peakfit: Finite mixture modelling of geochronological datasets

Description Usage Arguments Details Value References See Also Examples

View source: R/peakfit.R

Description

Implements the discrete mixture modelling algorithms of Galbraith and Laslett (1993) and applies them to fission track and other geochronological datasets.

Usage

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peakfit(x, ...)

## Default S3 method:
peakfit(x, k = "auto", sigdig = 2, log = TRUE,
  alpha = 0.05, ...)

## S3 method for class 'fissiontracks'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, alpha = 0.05, ...)

## S3 method for class 'UPb'
peakfit(x, k = 1, type = 4, cutoff.76 = 1100,
  cutoff.disc = c(-15, 5), exterr = TRUE, sigdig = 2, log = TRUE,
  alpha = 0.05, ...)

## S3 method for class 'PbPb'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, i2i = TRUE, alpha = 0.05, ...)

## S3 method for class 'ArAr'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, i2i = FALSE, alpha = 0.05, ...)

## S3 method for class 'KCa'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, i2i = FALSE, alpha = 0.05, ...)

## S3 method for class 'ReOs'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, i2i = TRUE, alpha = 0.05, ...)

## S3 method for class 'SmNd'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, i2i = TRUE, alpha = 0.05, ...)

## S3 method for class 'RbSr'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, i2i = TRUE, alpha = 0.05, ...)

## S3 method for class 'LuHf'
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
  log = TRUE, i2i = TRUE, alpha = 0.05, ...)

## S3 method for class 'ThU'
peakfit(x, k = 1, exterr = FALSE, sigdig = 2,
  log = TRUE, i2i = TRUE, alpha = 0.05, detritus = 0, Th02 = c(0,
  0), Th02U48 = c(0, 0, 1e+06, 0, 0, 0, 0, 0, 0), ...)

## S3 method for class 'UThHe'
peakfit(x, k = 1, sigdig = 2, log = TRUE,
  alpha = 0.05, ...)

Arguments

x

either an [n x 2] matrix with measurements and their standard errors, or an object of class fissiontracks, UPb, PbPb, ArAr, KCa, ReOs, SmNd, RbSr, LuHf, ThU or UThHe

...

optional arguments (not used)

k

the number of discrete age components to be sought. Setting this parameter to 'auto' automatically selects the optimal number of components (up to a maximum of 5) using the Bayes Information Criterion (BIC).

sigdig

number of significant digits to be used for any legend in which the peak fitting results are to be displayed.

log

take the logs of the data before applying the mixture model?

alpha

cutoff value for confidence intervals

exterr

propagate the external sources of uncertainty into the component age errors?

type

scalar valueindicating whether to plot the ^{207}Pb/^{235}U age (type=1), the ^{206}Pb/^{238}U age (type=2), the ^{207}Pb/^{206}Pb age (type=3), the ^{207}Pb/^{206}Pb-^{206}Pb/^{238}U age (type=4), or the (Wetherill) concordia age (type=5)

cutoff.76

the age (in Ma) below which the ^{206}Pb/^{238}U and above which the ^{207}Pb/^{206}Pb age is used. This parameter is only used if type=4.

cutoff.disc

two element vector with the maximum and minimum percentage discordance allowed between the ^{207}Pb/^{235}U and ^{206}Pb/^{238}U age (if ^{206}Pb/^{238}U < cutoff.76) or between the ^{206}Pb/^{238}U and ^{207}Pb/^{206}Pb age (if ^{206}Pb/^{238}U > cutoff.76). Set cutoff.disc=NA if you do not want to use this filter.

i2i

‘isochron to intercept’: calculates the initial (aka ‘inherited’, ‘excess’, or ‘common’) ^{40}Ar/^{36}Ar, ^{40}Ca/^{44}Ca, ^{207}Pb/^{204}Pb, ^{87}Sr/^{86}Sr, ^{143}Nd/^{144}Nd, ^{187}Os/^{188}Os or ^{176}Hf/^{177}Hf ratio from an isochron fit. Setting i2i to FALSE uses the default values stored in settings('iratio',...). When applied to data of class ThU, setting i2i to TRUE applies a detrital Th-correction.

detritus

detrital ^{230}Th correction (only applicable when x$format == 1 or 2.

0: no correction

1: project the data along an isochron fit

2: correct the data using an assumed initial ^{230}Th/^{232}Th-ratio for the detritus.

3: correct the data using the measured present day ^{230}Th/^{238}U, ^{232}Th/^{238}U and ^{234}U/^{238}U-ratios in the detritus.

Th02

2-element vector with the assumed initial ^{230}Th/^{232}Th-ratio of the detritus and its standard error. Only used if detritus==2

Th02U48

9-element vector with the measured composition of the detritus, containing X=0/8, sX, Y=2/8, sY, Z=4/8, sZ, rXY, rXZ, rYZ. Only used if isochron==FALSE and detritus==3

Details

Consider a dataset of n dates \{t_1, t_2, ..., t_n\} with analytical uncertainties \{s[t_1], s[t_2], ..., s[t_n]\}. Define z_i = \log(t_i) and s[z_i] = s[t_i]/t_i. Suppose that these n values are derived from a mixture of k>2 populations with means \{μ_1,...,μ_k\}. Such a discrete mixture may be mathematically described by:

P(z_i|μ,ω) = ∑_{j=1}^k π_j N(z_i | μ_j, s[z_j]^2 )

where π_j is the proportion of the population that belongs to the j^{th} component, and π_k=1-∑_{j=1}^{k-1}π_j. This equation can be solved by the method of maximum likelihood (Galbraith and Laslett, 1993). IsoplotR implements the Bayes Information Criterion (BIC) as a means of automatically choosing k. This option should be used with caution, as the number of peaks steadily rises with sample size (n). If one is mainly interested in the youngest age component, then it is more productive to use an alternative parameterisation, in which all grains are assumed to come from one of two components, whereby the first component is a single discrete age peak (\exp(m), say) and the second component is a continuous distribution (as descibed by the central age model), but truncated at this discrete value (Van der Touw et al., 1997).

Value

Returns a list with the following items:

peaks

a 3 x k matrix with the following rows:

t: the ages of the k peaks

s[t]: the estimated uncertainties of t

ci[t]: the widths of approximate 100(1-α)\% confidence intervals for t

props

a 2 x k matrix with the following rows:

p: the proportions of the k peaks

s[p]: the estimated uncertainties (standard errors) of p

L

the log-likelihood of the fit

legend

a vector of text expressions to be used in a figure legend

References

Galbraith, R.F. and Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks and Radiation Measurements, 21(4), pp.459-470.

van der Touw, J., Galbraith, R., and Laslett, G. A logistic truncated normal mixture model for overdispersed binomial data. Journal of Statistical Computation and Simulation, 59(4):349-373, 1997.

See Also

radialplot, central

Examples

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data(examples)
peakfit(examples$FT1,k=2)

peakfit(examples$LudwigMixture,k='min')

IsoplotR documentation built on Dec. 9, 2018, 1:04 a.m.