Kernel density estimation of calendar probability distributions

Aggregates calibrated radiocarbon dates and other calendar probability distributions using the composite kernel density estimate (cKDE) method method (Brown 2017) . This involves estimating the density of a set of dates by repeatedly computing the kernel density estimate of a random sample of ages drawn from their probability distributions.

Usage

cal_density(x, bw = 30, ..., times = 25, bootstrap = TRUE, strata = NULL)

# S3 method for class 'c14_cal'
density(x, ...)

Arguments

x: A cal vector of calendar probability distributions.
bw: Kernel bandwidth size passed to stats::density(). Can be either an integer value or a character selection rule, but the latter will likely result in a different bandwidth being applied to each bootstrapped sample and therefore should be avoided. Default: 30 (years).
...: Further arguments passed to stats::density().
times: Number of bootstrap samples to generate. The default of 25 is suitable for testing but should be set much higher in practice.
bootstrap: If TRUE (the default), randomly resamples with replacement from x before each KDE calculation.
strata: If not NULL, KDEs will be weighted to ensure equal representation of classes specified by a factor or character vector. If bootstrap = TRUE, bootstrap samples are generated using stratified resampling of the same classes.

Value

The result as a data frame or tibble::tibble with three columns: age (interpolated to common range of x), .estimate (mean of the bootstrapped KDEs), and .error (standard error of the bootstrapped KDEs).

Details

cal_density(..., bootstrap = TRUE) performs composite kernel density estimation with bootstrapping (McLaughlin 2019) , where sampling error. x is estimated by randomly resampling x before each KDE calculation.

See McLaughlin (2019) and Crema (2022) for discussions of bandwidth selection.

References

Brown WA (2017). “The Past and Future of Growth Rate Estimation in Demographic Temporal Frequency Analysis: Biodemographic Interpretability and the Ascendance of Dynamic Growth Models.” Journal of Archaeological Science, 80, 96–108. ISSN 0305-4403. doi:10.1016/j.jas.2017.02.003 .

Crema ER (2022). “Statistical Inference of Prehistoric Demography from Frequency Distributions of Radiocarbon Dates: A Review and a Guide for the Perplexed.” Journal of Archaeological Method and Theory, 29(4), 1387–1418. ISSN 1573-7764. doi:10.1007/s10816-022-09559-5 .

McLaughlin TR (2019). “On Applications of Space–Time Modelling with Open-Source 14C Age Calibration.” Journal of Archaeological Method and Theory, 26(2), 479–501. ISSN 1573-7764. doi:10.1007/s10816-018-9381-3 .

Examples

data(shub1_c14)
shub1_cal <- c14_calibrate(shub1_c14$c14_age, shub1_c14$c14_error)
cal_density(shub1_cal)
#> # A tibble: 14,792 × 3
#>           age .estimate   .error
#>          <yr>     <dbl>    <dbl>
#>  1 789 cal BP  2.83e-14 1.41e-13
#>  2 790 cal BP  1.90e-13 9.50e-13
#>  3 791 cal BP  3.52e-13 1.76e-12
#>  4 792 cal BP  5.14e-13 2.57e-12
#>  5 793 cal BP  6.75e-13 3.38e-12
#>  6 794 cal BP  8.37e-13 4.18e-12
#>  7 795 cal BP  9.99e-13 4.99e-12
#>  8 796 cal BP  1.16e-12 5.80e-12
#>  9 797 cal BP  1.32e-12 6.61e-12
#> 10 798 cal BP  1.48e-12 7.42e-12
#> # ℹ 14,782 more rows

# Stratify and weight bootstrap estimation by phase
cal_density(shub1_cal, strata = shub1_c14$phase)
#> # A tibble: 14,792 × 3
#>           age .estimate   .error
#>          <yr>     <dbl>    <dbl>
#>  1 789 cal BP  4.09e-14 1.79e-13
#>  2 790 cal BP  2.76e-13 1.20e-12
#>  3 791 cal BP  5.12e-13 2.23e-12
#>  4 792 cal BP  7.47e-13 3.25e-12
#>  5 793 cal BP  9.83e-13 4.28e-12
#>  6 794 cal BP  1.22e-12 5.30e-12
#>  7 795 cal BP  1.45e-12 6.33e-12
#>  8 796 cal BP  1.69e-12 7.35e-12
#>  9 797 cal BP  1.92e-12 8.38e-12
#> 10 798 cal BP  2.16e-12 9.40e-12
#> # ℹ 14,782 more rows