Proper use of boundaries

[dthu...@gmail.com]

Hello,

I am trying to understand the proper use of the boundary options in certain situations. It seems clear that a simple "boundary" is appropriate to define a phase that is constrained within a deposition stratum.  However, what would be the appropriate boundary constraint if I want to define a phase that is unconstrained in that way. For example, I want to define a phase as sites with a particular diagnostic artifact and an associated radiocarbon date. I do not know what the chronological limits of the phase are.

Is there a publication that describes the use of boundaries in more detail than the help file?

Thanks.

Dave Thulman

[MILLARD A.R.]

> From: dthu...@gmail.com
> Sent: 15 March 2013 12:22

>
> I am trying to understand the proper use of the boundary options in
> certain situations. It seems clear that a simple "boundary" is
> appropriate to define a phase that is constrained within a deposition
> stratum. However, what would be the appropriate boundary constraint
> if I want to define a phase that is unconstrained in that way. For
> example, I want to define a phase as sites with a particular
> diagnostic artifact and an associated radiocarbon date. I do not know
> what the chronological limits of the phase are.

But there was a time when such sites started to appear and a time when they stopped being created. Those are the events that boundaries would represent in this case, and they would help you to estimate the chronological limits of the phase.

> Is there a publication that describes the use of boundaries in more
> detail than the help file?

I'd recommend Bayliss et al. (2007) for simulations that show why you almost always need boundaries, as the scatter of dates you get when dating materials from a confined time-span is likely to mislead you about the size of that span. The original paper applying boundaries to typologically defined phases (Zeidler et al. 1998) may also be helpful as it lays things out in some detail.

Bayliss A, Bronk Ramsey C, der Plicht J, Whittle A. 2007. Bradshaw and Bayes: Towards a Timetable for the Neolithic. Cambridge Archaeological Journal 17 (Supplement 1): 1-28.
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=676108

Zeidler JA, Buck CE, Litton CD. 1998. Integration of archaeological phase information and radiocarbon results from the Jama River Valley, Ecuador: A Bayesian approach. Latin American Antiquity 9:160-179.
http://www.jstor.org/stable/10.2307/971992


Best wishes

Andrew
--
 Dr. Andrew Millard                       A.R.M...@durham.ac.uk  
 Durham University
 Senior Lecturer in Archaeology              Tel: +44 191 334 1147
 Archaeology:      http://www.dur.ac.uk/archaeology/       
Personal webpage: http://community.dur.ac.uk/a.r.millard/

[David Thulman]

Thank you Andrew, that's helpful. However, I wasn't clear in my question. I know I have to use boundaries, but which of the several options is most appropriate (Boundary, tau-boundary, zero-boundary, etc.).

Dave

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[MILLARD A.R.]

> From: David Thulman
> Sent: 15 March 2013 15:43

>
> Thank you Andrew, that's helpful. However, I wasn't clear in my
> question. I know I have to use boundaries, but which of the several
> options is most appropriate (Boundary, tau-boundary, zero-boundary,
> etc.).

Sorry, I misunderstood. In that case you want Christopher's paper:

Bronk Ramsey, C. (2009). Bayesian analysis of radiocarbon dates. Radiocarbon, 51(1), 337-360.
https://journals.uair.arizona.edu/index.php/radiocarbon/article/view/3494

[Rayfo...@aol.com]

Hi,

 

Can I just add that the paper referred to has:

 

"In principle,
more complicated distributions can also be defined, which require more parameters for their specification.
The most significant of these is perhaps the trapezium model (Karlsberg 2006), which
requires 4 parameters and might be appropriate in a number of archaeological situations where you
have a slow start and end to a phase. These more complicated models are not yet implemented in
OxCal."

 

In fact the latest revision of OxCal v 4.2 does indeed include the trapezium model and is explained in the manual.

 

This model may be appropriate where 'diagnostic artifacts' as you describe, display stylistic or find count changes over time.

 

"For each boundary in such a trapezium model, the program can return the start of the transition period, the end and the midpoint (which is returned as the boundary value itself)."

 

regards

 

Ray Kidd

 

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[dthu...@gmail.com]

Thanks Ray,

I also found the Lee and Ramsey 2012 article informative.

I think for my problem the trapezium model would best describe the phase I am working on.

I ran my dates in a Trapezium model using the code for that model in the help file, but the result was simply a list of the unmodeled dates. Looking at the help file, it seems that I need to include an expression that constrains the boundary. If so, how would such an expression look? 

Dave Thulman 

[Rayfo...@aol.com]

Hi Dave,

 

I suggest you use the help file model and modify it with your own dates as the help file model runs fine.  You don't need a specific expression unless there is a particular need for a further constraint.

 

On the other thread re combining, R_Combine is used when R_dates are from the same radiocarbon source and the test is Ward and Wilson 1978 ChiSq reported as "T=12.1(5%12.6)" the pass being that the T figure is less than the 5% figure.  R_Combination is done before calibration.

 

For items that may be coeval but from different sources the Combine is used.  The test is then Acomb and reported as (n=7 Acomb= 36.0% (An=26.7%).  The pass being that the Acomb figure is greater than the An figure. Combination is done after calibration.

 

regards

 

Ray

[David Thulman]

Hi Ray,

That was my issue: I used the help file modified with my own data and got the incomplete result (even though the program ran a long time).  I just looked at it again and the boundary language seems precisely like the help file. I know the data will run with simple "boundary" command. I'll run it again and see what happens.

As for the combine question, are you saying I should combine calibrated dates for coeval ages (like two pieces of charcoal from the same hearth)?  If so, that raises the next set of criteria, such as "coeval but from different sites in the same region," etc.

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[Rayfo...@aol.com]

Hi Dave,

 

There may be an issue with where the Phase dates are put in the Trapezium model.

 

e.g. Without Trapezium Boundaries:

 

• Plot()
  • Sequence()
    • Boundary("st")
    • Phase()
      • R_Date("A",3050,25)
      • R_Date("B",3010,25)
      • R_Date("C",3020,25)
      • R_Date("D",3000,25)
      • R_Date("E",3140,25)
      • R_Date("F",3060,25)
      • R_Date("G",3110,25)
      • R_Date("H",3080,25)
      • R_Date("I",3250,25)
      • R_Date("J",3110,25)
      • R_Date("K",3070,25)
      • R_Date("L",3200,25)
      • 
    • Boundary("end")
    • Span()
    • 
  • 
• 

But with Trapezium Boundaries;

 

• Plot()
  • Sequence()
    • Boundary("MidStart")
      • Transition("Duration Start")
      • Start("Start Start")
      • End("End Start")
      • 
    • Phase()
      • R_Date("A",3050,25)
      • R_Date("B",3010,25)
      • R_Date("C",3020,25)
      • R_Date("D",3000,25)
      • R_Date("E",3140,25)
      • R_Date("F",3060,25)
      • R_Date("G",3110,25)
      • R_Date("H",3080,25)
      • R_Date("I",3250,25)
      • R_Date("J",3110,25)
      • R_Date("K",3070,25)
      • R_Date("L",3200,25)
      • 
    • Boundary("Mid End")
      • Transition("Duration End")
      • Start("Start End")
      • End("End End")
      • 
    • Span()
    • 
  • 
• 

 

On combining:

 

If the radiocarbon determinations are from the same radiocarbon source (i.e. object) then the R-Combine function is used.  This function is performed by OxCal prior to calibration.  If the Chi Sq test fails then there is an issue as to why.  (different Labs, contamination etc.)  Ward and Wilson refer to this as Case I

 

If the radiocarbon determinations are thought to be coeval but not from the same source then they may be combined after calibration.  This iCombine function is performed by OxCal after calibration using the Acomb test.  Ward and Wilson refer to this as Case II  (actually Case IIa and Case IIb depending on whether sampling variance is an additional factor or not)

 

In your example of two charcoal samples from the same hearth, I would suggest they are not necessarily from the same source, (unless you sent bits of one object to different labs), so Combine (i.e. the one that happens after calibration) is appropriate.

 

Recall also that there is a charcoal outlier facility (maybe they were burning bog oak!).

 

Combining 'coeval but from different sites in the same region'  is permissible and should the Combine function fail the Acomb test then that may indicate they were not really coeval and can't be combined.  Or perhaps the error needs to be increased to account for sampling variance.

 

See Wilson and Ward for more on this.

Archaeometry 23, 1 (1981) 19-39. Printed in Great Britain
EVALUATION AND CLUSTERING OF RADIOCARBON AGE
DETERMINATIONS: PROCEDURES AND PARADIGMS

 

regards

 

Ray

[David Thulman]

Hey I can't fully express how helpful this is. 

Looking at your model, I see a Span(), which is not in the help file (so I didn't use it). What does that refer to?

As for the post-calibration procedure, I have never heard of that, nor seen it done as far as I can remember (and I've read hundreds of reports), so I was taken aback a wee bit.

[Rayfo...@aol.com]

Hi Dave,

 

Span - that was just me checking to see what difference it made using Trapezium and ordinary Boundaries.  'View plot intervals' shows the Span and on the table view the Trapezium example is 245 years vs 260 for the ordinary Boundaries. (rounded to 5 years).

 

The paper I referred to is the follow on from the normally referenced Ward and Wilson 1978, though the approach is different from OxCal, I think it can sometimes provide insights in identifying where splits occur in a set of dates, as opposed to outliers on the ends.  But it is not an alternative to OxCal.

 

regards

 

Ray

 

If the radiocarbon determinations are thought to be coeval but not from the same source then they may be combined after calibration.  This Combine function is performed by OxCal after calibration using the Acomb test.  Ward and Wilson refer to this as Case II  (actually Case IIa and Case IIb depending on whether sampling variance is an additional factor or not)

[David Thulman]

Ray, do you have a citation that speaks to the justification for averaging calibrated dates. I know my pals here will simply not believe it otherwise.

Dave

[Rayfo...@aol.com]

Hi Dave,

 

The paper by Ward and Wilson 1978 is the one always referenced in doing a ChiSq analysis of R_Combined radiocarbon determinations.

Archaeometry 20, (I), (1978) 19-31. Printed in Great Britain
PROCEDURES FOR COMPARING AND COMBINING
RADIOCARBON AGE DETERMINATIONS: A CRITIQUE

 

However, in that paper, they refer to a subsequent work:

 

"Methods for simultaneously comparing and combining a series of radiocarbon age determinations
(i.e. the clustering of determinations, using appropriate statistical criteria) are considered elsewhere (Wilson and Ward n.d.). 

This is the paper I referred to earlier, repeated here for convenience:

Wilson and Ward 1981.

Archaeometry 23, 1 (1981) 19-39. Printed in Great Britain
EVALUATION AND CLUSTERING OF RADIOCARBON AGE

DETERMINATIONS: PROCEDURES AND PARADIGMS.

 

It goes into fine detail about the combination of Radiocarbon determinations when the ages are from different sources and which may need additional sampling variance.  These are combined following calibration (as the OxCal Combine function does)

 

The maths is not too heavy (even I could follow it!)  It includes a computer program to do the calculations, however it is in ALGOL for punched card input.

 

I have redone the program in basic as an EXE file (detsplit.exe) which I can let anyone have.  If anyone wants it, I think I'd need Christopher's permission to attach it on the group e-mails.  Or privately by contacting me on rayfo...@aol.com

 

I will be going 'off-air in an hour, back on Thursday. 21st March

 

regards

 

Ray

[David Thulman]

I'll do some reading in your absence.

Enjoy yourself.

Dave