To simplify matters, I worked with a stylised calibration curve, which conveyed key features of the nonlinear structure of the real calibration curve – alternating regions where the radiocarbon date varied rapidly and very slowly with calendar age – whilst retaining strict monotonicity and having a simple analytical derivative.
Figure 1, a version of Figure 2 in the original article, shows the stylised calibration curve (black) along with the error distribution density for an example radiocarbon date determination (orange).
A calibration program is used to derive estimated calendar age probability density functions (PDFs) and uncertainty ranges from a radiocarbon determination.The standard calibration program Ox Cal that I concentrated on uses a subjective Bayesian method with a prior that is uniform over the entire calibration period, where a single artefact is involved.For both variants of the uniform prior subjective Bayesian method, probability matching is nothing like exact except in the unrealistic case where the sample is drawn equally from the entire calibration range” For many scientific and other users of statistical data, I think that would clinch the case in favour of using the objective Bayesian or the SRLR methods, rather than the subjective Bayesian method with a uniform prior.Primary results are generally given by way of an uncertainty range with specified probability percentages, not in the form of a PDF.A noninformative prior primarily reflects (at least in straightforward cases) how informative, at differing values of the parameter of interest, the data are expected to be about that parameter.
In the univariate parameter continuous case, Jeffreys’ prior is known to be the best noninformative prior, in the sense that, asymptotically, Bayesian posterior distributions generated using it provide closer probability matching than those resulting from any other prior. Jeffreys’ prior is the square root of the (expected) Fisher information.In the context we have here, with a datum – the measured C14 age (radiocarbon determination) ), is the critical practical difference between subjective and objective Bayesian approaches.In a subjective approach, the prior represents as a probability distribution the investigator’s existing degree of belief regarding varying putative values for the parameter being estimated.I also examined use of the non-Bayesian signed root log-likelihood ratio (SRLR) method, judging it by the same criterion.A quick recap on Bayesian parameter inference in the continuously-valued case, which is my exclusive concern here.There is no formal requirement for the choice of prior to be evidence-based, although in scientific inference one might hope that it often would be.