“Weighted Means Considered Harmful” – try the alternative here!
The accessory mineral zircon is widely used to constrain the timing of igneous processes such as magma crystallisation or eruption. However, zircon U-Pb ages record zircon crystallisation, which is not an instantaneous process. Zircon saturation calculations link zircon crystallisation, temperature, and melt fraction, allowing for the estimation of zircon crystallisation distributions as a function of time or temperature. Such distributions provide valuable prior information, enabling Bayesian estimates of magma eruption time and allowing for comparison of the relative accuracy of common weighted-mean and youngest-zircon age interpretations with synthetic datasets. We find that both traditional interpretations carry a risk of underestimating the uncertainty in eruption age; a low mean square of weighted deviates (MSWD) does not guarantee the accuracy of weighted-mean interpretations. In the absence of independent confirmation that crystallisation timescale is short relative to analytical uncertainties, a Bayesian approach frequently provides the most accurate results and is least likely to underestimate uncertainty. Since U-Pb zircon studies now routinely resolve geological age dispersion due to increasing analytical precision, such considerations are increasingly critical to future progress in resolving rates and dates of Earth processes.
Keller, C.B., Schoene, B., & Samperton, K.M. (2018). A Stochastic Sampling Approach to Zircon Eruption Age Interpretation. Geochemical Persectives Letters 8, 31-35