Example artificial data requiring multiple calibration curves - Uniform Phase

40 simulated radiocarbon determinations that are set up to need calibration against multiple curves (and with $\Delta R$ offsets for the marine samples). As for pp_uniform_phase, the samples are simulated with underlying calendar ages drawn (uniformly at random) from the period 550–500 cal yr BP $$f(\theta) = U[550, 500]$$ however in this case they are assumed to come from different environments - covering the Northern Hemisphere (NH - IntCal20), Southern Hemisphere (HS - SHCal20), and marine/surface ocean (Marine20). The observational uncertainty of each determination is set to be 15 ${}^{14}$C yrs.

The corresponding ${}^{14}$C ages are then simulated based upon the relevant (environment based) calibration curve (convolved with the 15 ${}^{14}$C yr measurement uncertainty): $$X_i | \theta_i \sim N(m(\theta_i), \rho(\theta_i)^2 + 15^2),$$ where $m(\theta_i)$ and $\rho(\theta_i)$ are the calibration curve pointwise means and uncertainties.

For the marine samples, we have incorporated into the simulation a $\Delta R$ of 100 $\pm$ 20 ${}^{14}$C yr.

Usage

pp_uniform_phase_mixed

Format

`pp_uniform_phase_mixed`

A data frame with 40 rows and 7 columns:

c14_age: The simulated ${}^{14}$C age (in ${}^{14}$C yr BP)
c14_sig: The (fixed) ${}^{14}$C age measurement uncertainty used in the simulation (set at 15 ${}^{14}$C yrs)
sample_source: The environmental source of the sample (i.e., NH, SH, or Marine). This determines the calibration curve that needs to be used
delta_r: The $\Delta R$ offset to the relevant calibration curve, set at 0 ${}^{14}$C yrs for all atmospheric (NH or SH) samples and 100 ${}^{14}$C yrs for marine samples
delta_r_sig: The (1$\sigma$) uncertainty in the $\Delta R$ offset. Set at 20 ${}^{14}$C yrs for marine samples
f14c: The corresponding simulated values of F${}^{14}$C concentration
f14c_sig: The (fixed) corresponding F${}^{14}$C measurement uncertainty used in the simulation