Age-Depth Modeling

Computes the age-depth curve from the output of the MCMC algorithm and the known depth of each dated samples.

Usage

bury(object, depth, ...)

# S4 method for class 'EventsMCMC,numeric'
bury(object, depth, span = 0.75, degree = 2)

# S4 method for class 'AgeDepthModel'
predict(object, newdata)

# S4 method for class 'AgeDepthModel,missing'
plot(
  x,
  level = 0.95,
  calendar = get_calendar(),
  main = NULL,
  sub = NULL,
  ann = graphics::par("ann"),
  axes = TRUE,
  frame.plot = axes,
  panel.first = NULL,
  panel.last = NULL,
  ...
)

Arguments

object: An EventsMCMC object.
depth: A numeric vector giving of the depths of the dated samples.
...: Other graphical parameters may also be passed as arguments to this function, particularly, border, col, lwd, lty or pch.
span: A length-one numeric vector giving the regression parameter (see stats::loess()).
degree: A length-one numeric vector giving the degree of the polynomials to be used (see stats::loess()).
newdata: A numeric vector giving the depths at which ages will be predicted. If missing, the original data points are used.
x: An AgeDepthModel object.
level: A length-one numeric vector giving the confidence level.
calendar: A aion::TimeScale object specifying the target calendar (see aion::calendar()).
main: A character string giving a main title for the plot.
sub: A character string giving a subtitle for the plot.
ann: A logical scalar: should the default annotation (title and x and y axis labels) appear on the plot?
axes: A logical scalar: should axes be drawn on the plot?
frame.plot: A logical scalar: should a box be drawn around the plot?
panel.first: An an expression to be evaluated after the plot axes are set up but before any plotting takes place. This can be useful for drawing background grids.
panel.last: An expression to be evaluated after plotting has taken place but before the axes, title and box are added.

Value

bury() returns an AgeDepthModel object.
predict() returns an EventsMCMC object.
plot() is called it for its side-effects: it results in a graphic being displayed (invisibly returns x).

Details

We assume it exists a function \(f\) relating the age and the depth \(age = f(depth)\). We estimate the function using local regression (also called local polynomial regression): \(f = loess(age ~ depth)\). This estimated function \(f\) depends on the unknown dates. However, from the posterior distribution of the age/date sequence, we can evaluate the posterior distribution of the age function for each desired depth.

References

Jha, D. K., Sanyal, P. & Philippe, A. (2020). Multi-Proxy Evidence of Late Quaternary Climate and Vegetational History of North-Central India: Implication for the Paleolithic to Neolithic Phases. Quaternary Science Reviews, 229: 106121. doi:10.1016/j.quascirev.2019.106121 .

Ghosh, S., Sanyal, P., Roy, S., Bhushan, R., Sati, S. P., Philippe, A. & Juyal, N. (2020). Early Holocene Indian Summer Monsoon and Its Impact on Vegetation in the Central Himalaya: Insight from dD and d13C Values of Leaf Wax Lipid. The Holocene, 30(7): 1063-1074. doi:10.1177/0959683620908639 .

Author

A. Philippe

Examples

## Coerce to MCMC
eve <- matrix(rnorm(6000, (1:6)^2), ncol = 6, byrow = TRUE)
eve <- as_events(eve, calendar = CE())

## Compute an age-depth curve
age <- bury(eve, depth = 1:6)
plot(age)


## Predict new values
new <- predict(age, newdata = 1.5:5.5)
summary(new)
#>   mad mean sd min q1 median q3 max start end
#> 1   2    2  2   0  2      2  3   5     1   4
#> 2   6    6  2   4  6      6  7   9     5   8
#> 3  12   12  2   9 12     12 13  15    11  14
#> 4  20   20  2  18 20     20 21  23    19  22
#> 5  30   30  2  28 30     30 31  33    29  32

plot(eve)

plot(new)