Function to fit the maximum age model to De data. This is a wrapper function that calls calc_MinDose and applies a similar approach as described in Olley et al. (2006).
calc_MaxDose(
data,
sigmab,
log = TRUE,
par = 3,
bootstrap = FALSE,
init.values = NULL,
plot = TRUE,
...
)Please see calc_MinDose.
RLum.Results or data.frame (required):
for data.frame: two columns with (data[, 1]) and De error (data[, 2]).
numeric (required):
additional spread in De values, representing the expected overdispersion in
the data should the sample be well-bleached (Cunningham & Wallinga 2012, p. 100).
This value must be expressed as a ratio, e.g. 0.2 (for 20 %), independently
of the log argument.
Note: Up to v1.2.1, it was required that the unlogged model specified
sigmab in the same absolute units of the De values (seconds or Gray). This
is no longer the case, and an error will be thrown if values of sigmab
greater than 1 are assigned.
logical (with default):
whether the logged minimum dose model should be fit to De data (TRUE by
default).
numeric (with default): number of parameters in the minimum age model, either 3 (default) or 4.
logical (with default): apply the recycled bootstrap approach of Cunningham & Wallinga 2012. See details for default values and options to modify them.
numeric (optional):
a named list with starting values for gamma, sigma, p0 and mu
(e.g. list(gamma=100, sigma=1.5, p0=0.1, mu=100)). If no values are
provided, reasonable values will be estimated from the data.
Note: the initial values must always be given in the absolute units.
If a logged model is applied (log = TRUE), the provided init.values
are automatically log-transformed.
logical (with default): enable/disable the plot output.
further arguments for bootstrapping (bs.M, bs.N, bs.h, sigmab.sd).
See details for their usage.
0.3.2
Burow, C., 2026. calc_MaxDose(): Apply the maximum age model to a given De distribution. Function version 0.3.2. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J., Mercier, N., Philippe, A., Riedesel, S., Autzen, M., Mittelstrass, D., Gray, H.J., Galharret, J., Colombo, M., Steinbuch, L., Boer, A.d., Bluszcz, A., 2026. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 1.3.0. https://r-lum.github.io/Luminescence/
Christoph Burow, University of Cologne (Germany)
Based on a rewritten S script of Rex Galbraith, 2010
, RLum Developer Team
Data transformation
To estimate the maximum dose population and its standard error, the three parameter minimum age model of Galbraith et al. (1999) is adapted. The measured De values are transformed as follows:
convert De values to natural logs
multiply the logged data to create a mirror image of the De distribution
shift De values along x-axis by the smallest x-value found to obtain only positive values
combine in quadrature the measurement error associated with each De value
with a relative error specified by sigmab
apply the MAM to these data
When all calculations are done the results are then converted as follows
subtract the x-offset
multiply the natural logs by -1
take the exponent to obtain the maximum dose estimate in Gy
Further documentation
Please see calc_MinDose.
Arnold, L.J., Roberts, R.G., Galbraith, R.F. & DeLong, S.B., 2009. A revised burial dose estimation procedure for optical dating of young and modern-age sediments. Quaternary Geochronology 4, 306-325.
Galbraith, R.F. & Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks Radiation Measurements 4, 459-470.
Galbraith, R.F., Roberts, R.G., Laslett, G.M., Yoshida, H. & Olley, J.M., 1999. Optical dating of single grains of quartz from Jinmium rock shelter, northern Australia. Part I: experimental design and statistical models. Archaeometry 41, 339-364.
Galbraith, R.F., 2005. Statistics for Fission Track Analysis, Chapman & Hall/CRC, Boca Raton.
Galbraith, R.F. & Roberts, R.G., 2012. Statistical aspects of equivalent dose and error calculation and display in OSL dating: An overview and some recommendations. Quaternary Geochronology 11, 1-27.
Olley, J.M., Roberts, R.G., Yoshida, H., Bowler, J.M., 2006. Single-grain optical dating of grave-infill associated with human burials at Lake Mungo, Australia. Quaternary Science Reviews 25, 2469-2474
Further reading
Arnold, L.J. & Roberts, R.G., 2009. Stochastic modelling of multi-grain equivalent dose (De) distributions: Implications for OSL dating of sediment mixtures. Quaternary Geochronology 4, 204-230.
Bailey, R.M. & Arnold, L.J., 2006. Statistical modelling of single grain quartz De distributions and an assessment of procedures for estimating burial dose. Quaternary Science Reviews 25, 2475-2502.
Cunningham, A.C. & Wallinga, J., 2012. Realizing the potential of fluvial archives using robust OSL chronologies. Quaternary Geochronology 12, 98-106.
Rodnight, H., Duller, G.A.T., Wintle, A.G. & Tooth, S., 2006. Assessing the reproducibility and accuracy of optical dating of fluvial deposits. Quaternary Geochronology 1, 109-120.
Rodnight, H., 2008. How many equivalent dose values are needed to obtain a reproducible distribution?. Ancient TL 26, 3-10.
calc_CentralDose, calc_CommonDose, calc_FiniteMixture, calc_FuchsLang2001, calc_MinDose
## load example data
data(ExampleData.DeValues, envir = environment())
# apply the maximum dose model
calc_MaxDose(ExampleData.DeValues$CA1, sigmab = 0.2, par = 3)
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