Luminescence (version 0.2.2)

Calc_FiniteMixture: Apply the finite mixture model (FMM) after Galbraith (2005) to a given De distribution

Description

This function fits a k-component mixture to a De distribution with differing known standard errors. Parameters (doses and mixing proportions) are estimated by maximum likelihood assuming that the log dose estimates are from a mixture of normal distributions.

Usage

Calc_FiniteMixture(input.data, 
                   sigmab, 
                   n.components,
                   sample.id = "unknown sample",
                   n.iterations = 200,
                   grain.probability = FALSE, 
                   output.file = FALSE, 
                   output.filename = "default")

Arguments

input.data

data.frame (required): two column data frame with De values and corresponding De errors

sigmab

numeric (required): spread in De values given as a fraction (e.g. 0.2). This value represents the expected overdispersion in the data should the sample be well-bleached (Cunningham & Walling 2012, p. 100).

n.components

numeric (required): number of components to be fitted

sample.id

character (with default): sample id

n.iterations

numeric (with default): number of iterations for maximum likelihood estimates

grain.probability

logical (with default): prints the estimated probabilities of which component each grain is in

output.file

logical (with default): save results to file. See output.filename.

output.filename

character (with default): desired filename, else results are saved to default.res

Value

• Returns a terminal output and a file containing statistical results if wanted. In addition a list is returned containing the following elements:
• mle.matrix
  covariance matrix of maximum likelihood estimates.
• grain.probability
  matrix with estimated probabilities of which component each grain is in.
• meta
  data frame containing model parameters (sample.id, sigmab, n.components, llik, bic).
• components
  data frame containing fitted components.
• single.comp
  data frame containing log likelihood and BIC for a single component.

Details

This model uses the maximum likelihood and Bayesian Information Criterion (BIC) approaches. Indications of overfitting are: - increasing BIC - repeated dose estimates - covariance matrix not positive definite - convergence problems

References

Galbraith, R.F. & Green, P.F., 1990. Estimating the component ages in a finite mixture. Nuclear Tracks and Radiation Measurements, 17, pp. 197-206. Galbraith, R.F. & Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks Radiation Measurements, 4, pp. 459-470. 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, pp. 1-27. Roberts, R.G., Galbraith, R.F., Yoshida, H., Laslett, G.M. & Olley, J.M., 2000. Distinguishing dose populations in sediment mixtures: a test of single-grain optical dating procedures using mixtures of laboratory-dosed quartz. Radiation Measurements, 32, pp. 459-465. Galbraith, R.F., 2005. Statistics for Fission Track Analysis, Chapman & Hall/CRC, Boca Raton. 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, pp. 204-230. Cunningham, A.C. & Wallinga, J., 2012. Realizing the potential of fluvial archives using robust OSL chronologies. Quaternary Geochronology, 12, pp. 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, pp. 109-120. Rodnight, H. 2008. How many equivalent dose values are needed to obtain a reproducible distribution?. Ancient TL, 26, pp. 3-10.

See Also

Calc_CentralDose, Calc_CommonDose, Calc_FuchsLang2001, Calc_MinDose3, Calc_MinDose4

Examples

## load example data
data(ExampleData.DeValues)

## apply the finite mixture model
Calc_FiniteMixture(ExampleData.DeValues,
                   sigmab = 0.08, n.components = 2,
                   grain.probability = TRUE, output.file = FALSE)