INSTAR
Bayesian archaeology:
black box or lighting the
darkness?
Rick Schulting
School of Archaeology
University of Oxford
2360 BC
Calibrated 14C date on cremated human bone from
Largantea wedge tomb
Schulting, R.J., Sheridan, A., Clarke, S.R., and Bronk Ramsey, C. 2008. Largantea
and the dating of Irish wedge tombs. Journal of Irish Archaeology 17: 1-17.
Bayesian modelling
Essay Towards Solving a Problem in the Doctrine of Chances
?
Thomas Bayes, c. 1702 - 1761
Bayesian modelling
Bayes’ Theorem
P(A|B) =
P(B|A) P(A)
P(B)
P(A) = marginal or prior probability of A
P(B) = prior probability of B
P(A|B) = conditional or posterior probability of A given B
P(B|A) = posterior probability of B given A
  A prescription for modifying one’s beliefs in the light of
new information, i.e., beliefs about the likelihood of A are
modified by having observed B
Two kinds of Bayesian models:
Case 1. We have strong reasons for assigning a
chronological order to a series of events (e.g., stratigraphy).
This information should strongly affect the outcome of the
model, and so is known as an ‘informative prior
belief’ (Bayliss et al. 2007).
Case 2. We have no stratigraphic information, only
assumptions about the mathematical distribution of dates
in a single phase of activity. This is known as an
‘uninformative prior belief’.
A common assumption for the distribution of dates in a
phase takes the form of a simple black box…
Activity starts
Activity ends
Wayland’s Smithy I long barrow
Whittle, A., Bayliss, A., and Wysocki, M. 2007. Once in a lifetime: the date of the Wayland's
Smithy long barrow. Cambridge Archaeological Journal 17: 103-121.
“The new radiocarbon revolution”
Wayland’s Smithy I
modelled dates
Bayliss, A., and Whittle, A.
2007. Histories of the dead:
building chronologies for five
southern British long barrows.
Cambridge Archaeological
Journal 17.
The new radiocarbon dating
revolution. 2007. Current
Archaeology 209: 9-20.
Case I: Bayesian
modelling with
stratigraphy
Bayliss, A., and Whittle, A.
2007. Histories of the dead:
building chronologies for five
southern British long barrows.
Cambridge Archaeological
Journal 17.
The new radiocarbon dating
revolution. 2007. Current
Archaeology 209: 9-20.
Bayesian modelling of English Early Neolithic monuments
The new radiocarbon dating revolution. 2007. Current Archaeology 209: 9-20.
Case 1. Bayesian modelling with stratigraphy
A court tomb somewhere in the west…
RJS-1 hazelnut shell 4950 ± 30 BP
RJS-2 human tooth 5000 ± 30 BP
(not this one)
RJS-1 hazelnut shell 4950 ± 30 BP: 3787-3656 BC
RJS-2 human tooth 5000 ± 30 BP: 3939-3702 BC
We should be able to do a bit better than this. We know (or at
least strongly suspect) that the hazelnut was deposited before the
tooth. This is our ‘prior belief’ and can be incorporated into a
Bayesian model as such.
Because it is based on stratigraphy, it should strongly affect the
outcome of the model, and so is known as an ‘informative prior
belief’.
RJS-1 hazelnut shell 4950 ± 30 BP: 3787-3656 BC
RJS-2 human tooth 5000 ± 30 BP: 3939-3702 BC
Modelled probability distributions (2 sigma date ranges)
RJS-1 hazelnut shell 4950 ± 30 BP: 3798-3706 BC
RJS-2 human tooth 5000 ± 30 BP: 3790-3695 BC
4900 ± 30
4950 ± 30
3787-3656 BC = 131 years > 3798-3706 BC = 92 years
3939-3702 BC = 237 years > 3790-3695 BC = 95 years
Case study 2: ‘Oakgrove’, Gransha site 12
Case study 2. Bayesian modelling without stratigraphy
Gransha site 12, Co. Londonderry/Derry
Sample
material
charcoal
OG1
OG2
OG3
OG4
OG5
OG6
hazelnut shell
wheat
wheat
hazelnut shell
naked barley
naked barley
Context Lab no.
Beta-227762
628
628
628
613
628
628
14
C BP
4930
±
70
δ13C
-26.5
UBA-10037
4828
44 -24.2
UBA-10038
4851
36 -23.6
UBA-10039
4831
49 -26.9
UBA-10040
4906
34 -24.3
UBA-10041
4832
32 -30.8
UBA-10043
4914
26 -23.8
All dates combined (95%)
All dates
Boundary start
Boundary end
'Span' 68%
'Span' 95%
2σ cal BC
3943 3640
3702
3705
3708
3715
3694
3761
3696
3521
3533
3388
3640
3527
3644
3638
3696
3689
0
0
3638
3597
48
115
With thanks to Robert Chapple, Northern Archaeological Consultancy, for
providing the samples and to Paula Reimer and 14CHRONO for funding them
Calibrated 14C dates from Gransha site 12
Calibrated date BC
Seems to span about 200-300 years ? …
Based on these dates, how long was this site in use?
In this case our prior beliefs are ‘uniformative’; they are based
only on assumptions about the mathematical distribution of
dates in a single phase of activity.
Calibrated date BC
If activity really began at this site from 3960 calBC and ended
3400 calBC, and we randomly took 7 samples for dating, how
likely is that their calibrated ranges would look like this?
Not very likely at all!
Calibrated date BC
What if activity began at 3800 calBC and ended 3500 calBC…
More likely, but the actual dates still do not fit this very well.
They would be expected to show a wider calibrated range.
The OxCal programme more or less shifts the boundaries of the ‘box’
and asks this questions a lot of times (100s of thousands to millions),
until it comes up with its best solution, i.e., its best estimate of the
true span of activity sampled by the dates input into the model.
Modelled dates from Gransha site 12
Charcoal date
prior probability
posterior
probability
Modelled dates from Gransha site 12
Basic calibrated
date
posterior
probability
prior probability
Hazelnut shell date from Gransha site 12
Gransha unmodelled and modelled dates
Note quite the end of the story… the 7 samples we happen to
have selected from our phase of activity may not represent its
actual duration adequately.
Boundary ‘start’ and ‘end’ provide estimates for this.
2σ
Gransha site 12, Co. Londonderry/Derry
Sample
material
charcoal
OG1
OG2
OG3
OG4
OG5
OG6
hazelnut shell
wheat
wheat
hazelnut shell
naked barley
naked barley
Context Lab no.
Beta-227762
628
628
628
613
628
628
14
C BP
4930
±
70
δ13C
-26.5
UBA-10037
4828
44 -24.2
UBA-10038
4851
36 -23.6
UBA-10039
4831
49 -26.9
UBA-10040
4906
34 -24.3
UBA-10041
4832
32 -30.8
UBA-10043
4914
26 -23.8
All dates combined (95%)
All dates
Boundary start
Boundary end
'Span' 68%
'Span' 95%
2σ cal BC
3943 3640
3702
3705
3708
3715
3694
3761
3696
3521
3533
3388
3640
3527
3644
3638
3696
3689
0
0
3638
3597
48
115
With thanks to Robert Chapple, Northern Archaeological Consultancy, for
providing the samples and to Paula Reimer and 14CHRONO for funding them
Case study 3: The Mound of the Hostages, Tara
O'Sullivan, M. 2005. Duma na nGiall - The Mound of the Hostages, Tara.
Dublin: Wordwell and University College Dublin.
The Mound of the Hostages, Tara
Mound of the Hostages, Tara – a selection from the 61 dates available
Pre-cairn
charcoal
dates
Human
bone from
chamber
Brindley, A.L., Lanting, J.N., and van der Plicht, J. 2005. Radiocarbon-dated samples from the Mound of the Hostages. In: M.
O'Sullivan (ed.), Duma na nGiall-The Mound of the Hostages, Tara: pp. 281-296. Dublin: Wordwell and University College Dublin.
Basic calibrated series
Bayesian modelled series
GrA-17676, 4485 ± 40 BP
Pre-cairn charcoal
3350-3028 BC
3352-3110 BC
GrA-17679, 4415 ± 40 BP
Human bone from chamber
3327-2916 BC
3062-2913 BC
GrA-18354, 4230 ± 50 BP
Human bone from chamber
2921-2634 BC
3021-2857 BC
Bayesian modelled series
A possible gap?
Mound of the Hostages, Tara
Modelled ‘interval’ between pre-cairn and primary use phases:
0-152 years at 1 sigma
0-266 years at 2 sigma
“All models are wrong, some models are useful”
(Box 1979 quoted in Bayliss et al. 2007)
Bayliss, A., Bronk Ramsey, C., van der Plicht, J., and Whittle, A.
2007. Bradshaw and Bayes: towards a timetable for the Neolithic.
Cambridge Archaeological Journal 17: 1-28.