A radiocarbon-based model to detect the change of burial rites.

[kuri...@gmail.com]

Dear all,

I‘d be grateful for an advice. I have a set of 45 radiocarbon dates from inhumation and cremation burials from cemeteries distributed within a certain region well defined as an archaeological culture. I have a good reason to presume that inhumation was practiced in the initial stage of the culture, and the earliest cremations appeared somewhere in the south of the region and that there had been a certain period of spread of cremation towards the north until it became dominant throughout the whole region. I can also presume some stages of biritualism in micro-regions throughout this time and space, as it can be seen in some individual cemeteries. This is, however, the model created only on relative archaeological chronology.

What I‘d like to create is some radiocarbon-based visual model of change of the burial rite. Maybe anyone has made an analysis with a somewhat similar goal and would suggest a solution. I was thinking of two phases for both the inhumations and cremations. But three issues: 1) how to include both the diminishing inhumanions and cremations replacing them into one model, 2) how to achieve a good visual output for this, 3) and last but not least, how to add the spatial dimension of the process (maybe to simply arrange the dates after the cemeteries‘ Y coordinate – S-N and N-S?).

Not sure if I managed to express myself clearly and if at all this can be achieved within a single script. But anyway, thank you in advance for any idea.

Lauryans

[Thomas S. Dye]

Aloha Lauryans,

See the manual section "Cross referencing" for some ideas on how
this might be done.

I build a master sequence that incorporates all the age
determinations and the chronological prior information, and then
break out subsets into phases using cross references. The
functions First() and Last() are useful in the subset phases. In
your case, you might break out cremation and inhumation phases.

Take care to use Boundary() commands only when you absolutely need
them, and make sure you don't "double up" on them in the master
sequence and the subset phases.

For visual output, I wrote generalizations of First() and Last()
called "occurrence plot" and "tempo plot" for the ArchaeoPhases
package based on R. You might find them useful.

ArchaeoPhases also has functions for comparing intervals with the
Allen algebra, which might be useful when you compare the
cremation occurrences with the inhumation occurrences. At the
least, the Allen algebra establishes a vocabulary for the 13 basic
interval relations.

Hope this helps.

All the best,
Tom

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

[kuri...@gmail.com]

Thank you, Tom. Yes, seems that cross referencing should be the solution to what I generally seek. The first attempts seem to have sense. Still need a great deal of studying, but I think setting boundaries Boundary ...Phase of inhumations... Zero_Boundary and Zero_Boundary ... Phase of cremations... Boundary should work. In my case, I will experiment to arrange the dates ater their Y coordinates first.

Thanks again,

Laurynas

[Thomas S. Dye]

Aloha Lauryans,

Good news.

Note that with cross references you can try out several models at
the same time, so the effect of model choice can be monitored.

In any case, I'd recommend that one of the models use separate
phases for cremations and inhumations, without a boundary between
them. You can use First() and Last() in the separate phases.
That way, you'll have a baseline for assessing the effects of the
different boundary commands, and can compare the Firsts and Lasts
with the various Boundary estimates.

[MILLARD, ANDREW R.]

Hi Tom

If you cross reference two models at the same time then they will influence on another because the cross-references force the dates in each model to be equal at each iteration.

For example, in this simple example the dates AA and BB have identical distributions in both the models.

Plot()
{
Phase("List of dates")
{
R_Date("AA", 1000, 25);
R_Date("BB", 1010, 25);
};
Sequence("Model 1")
{
Boundary("Start 1");
Date("=AA");
Date("=BB");
Tau_Boundary("End 1");
};
Sequence("Model 2")
{
Tau_Boundary("Start 2");
Date("=AA");
Date("=BB");
Boundary("End 2");
};
};




Best wishes
Andrew
--
Dr. Andrew Millard
Associate Professor of Archaeology,
Durham University, UK
Email: A.R.M...@durham.ac.uk 
Personal page: https://www.dur.ac.uk/directory/profile/?id=160
Scottish Soldiers Project: https://www.dur.ac.uk/scottishsoldiers
Dunbar 1650 MOOC: https://www.futurelearn.com/courses/battle-of-dunbar-1650


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Subject: Re: A radiocarbon-based model to detect the change of burial rites.

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[Thomas S. Dye]

Aloha Andrew,

This is a good example of "doubling up" on Boundary commands.
Thanks for pointing out why OP shouldn't do it.

I'm urging OP to compare various boundary models with a model that
doesn't use boundaries, so the effect of the different boundary
commands can be identified.

In OP's case, I think First and Last are the way to go and I don't
see any compelling reason to choose one boundary model over
another, though OP may certainly have or find one.

All the best,
Tom

[kuri...@gmail.com]

Hello,

May I ask little more assistance with the code. I was thinking this would be correct to achieve what I seek? But I’m not sure how can I avoid using boundaries. In my case, start of inhumation and end of inhumation are beyond my interest.

Plot()
 {
  Phase()
  {
   Sequence()
   {
    Boundary("Start Inhumations");
    Phase("Inhumation")
    {
     R_Date("Inhumation_1",1750,30);
     R_Date("Inhumation_2",1700,30);
     R_Date("Inhumation_3",1650,30);

     Last("Last Inhumations");
    };
    Tau_Boundary("End Inhumations");
   };
   Sequence()
   {
    Tau_Boundary("Start Cremations");
    Phase("Cremation")
    {
     R_Date("Cremation_1",1700,30);
     R_Date("Cremation_2",1650,30);
     R_Date("Cremation_3",1600,30);

     First("First Cremations");
    };
    Boundary("End Cremations");
   };
  };
 };

And I came across a very basic issue. I've never used ArchaeoPhases. Seems it can be helpful with spatial analysis. I was trying to use the online version, but how can I import the rax data from OxCal?

Thanks in advance and all the best,

Laurynas

[Thomas S. Dye]

Aloha Lauryans,

Your code looks fine to me, but others in the group are more
experienced than I am and might be able to offer advice.

I'm suggesting you run a separate project that doesn't use
boundaries for comparison. I was mistaken that it could live in a
project where the boundary commands were used. Sorry for that
confusion.

Here is what I have in mind.

Plot()
{
Sequence()
{
Phase()
{

R_Date("Inhumation_1",1750,30);
R_Date("Inhumation_2",1700,30);
R_Date("Inhumation_3",1650,30);

R_Date("Cremation_1",1700,30);
R_Date("Cremation_2",1650,30);
R_Date("Cremation_3",1600,30);

};
C_Date(1950,0.1);
};
Phase("Inhumation")
{
Date("=Inhumation_1");
Date("=Inhumation_2");
Date("=Inhumation_3");
Last("Last Inhumations");
};
Phase("Cremation")
{
Date("=Cremation_1");
Date("=Cremation_2");
Date("=Cremation_3");
First("First Cremations");
};
};

If you want to use ArchaeoPhases (which doesn't support spatial
modeling) then you'll need to use the MCMC_Sample command, which
will output the MCMC samples to a file that ArchaeoPhases can read
with the read_oxcal() function.

[Christopher Ramsey]

The issue with not using boundaries is that the spread of the groups of dates are over-estimated. You can show this with some simple simulations - a real phase that is say 20-30 years will look as if it is a couple of hundred years typically (depending on where you are in the curve). The purpose of the boundaries - ie grouping into phases - is to overcome this. You just should not apply the model twice.

The issue in the end is a statistical one. If you think of dates as integers (it also applied to real numbers but is harder to see) there are far more possible combinations with long phases than with short - and so a simplistic approach will over-weight long phases without intending to.

It should be stressed that this simple model without boundaries is not mathematically wrong. It is the right model if the dates are completely unrelated to each other and are randomly selected from all time - then it is indeed very unlikely they are, for example all from the same decade. Usually however this is an inappropriate model for archaeological events which are related to a specific phase of activity.

In your case probably all you need is:

Plot()
{
Sequence()
{
Boundary("Start");

Phase()
{
R_Date("Inhumation_1",1750,30);
R_Date("Inhumation_2",1700,30);
R_Date("Inhumation_3",1650,30);
R_Date("Cremation_1",1700,30);
R_Date("Cremation_2",1650,30);
R_Date("Cremation_3",1600,30);
};

Boundary("End");

C_Date(1950,0.1);
};
Phase("Inhumation")
{
Date("=Inhumation_1");
Date("=Inhumation_2");
Date("=Inhumation_3");
Last("Last Inhumations");
};
Phase("Cremation")
{
Date("=Cremation_1");
Date("=Cremation_2");
Date("=Cremation_3");
First("First Cremations");
};
};

You will get a warning if there is no boundary in the model.

Best wishes

Christopher

> To view this discussion on the web visit https://groups.google.com/d/msgid/oxcal/87r17uvin7.fsf%40tsdye.online.

[Thomas S. Dye]

Aloha Christopher,

This is an interesting example.

When I run your model, Boundary Start = 204-410 and Boundary End =
388-587. These estimates are outside First Cremations = 266-418
and Last Inhumations = 357-478.

When I run my model, the estimates First Cremations = 254-416 and
Last Inhumations = 353-536 are slightly earlier and later,
respectively, than in your model. Nevertheless, they are both
inside the Boundary Start and Boundary End estimates.

The Boundary Start estimate implies that there are earlier
inhumations that haven't been dated and Boundary end estimate
implies there are later cremations that haven't been dated, i.e.,
that the unknown spread of the groups of dates are wider than the
known spread. If Lauryans were to interpret the boundaries
directly, then a method to constrain the spread of groups of dates
would paradoxically spread the estimate beyond what was observed.

In my model, Inhumation_2 and Cremation_1, which have identical
14C ages, yield identical age estimates. The same is true for
Inhumation_3 and Cremation_2.

In your model, Inhumation_2 and Cremation_1 yield identical age
estimates, but Inhumation_3 is 345-478 and Cremation_2 is 345-506.
This difference appears due to application of boundaries.

The rationale for the boundary model is clear in the case where
dates are grouped stratigraphically. The fundamental unit of
stratigraphy is, by definition, a region of space-time. Dates
collected from within this region usefully estimate the temporal
boundaries of the region, given a particular model of deposition.

Presumably, the burials in Lauryans' research are not related
stratigraphically. The practices they represent don't necessarily
occupy the same region of space-time; obsolete practices can be
reintroduced at any later time. In this situation, it is change
in the nature and relations of practices that is of interest. As
the differing age estimates for Inhumation_3 and Cremation_2 in
your model shows, the boundary model changes relations of
practices. This complicates interpretation, in my opinion.

I'm arguing that the issue in the end is statistical *and*
archaeological. In situations where dates are grouped
stratigraphically, then phases with boundaries are indicated. In
situations where they are not grouped stratigraphically and the
interest is changes in the nature and relations of practices, then
phases without boundaries is usually the appropriate model.

All the best,
Tom

[Christopher Ramsey]

Tom

Yes - but they don't have to be grouped stratigraphically for us to have information they are related. The same goes for any cultural phasing - though you might prefer to use a different phase distribution - such as trapezium. It would be very rare for any group of dates being studied archaeologically to be really independent and unrelated.

You are right that the boundaries will be outside the dated events - and first and last can be used within the main phase too. It is just important that there is one grouping in the model - otherwise you will essentially exclude all short duration interpretations due to the strong bias to longer durations. If you know the phenomena are on a much longer timescale than the dating resolution this becomes much less important - but that does not seem to be the case here.

Christopher

> To view this discussion on the web visit https://groups.google.com/d/msgid/oxcal/87pmnev2ty.fsf%40tsdye.online.

[kuri...@gmail.com]

Dear all,

Thank you for interesting discussion. I’ve made experiments in all ways you suggested and arranging my dates randomly and after the N-S and S-N coordinates. Yes, it depends a lot on how much related you suppose your samples are, and yes, there can never be samples completely unrelated in archaeology. Moreover, you can consider the same set of samples both related or unrelated, depending on the context and, above all, what question you have. The very idea of something “being related” is one of the fundamental in archaeology.

Now I’m getting to the ways of spatial analysis. Thank you once again for a good advancement of my knowledge.

Laurynas