plots.

Q: Can I change the boundaries for the central_D?

A: Yes, we made it possible, but we DO NOT recommend it, except you know what you are doing!
Example: `method_control = list(lower_centralD = 10))`

Q: The lines in the baSAR-model appear to be in a wrong logical order?

A: This is correct and allowed (cf. JAGS manual)

**Additional arguments support via the ... argument**

This list summarizes the additional arguments that can be passed to the internally used functions.

Supported argument |
Corresponding function |
Default |
**Short description ** |

`threshold` |
verify_SingleGrainData | `30` |
change rejection threshold for curve selection |

`sheet` |
readxl::read_excel | `1` |
select XLS-sheet for import |

`col_names` |
readxl::read_excel | `TRUE` |
first row in XLS-file is header |

`col_types` |
readxl::read_excel | `NULL` |
limit import to specific columns |

`skip` |
readxl::read_excel | `0` |
number of rows to be skipped during import |

`n.records` |
read_BIN2R | `NULL` |
limit records during BIN-file import |

`duplicated.rm` |
read_BIN2R | `TRUE` |
remove duplicated records in the BIN-file |

`pattern` |
read_BIN2R | `TRUE` |
select BIN-file by name pattern |

`position` |
read_BIN2R | `NULL` |
limit import to a specific position |

`background.count.distribution` |
calc_OSLLxTxRatio | `"non-poisson"` |
set assumed count distribution |

`fit.weights` |
plot_GrowthCurve | `TRUE` |
enables / disables fit weights |

`fit.bounds` |
plot_GrowthCurve | `TRUE` |
enables / disables fit bounds |

`NumberIterations.MC` |
plot_GrowthCurve | `100` |
number of MC runs for error calculation |

`output.plot` |
plot_GrowthCurve | `TRUE` |
enables / disables dose response curve plot |

`output.plotExtended` |
plot_GrowthCurve | `TRUE` |
enables / disables extended dose response curve plot |

Combes, B., Philippe, A., Lanos, P., Mercier, N., Tribolo, C., Guerin, G., Guibert, P., Lahaye, C., 2015. A Bayesian central equivalent dose model for optically stimulated luminescence dating. Quaternary Geochronology 28, 62-70. doi:10.1016/j.quageo.2015.04.001

Mercier, N., Kreutzer, S., Christophe, C., Guerin, G., Guibert, P., Lahaye, C., Lanos, P., Philippe, A., Tribolo, C., 2016. Bayesian statistics in luminescence dating: The 'baSAR'-model and its implementation in the R package 'Luminescence'. Ancient TL 34, 14-21.

**Further reading**

Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B., 2013. Bayesian Data Analysis, Third Edition. CRC Press.

Murray, A.S., Wintle, A.G., 2000. Luminescence dating of quartz using an improved single-aliquot regenerative-dose protocol. Radiation Measurements 32, 57-73. doi:10.1016/S1350-4487(99)00253-X

Plummer, M., 2017. JAGS Version 4.3.0 user manual. https://sourceforge.net/projects/mcmc-jags/files/Manuals/4.x/jags_user_manual.pdf/download

read_BIN2R, calc_OSLLxTxRatio, plot_GrowthCurve, readxl::read_excel, verify_SingleGrainData, rjags::jags.model, rjags::coda.samples, boxplot.default

# NOT RUN { ##(1) load package test data set data(ExampleData.BINfileData, envir = environment()) ##(2) selecting relevant curves, and limit dataset CWOSL.SAR.Data <- subset( CWOSL.SAR.Data, subset = POSITION%in%c(1:3) & LTYPE == "OSL") # } # NOT RUN { ##(3) run analysis ##please not that the here selected parameters are ##choosen for performance, not for reliability results <- analyse_baSAR( object = CWOSL.SAR.Data, source_doserate = c(0.04, 0.001), signal.integral = c(1:2), background.integral = c(80:100), fit.method = "LIN", plot = FALSE, n.MCMC = 200 ) print(results) ##XLS_file template ##copy and paste this the code below in the terminal ##you can further use the function write.csv() to export the example XLS_file <- structure( list( BIN_FILE = NA_character_, DISC = NA_real_, GRAIN = NA_real_), .Names = c("BIN_FILE", "DISC", "GRAIN"), class = "data.frame", row.names = 1L ) # } # NOT RUN { # }