Identifying activity pulses in radiocarbon sequences: A Monte Carlo kernel–minima approach and simulation assessment

Abstract

Radiocarbon date frequencies are widely used to reconstruct temporal variation in human activity, with peaks and gaps in kernel density estimates (KDEs) often read as discrete episodes. Such readings usually lack explicit segmentation criteria and are sensitive to sampling variability, calibration-curve structure and smoothing choices. This paper proposes and evaluates a Monte Carlo KDE–minima procedure for descriptive segmentation of dated-event intensity. Calibrated posterior distributions for individual dates are sampled to generate an ensemble of KDEs on a fixed calendar grid; local minima are retained as pulse boundaries only when they occur in both the median KDE and its 95% envelope, making the rule explicitly dependent on bandwidth and smoothing scale.

Performance is assessed with two simulation designs. Level A operates in calendar time with three pulses plus background, varying sample size, pulse separation and bandwidth. Pulse width is fixed at 400 yr and separation

is defined as the centre-to-centre distance between adjacent pulses. Level B incorporates full radiocarbon calibration under three setups (IntCal20, SHCal20 and Mixed) and compares the envelope rule with a naive single-KDE minima rule and a Poisson changepoint model for binned counts. The bandwidth range

h equals 80 h = 80 $h = 80$

–120 yr is treated as a decision-relevant multi-century smoothing regime, not as an optimal selector. High probabilities of recovering the three-pulse structure arise only when episodes are widely separated (

tilde 800 ∼ 800 $ \sim 800$

yr) and supported by at least

tilde 100 ∼ 100 $ \sim 100$

–200 dates. Calibration further degrades performance. Differences among curves are small relative to sample size, bandwidth and segmentation rule, indicating that curve choice is second-order at this scale. Conditional on correct pulse-count recovery, naive KDE typically places boundaries more tightly, but at the cost of substantially more over-segmentation. The envelope rule is therefore better understood as a low-risk device for suppressing unstable minima than as a precision estimator. Under the calibrated design examined here, the Poisson changepoint model systematically over-segments. The study sets quantitative limits on what KDE-based pulse detection can recover and provides a conservative rule for summarising broad episodes of dated activity rather than estimating population history directly.