# After constraint and Sequence

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### t...@tsdye.online

Jun 29, 2022, 3:27:20 PMJun 29
to OxCal
Aloha all,

With the following code, I'm expecting the After "constraint" to apply only to the dates in Phase E, and that Sequence C should impose that limit. Instead, the constraint is applied to the other dates in Phase B, as well, past the Sequence C closing brace.  How can I limit the effect of the constraint?

Sequence("A")
{
Boundary("start");
Phase("B")
{
Sequence("C")
{
After("D")
{
C_Date("constraint", 510, 0);
};
Phase("E")
{
R_Date(1611, 18);
R_Date(1592, 17);
R_Date(1587, 19);
R_Date(1561, 20);
R_Date(1548, 20);
R_Date(1496, 22);
};
};
R_Date("don't", 1606, 20);
R_Date("on", 1567, 19);
R_Date("me", 1561, 21);
};
Boundary("end");
};

All the best,
Tom

### Richard Staff

Jun 29, 2022, 5:56:02 PMJun 29
Aloha Tom!

My first comment on your issue is that I think that your "After" function is superfluous; you already have the C_Date before your Phase E within a Sequence, so that already achieves the desired constraint without the need of an After function.

I.e.,:

Plot()
{
Sequence("A")
{
Boundary("start");
Phase("B")
{
Sequence("C")
{
C_Date("constraint", 510, 0);
Phase("E")
{
R_Date(1611, 18);
R_Date(1592, 17);
R_Date(1587, 19);
R_Date(1561, 20);
R_Date(1548, 20);
R_Date(1496, 22);
};
};
R_Date("don't", 1606, 20);
R_Date("on", 1567, 19);
R_Date("me", 1561, 21);
};
Boundary("end");
};
};

This is allowing the other 4 dates in B to pre-date your "After" constraint, although it is hard to see because the distribution of modelled dates within the Phase is "neater" if the modelled distributions of those other dates are also constrained to post-date (or closely pre-date) "constraint".

If you tweak those 4 R_Dates - e.g., to all be 100 14C years older than you have them at present - you can then see that your model coding is working as desired:

Plot()
{
Sequence("A")
{
Boundary("start");
Phase("B")
{
Sequence("C")
{
C_Date("constraint", 510, 0);
Phase("E")
{
R_Date(1611, 18);
R_Date(1592, 17);
R_Date(1587, 19);
R_Date(1561, 20);
R_Date(1548, 20);
R_Date(1496, 22);
};
};
R_Date("don't", 1706, 20);
R_Date("on", 1667, 19);
R_Date("me", 1661, 21);
};
Boundary("end");
};
};

Hope this helps!

All the best,

Richard 🙂

Dr Richard Staff
Research Fellow in Quaternary Geochronology
Scottish Universities Environmental Research Centre (SUERC)
University of Glasgow
Tel.: +44 (0)1355 270198

Sent: 29 June 2022 20:27
Subject: After constraint and Sequence

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### t...@tsdye.online

Jun 29, 2022, 7:03:29 PMJun 29
to OxCal
Aloha Richard,

Thanks very much!  It does help to know that the After function is superfluous here.

I'm confused by the notion of "neater" within Phase B.  I thought that dates within a Phase are unordered, and so not subject to "neat" ordering.  Is this not the case?  My expectation is that the modeled posterior for a date in Phase B outside of Sequence C will approximate the unmodeled posterior because there are no constraints operating on it.

All the best,
Tom

### Richard Staff

Jun 29, 2022, 8:17:19 PMJun 29
Thanks Tom.

Well, this is the multiplot with your actual (unaltered) R_Dates:

So, because the posterior distributions on the R_Dates in Phase E end up tightly constrained (as a result of your TPQ constraint), it is more likely that the posterior distributions of the other four R_Dates are also in close agreement. This is because of the standard "uniform Phase prior" imposed by the twin Boundaries constraining the overall Phase Sequence. I.e., if the posterior distributions of the final 4 dates instead extended earlier in time, this would produce a distribution of ages within the Phase that was less uniformly distributed, and therefore in less good agreement with our implied prior.

In the example below, where I manipulated those later four samples to be 100 14C years older, their unmodelled probability distributions are inconsistent with the tighter grouping (above) and so you don't really see the same truncation of their probability distributions in the posteriors.

Hope that makes sense - it's a complicated thing to try to explain without drawing out a whole load more figures!

Richard 🙂

Dr Richard Staff
Research Fellow in Quaternary Geochronology
Scottish Universities Environmental Research Centre (SUERC)
University of Glasgow
Tel.: +44 (0)1355 270198

Sent: 30 June 2022 00:03
Subject: Re: After constraint and Sequence

### t...@tsdye.online

Jun 29, 2022, 9:06:46 PMJun 29
to OxCal
Aloha Richard,

Got it.  Thanks!

I can see how the constraint in concert with the Phase E dates affects the Phase B dates through the uniform prior introduced by the Boundary commands.

I appreciate your patient and informative guidance.

All the best,
Tom

### Richard Staff

Jun 30, 2022, 3:51:14 AMJun 30
Thanks Tom.

Just to add, by way of confirmation, that if you were to run that same model without Boundaries - which is probably not something that you would generally want to do - then you see the posteriors on those final 4 dates unmodified from their unmodelled distributions:

I think that this is more like what you were anticipating the model output to look like(?).

It hopefully helps to clarify the role of the uniform Phase prior in generating the more tightly constrained posterior distributions in the model output below.

Once again, all the best,

Richard 🙂

Dr Richard Staff
Research Fellow in Quaternary Geochronology
Scottish Universities Environmental Research Centre (SUERC)
University of Glasgow
Tel.: +44 (0)1355 270198

Sent: 30 June 2022 02:06

### MILLARD, ANDREW R.

Jun 30, 2022, 5:48:17 AMJun 30

Hi Tom,

I think your original model was correct, and I would not make Richard’s change. The After indicates that everything stratigraphically later than this sample dates after it, but it has no known chronological relationship to stratigraphically earlier events. In your model, the only earlier event is the Boundary Start. However, Constraint can indirectly affect Start and the Phase D dates as it modifies the distributions for samples in Phase E, and these are used in calculating Start. This is what you were seeing initially. Your model is saying that a priori you do not know how Start is related to Constraint.

If I run your model with all the C14 dates shifted 100 years later, it is clear that Start is not required to be earlier than Constraint.

.

In the model without After, Start is forced to predate Constraint. I suspect this is not what you want your model to do.

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

Sent: 30 June 2022 08:51
Subject: Re: After constraint and Sequence

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### Richard Staff

Jun 30, 2022, 5:54:43 AMJun 30
Yes - that's true (the inclusion of the 'After' function)...
Good point Andrew, 🙂

Sent: 30 June 2022 10:48
Subject: RE: After constraint and Sequence

### t...@tsdye.online

Jun 30, 2022, 1:58:12 PMJun 30
to OxCal
Aloha Richard and Andrew,

This discussion is extremely helpful.  Thanks!

My example intends to estimate the ages of ten stratigraphically independent contexts, each of which represents a brief time interval.  Richard's counter example without the Boundary commands does indeed produce results that meet my expectations.  As I see it now, the Boundary command treats dates within its scope as if they were stratigraphically related, and this yields estimates for the unconstrained contexts that reflect the model more than they do the actual dating evidence.

I appreciate Andrew's insight into the effects of After.  I have several other models with stratigraphic constraints where I couldn't decide whether or not to use After.  Now that I understand its effects, I'll want to take a closer look.  I suspect I was looking in the wrong place!

All the best,
Tom