Computing probabilities of temporal rank and order

[Rob Witter]

Hello OxCal folks,

In their wonderful paper on the Late Glacial reoccupation of north-western Europe, Blackwell and Buck (2003) use a very simple and intuitive approach to evaluate human activity behind the retreating ice sheet. The model they advocate offers "a coherent and flexible framework in which the data might be interpreted and within which uncertainty can be readily quantified." I feel their approach may have important applications outside of archeology, like in my field, earthquake science.

Blackwell and Buck describe a model to interpret radiocarbon data bearing on reoccupation that computes the probabilities of the earliest date of reoccupation by region and the likelihood of the order that the regions were reoccupied. The results are presented in two tables: "Table 2  The probability that each region is temporally ranked 1 through 8 (1 = earliest, 8  latest); and "Table 3  The ten most likely orders for the reoccupation of the eight regions under study."  

My question for the OxCal Group: is there a way to implement this approach in OxCal?

I want to use an approach similar to that of Blackwell and Buck to evaluate the order of earthquakes by region by (1) ranking the earthquakes temporally, and (2) computing the most likely ordering. I've discovered that the Order command computes the pair-wise relative probabilities that one event occurred before another. However, I haven't found a way, using OxCal, to model the temporal ranking of more than two events, and the likely ordering of a series of events.

I feel I'm close but missing something. Suggestions?

[MILLARD, ANDREW R.]

Hello Rob,

 

It is a bit complicated but can be done by manipulating the OxCal output. There are two ways. First is to use the MCMC_Sample command, capture the sample and analyse the frequencies of the different orderings. Second is to use algebra to go from the pairwise to sequence probabilities.

 

As an example of the second approach with three events, A, B , C.

Order gives six pairwise probabilities p(A < B), p(A < C), p(B < A), p(B < C), p(C < A), and p(C < B).

We are interested in the six full order probabilities : p(A < B < C), p(A < C < B), p(B < A < C), p(B < C < A), p(C < A < B), and p(C < B < A).

We know that p(A < B) = p(A < B < C) + p(A < C < B) + p(C < A < B).

The other pairwise probabilities can similarly be expressed as sums of full order probabilities.

This gives a system of linear equations which can be solved to give the full order probabilities.

This gets complicated, especially with larger numbers of events, so the best way to solve the equations is to use matrix algebra tools such as solve() in R or np.linalg.solve() in Python.

 

Best wishes 

Andrew 

-- 

Prof. Andrew Millard 

Department of Archaeology,

Durham University, UK 

Email: A.R.M...@durham.ac.uk  

Personal page: https://www.durham.ac.uk/staff/a-r-millard/ 

Dunbar 1650 MOOC: https://www.futurelearn.com/courses/battle-of-dunbar-1650 

Durham research: http://www.durham.ac.uk/global-research-brochure

 

 

From: ox...@googlegroups.com <ox...@googlegroups.com> On Behalf Of Rob Witter
Sent: 01 December 2025 19:24
To: OxCal <ox...@googlegroups.com>
Subject: Computing probabilities of temporal rank and order

 

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