Using boundaries

[U.A.]

Hi there,

I am struggling with figuring out the appropriate code for calibrating a group of dates from a cemetery that was in use over a period of about 100-200 years, with a defined end date.

If I have understood things correctly from reading the Manual, I need to use Boundaries to tell the model that the dates are related, but this seems to have the effect that the model assumes all burials must have occurred at the same time. It then groups the majority of the burials into a very short time frame which represents the overlap of the calibrated ranges (this also results in the earliest burials of the cemetery to be labelled with "poor agreement"). Is there a way to instruct the model to consider a defined end date of the cemetery but NOT assume that the burials occurred at the same time? The assumption is that the cemetery was used by several generations and the radiocarbon dated individuals represent both the younger and the older burials.

My main goal is obtaining RE corrected calibrated age ranges for a selection of burials from this cemetery, so not specifically chronological modeling of the burial activity, but obviously that would be pretty handy if the model could also produce an estimated sequence of the burials from oldest to youngest.

This is the code I have been working with thus far:

Plot()
 {
  Sequence()
  {
   Boundary("Start");
   Phase()
{
Curve("IntCal20","intcal20.14c");
Curve("Marine20","marine20.14c")
  {
  Reservoir(300,100);
  };
 Mix_Curves("Mixed_a","IntCal20","Marine20",11,6);
    R_Date("V1",880,30);
    Mix_Curves("Mixed_b","IntCal20","Marine20",13,7);
    R_Date("V2",805,30);
    Mix_Curves("Mixed_c","IntCal20","Marine20",11,7);
    R_Date("V3",920,30);
    Mix_Curves("Mixed_d","IntCal20","Marine20",9,6);
    R_Date("V4",695,30);
    Mix_Curves("Mixed_e","IntCal20","Marine20",12,7);
    R_Date("V5",790,30);
    Mix_Curves("Mixed_f","IntCal20","Marine20",10,6);
    R_Date("V6",710,30);
    Mix_Curves("Mixed_g","IntCal20","Marine20",13,7);
    R_Date("V7",775,30);
    Mix_Curves("Mixed_h","IntCal20","Marine20",11,6);
    R_Date("V8",785,30);
    Mix_Curves("Mixed_i","IntCal20","Marine20",12,7);
    R_Date("V9",775,30);
    Mix_Curves("Mixed_j","IntCal20","Marine20",13,7);
    R_Date("V10",795,30);
    Mix_Curves("Mixed_k","IntCal20","Marine20",14,7);
    R_Date("V11",785,30);    
    Mix_Curves("Mixed_l","IntCal20","Marine20",15,7);
    R_Date("V12",885,30);
  };
Boundary("End");
Date("End",N(AD(1300),20));
  };
 };

This is my first time doing complex models with OxCal so any advice is much appreciated! Thank you!

[MILLARD, ANDREW R.]

Hello U,

Apart from changing the end of your model to Boundary("End", N(1300,20)), which makes little difference, I would model as you have done. I think the calculations are proceeding as expected. Burials V2 and V4-V11 all have dates which have little probability density before 1300, and none of them have a unmodelled 95% range that extends before 1220. If 9 of 12 burials all occurred in less than a century, and they are selected at random from the time range of the cemetery, then that suggests that the cemetery was quite short lived, which is what the model shows. If I add an Interval command in the phase, the duration is estimated to lie between 0 and 80 years at 95% probability. That's a bit shorter than your expectation. Within that period, and with the uncertainties on the dates, radiocarbon dating cannot resolve the order, and the posterior distributions therefore all look very similar.  

If there is archaeological indication that the burials are not uniformly distributed in time, you might consider alternative models to the uniform phase. For example, if you think more of them are towards the end of use you might use tau boundary or a zero boundary for the start, as described in the manual https://c14.arch.ox.ac.uk/oxcalhelp/hlp_analysis_oper.html#group  A zero boundary, for instance, suggests a slightly wider possible range for duration of 0-120 years at 95%, but still has the modal estimate at zero years.

Best wishes 

Andrew 

-- 

Dr. Andrew Millard 

Associate Professor 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 

 

---

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Sent: Tuesday, June 11, 2024 20:10
To: OxCal <ox...@googlegroups.com>
Subject: Using boundaries

 

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[Thomas S. Dye]

Aloha U.A.,

As Andrew points out, the Boundary() command does not assume all
burials must have occurred at the same time, but instead assumes
that they are uniformly distributed through time. The uniform
distribution assumption gives OxCal license to report age
estimates for individual burials that differ from the age estimate
that would be reported if the burials were calibrated
individually. Given your main goal of obtaining reservoir
corrected age estimates for individual burials, if I understand
correctly, then this behavior might not be what you want.

An alternative to the Boundary() command in this case might be the
First() and Last() commands, which will estimate the age of the
first and last burials in your selection, regardless of which
burial was first or last. Also, the estimates of individual
burial ages will approximate the estimates yielded by calibration
individually, due to relaxing the uniform distribution assumption.
ArchaeoPhases software for R, which post-processes the
MCMC_Sample() output from OxCal, includes an occurrence plot
function that generalizes First() and Last() to yield age
estimates for the first, second, third, ... last burials.
Post-processing the MCMC_Sample() output in R opens up the
possibility of estimating a sequence of the burials by, e.g.
calculating the probability that burial V1 was first, second,
third, ... last. As Andrew notes, this is unlikely to yield a
confident sequence due to the uncertainties of 14C calibration.

My colleagues and I recently made an argument for distinguishing
substance time from event time in Bayesian chronology
construction, with a worked example based on human bone dates from
Anglo-Saxon female burials. We published this in Journal of
Archaeological Science 153 (2023). In our terms, you appear to be
after estimates in substance time, but the Boundary() command
instructs OxCal to yield estimates in event time.

hth,
Tom

--
Thomas S. Dye
https://tsdye.online/tsdye