Bayesian updating formula

However, even if that body of knowledge is common to two people, their probability evaluations are not required to agree,[2] and may for neither of them properly reflect the knowledge on which they are based.

I do not regard this as a satisfactory paradigm for scientific inference.

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Both the radiocarbon determination and the calibration curve are uncertain, but errors in them are random and in practice can be combined.

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.

In April 2014 I published a guest article about statistical methods applicable to radiocarbon dating, which criticised existing Bayesian approaches to the problem.

A standard – subjective Bayesian – method of inference about the true calendar age of a single artefact from a radiocarbon date determination (measurement) involved using a uniform-in-calendar-age prior.

I argued that this did not, as claimed, equate to not including anything but the radiocarbon dating information, and was not a scientifically sound method for inference about isolated examples of artefacts.[1] My article attracted many comments, not all agreeing with my arguments.

This article follows up and expands on points in my original article, and discusses objections raised. Radiocarbon dating involves determining the radiocarbon age of (a sample from) an artefact and then converting that determination to an estimate of the true calendar age , using a highly nonlinear calibration curve.

Calendar age uncertainty ranges for an artefact whose radiocarbon age is determined (subject to measurement error) can be derived from the resulting posterior PDFs.

They can be constructed either from one-sided credible intervals (finding the values at which the cumulative distribution function (CDF) – the integral of the PDF – reaches the two uncertainty bound probabilities), or from highest probability density (HPD) regions containing the total probability in the uncertainty range.

In the subjective Bayesian paradigm, probability represents a purely personal degree of belief.

That belief should reflect existing knowledge, updated by new observational data.


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