Implements the discrete mixture modelling algorithms of Galbraith and Laslett (1993) and applies them to fission track and other geochronological datasets.
peakfit(x, ...)# S3 method for default
peakfit(x, k = "auto", sigdig = 2, log = TRUE,
alpha = 0.05, ...)
# S3 method for fissiontracks
peakfit(x, k = 1, exterr = TRUE, sigdig = 2,
log = TRUE, alpha = 0.05, ...)
# S3 method for 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 PbPb
peakfit(x, k = 1, exterr = TRUE, sigdig = 2, log = TRUE,
i2i = TRUE, alpha = 0.05, ...)
# S3 method for ArAr
peakfit(x, k = 1, exterr = TRUE, sigdig = 2, log = TRUE,
i2i = FALSE, alpha = 0.05, ...)
# S3 method for ReOs
peakfit(x, k = 1, exterr = TRUE, sigdig = 2, log = TRUE,
i2i = TRUE, alpha = 0.05, ...)
# S3 method for SmNd
peakfit(x, k = 1, exterr = TRUE, sigdig = 2, log = TRUE,
i2i = TRUE, alpha = 0.05, ...)
# S3 method for RbSr
peakfit(x, k = 1, exterr = TRUE, sigdig = 2, log = TRUE,
i2i = TRUE, alpha = 0.05, ...)
# S3 method for LuHf
peakfit(x, k = 1, exterr = TRUE, sigdig = 2, log = TRUE,
i2i = TRUE, alpha = 0.05, ...)
# S3 method for ThU
peakfit(x, k = 1, exterr = FALSE, sigdig = 2, log = TRUE,
i2i = TRUE, alpha = 0.05, ...)
# S3 method for UThHe
peakfit(x, k = 1, sigdig = 2, log = TRUE, alpha = 0.05,
...)
either an [n x 2] matrix with measurements and their
standard errors, or an object of class fissiontracks,
UPb, PbPb, ArAr, ReOs, SmNd,
RbSr, LuHf, ThU or UThHe
optional arguments (not used)
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).
number of significant digits to be used for any legend in which the peak fitting results are to be displayed.
take the logs of the data before applying the mixture model?
cutoff value for confidence intervals
propagate the external sources of uncertainty into the component age errors?
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)
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.
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.
`isochron to intercept': calculates the initial (aka
`inherited', `excess', or `common')
\(^{40}\)Ar/\(^{36}\)Ar, \(^{207}\)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.
Returns a list with the following items:
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 studentised \(100(1-\alpha)\%\) confidence
interval for t
a 2 x k matrix with the following rows:
p: the proportions of the k peaks
s[p]: the estimated uncertainties of p
the log-likelihood of the fit
the \(100(1-\alpha/2)\%\) percentile of the t-distribution with \((n-2k+1)\) degrees of freedom
a vector of text expressions to be used in a figure legend
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 \(\{\mu_1,...,\mu_k\}\). Such a discrete mixture may be mathematically described by:
\(P(z_i|\mu,\omega) = \sum_{j=1}^k \pi_j N(z_i | \mu_j, s[z_j]^2 )\)
where \(\pi_j\) is the proportion of the population that belongs
to the \(j^{th}\) component, and
\(\pi_k=1-\sum_{j=1}^{k-1}\pi_j\). 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).
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.
# NOT RUN {
data(examples)
peakfit(examples$FT1,k=2)
peakfit(examples$LudwigMixture,k='min')
# }
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