Detrital zircon age distributions provide robust insights into past sedimentary systems,
but these age distributions are often complex and multi-peaked, with sample sizes too
small to confidently resolve population distributions. This limited sampling hinders
existing quantitative methods for comparing detrital zircon age distributions, which
show systematic dependence on the sizes of compared samples. The proliferation of
detrital zircon studies motivates the development of more robust quantitative methods.
We present the first attempt, to our knowledge, to infer probability model ensembles
(PMEs) for samples of detrital zircon ages using a Bayesian method. Our method infers
the parent population age distribution from which a sample is drawn, using a Monte
Carlo approach to aggregate a representative set of probability models that is consistent
with the constraints that the sample data provide.
Using the PMEs inferred from sample data, we develop a new estimate of correspondence
between detrital zircon populations called Bayesian Population Correlation
(BPC). Tests of BPC on synthetic and real detrital zircon age data show that it is nearly
independent from sample size bias, unlike existing correspondence metrics. Robust
BPC uncertainties can be readily estimated, enhancing interpretive value.
When comparing two partially overlapping zircon age populations where the shared
proportion of each population is independently varied, BPC results conform almost perfectly
to expected values derived analytically from probability theory. This conformity
of experimental and analytical results permits direct inference of the shared proportions
of two detrital zircon age populations from BPC. We provide MATLAB scripts to facilitate the procedures we describe.
Using the statistical programming package R ( https://cran.r-project.org/), and JAGS (Just Another Gibbs Sampler, http://mcmc-jags.sourceforge.net/), we processed multiple estimates of the Laurentian Great Lakes water balance components -- over-lake precipitation, evaporation, lateral tributary runoff, connecting channel flows, and diversions -- feeding them into prior distributions (using data from 1950 through 1979), and likelihood functions. The Bayesian Network is coded in the BUGS language. Water balance computations assume that monthly change in storage for a given lake is the difference between beginning of month water levels surrounding each month. For example, the change in storage for June 2015 is the difference between the beginning of month water level for July 2015 and that for June 2015., More details on the model can be found in the following summary report for the International Watersheds Initiative of the International Joint Commission, where the model was used to generate a new water balance historical record from 1950 through 2015: https://www.glerl.noaa.gov/pubs/fulltext/2018/20180021.pdf, and This data set has a shorter timespan to accommodate a prior which uses data not used in the likelihood functions.