Creates one or more kernel density estimates using a combination of the Botev (2010) bandwidth selector and the Abramson (1982) adaptive kernel bandwidth modifier.
kde(x, ...)# S3 method for default
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, ...)
# S3 method for UPb
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, type = 4,
cutoff.76 = 1100, cutoff.disc = c(-15, 5), common.Pb = 0, ...)
# S3 method for detritals
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, ncol = NA,
samebandwidth = TRUE, normalise = TRUE, ...)
# S3 method for PbPb
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, common.Pb = 1, ...)
# S3 method for ArAr
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, i2i = FALSE, ...)
# S3 method for ThU
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [ka]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, i2i = FALSE, ...)
# S3 method for ReOs
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, i2i = TRUE, ...)
# S3 method for SmNd
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, i2i = TRUE, ...)
# S3 method for RbSr
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, i2i = TRUE, ...)
# S3 method for LuHf
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, i2i = TRUE, ...)
# S3 method for UThHe
kde(x, from = NA, to = NA, bw = NA, adaptive = TRUE,
log = FALSE, n = 512, plot = TRUE, pch = NA, xlab = "age [Ma]",
ylab = "", kde.col = rgb(1, 0, 1, 0.6), hist.col = rgb(0, 1, 0, 0.2),
show.hist = TRUE, bty = "n", binwidth = NA, ...)
# S3 method for fissiontracks
kde(x, from = NA, to = NA, bw = NA,
adaptive = TRUE, log = FALSE, n = 512, plot = TRUE, pch = NA,
xlab = "age [Ma]", ylab = "", kde.col = rgb(1, 0, 1, 0.6),
hist.col = rgb(0, 1, 0, 0.2), show.hist = TRUE, bty = "n",
binwidth = NA, ...)
a vector of numbers OR an object of class UPb,
PbPb, ArAr, ReOs, SmNd,
RbSr, UThHe, fissiontracks, ThU or
detrital
optional arguments to be passed on to R's
density function.
minimum age of the time axis. If NULL, this is
set automatically
maximum age of the time axis. If NULL, this is set
automatically
the bandwidth of the KDE. If NULL, bw will
be calculated automatically using the algorithm by Botev et
al. (2010).
logical flag controlling if the adaptive KDE modifier of Abramson (1982) is used
transform the ages to a log scale if TRUE
horizontal resolution (i.e., the number of segments) of the density estimate.
show the KDE as a plot
the symbol used to show the samples. May be a vector.
Set pch=NA to turn them off.
the x-axis label
the y-axis label
the fill colour of the KDE specified as a four
element vector of r, g, b, alpha values
the fill colour of the histogram specified as a
four element vector of r, g, b, alpha values
logical flag indicating whether a histogram should be added to the KDE
change to "o", "l", "7",
"c", "u", or "]" if you want to draw a box
around the plot
scalar width of the histogram bins, in Myr if
log = FALSE, or as a fractional value if log =
TRUE. Sturges' Rule (\(\log_2[n]+1\), where \(n\) is the
number of data points) is used if binwidth = NA
scalar indicating 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 minimum (negative)
and maximum (positive) 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.
apply a common lead correction using one of three methods:
1: use the isochron intercept as the initial Pb-composition
2: use the Stacey-Kramer two-stage model to infer the initial
Pb-composition
3: use the Pb-composition stored in
settings('iratio','Pb206Pb204') and
settings('iratio','Pb207Pb204')
scalar value indicating the number of columns over which the KDEs should be divided.
logical flag indicating whether the same
bandwidth should be used for all samples. If
samebandwidth = TRUE and bw = NULL, then the
function will use the median bandwidth of all the samples.
logical flag indicating whether or not the KDEs should all integrate to the same value.
`isochron to intercept': calculates the initial (aka
`inherited', `excess', or `common')
\(^{40}\)Ar/\(^{36}\)Ar, \(^{87}\)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.
If x has class UPb, PbPb, ArAr,
ReOs, SmNd, RbSr, UThHe,
fissiontracks or ThU, returns an object of class
KDE, i.e. a list containing the following items:
horizontal plot coordinates
vertical plot coordinates
the base bandwidth of the density estimate
the data values from the input to
the kde function
copied from the input
or, if x has class =detritals, an object of class
KDEs, i.e. a list containing the following items:
a named list with objects of class KDE
the beginning of the common time scale
the end of the common time scale
the maximum probability density of all the KDEs
the x-axis label to be used by plot.KDEs(...)
Given a set of \(n\) age estimates \(\{t_1, t_2, ..., t_n\}\), histograms and KDEs are probability density estimators that display age distributions by smoothing. Histograms do this by grouping the data into a number of regularly spaced bins. Alternatively, kernel density estimates (KDEs; Vermeesch, 2012) smooth data by applying a (Gaussian) kernel:
\(KDE(t) = \sum_{i=1}^{n}N(t|\mu=t_i,\sigma=h[t])/n\)
where \(N(t|\mu,\sigma)\) is the probability of observing a
value \(t\) under a Normal distribution with mean \(\mu\) and
standard deviation \(\sigma\). \(h[t]\) is the smoothing
parameter or `bandwidth' of the kernel density estimate, which may
or may not depend on the age \(t\). If \(h[t]\) depends on
\(t\), then \(KDE(t)\) is known as an `adaptive' KDE. The
default bandwidth used by IsoplotR is calculated using the
algorithm of Botev et al. (2010) and modulated by the adaptive
smoothing approach of Abramson (1982). The rationale behind
adaptive kernel density estimation is to use a narrower bandwidth
near the peaks of the sampling distribution (where the ordered
dates are closely spaced in time), and a wider bandwidth in the
distribution's sparsely sampled troughs. Thus, the resolution of
the density estimate is optimised according to data availability.
Abramson, I.S., 1982. On bandwidth variation in kernel estimates-a square root law. The annals of Statistics, pp.1217-1223.
Botev, Z. I., J. F. Grotowski, and D. P. Kroese. "Kernel density estimation via diffusion." The Annals of Statistics 38.5 (2010): 2916-2957.
Vermeesch, P., 2012. On the visualisation of detrital age distributions. Chemical Geology, 312, pp.190-194.
# NOT RUN {
kde(examples$UPb)
dev.new()
kde(examples$FT1,log=TRUE)
dev.new()
kde(examples$DZ,from=1,to=3000,kernel="epanechnikov")
# }
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