Follow up: First earlier than Starting Boundary

[Erik]

Hello everyone -

This is a follow up post, as a new thread, to a recent one on the same topic.

I want to thank all those who replied in the previous thread - I learned a lot. I have since been able to construct a better model and have a better idea of what I am modeling.

The best option was the Phase of Boundaries Model - basically a phase consisting of starting boundaries (cross-referenced) from models for individual sites (treated as their founding dates).

Now, my two important pieces of data are (1) the starting boundary of the Phase of Boundaries: 3490 BP, sigma 73.

AND (2) the First query, which oddly returns a date earlier than the starting boundary: 3580 BP, sigma 56.

How can interpret this? From what I understand (from the the previous forum discussion), the First date shouldn't be earlier than the Starting Boundary.

Thanks, as usual, for advice and suggestions -

Erik

[Bayliss, Alex]

Hi Erik,

 

Have you calculated your ‘First’ parameter from within the bounded phase of starting boundaries?

 

Alex

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[Erik]

Yes, Alex, exactly. Is that a problem?

[Erik]

I'm attaching images of the distributions of both the starting boundary and First query. Maybe they will help. What is with the spike? is that normal?

[Rayfo...@aol.com]

Hello Erik,

 

Not to interrupt Alex's reply, but on the spike, I had a similar problem with dates around that period,  Christopher's advice was as follows:

"

Ray

Interesting one this.

What is happening here is that there is a possibility (although small) that the phase is very short.  The MCMC algorithm with the default settings uses the first few passes to determine the range of likely outputs.  In this case it narrows the possibilities down too much - then in subsequent runs the program gets stuck at the ends of these limits producing the sharp spikes you see.

The problem can be eliminated by making sure that the program does more iterations each pass.  For example the following code:

Options()
{
  kIterations=1000;
};
Plot()
{
  Phase()
  {
   Sequence()
   {
    Boundary("Start SC");
    Phase("2")
    {

seems to run fine to completion

"

  Hope this helps

 

Regards

 

Ray

 

In a message dated 22/10/2013 04:12:57 GMT Daylight Time, erik....@gmail.com writes:

I'm attaching images of the distributions of both the starting boundary and First query. Maybe they will help. What is with the spike? is that normal?

[Erik]

Great idea, Ray. I actually remember seeing that post, but couldn't find it again.

The explanation makes a lot of sense in my case - I in fact think it was a very short phase.

I am running it again with the kiterations option. If it worked for you, I'm optimistic. Thanks!

But it probably won't solve my dilemma of the First date being earlier than the Starting Boundary.

However, this may also be explained by the fact that I may have a very short phase.

Erik

[Rayfo...@aol.com]

Hi Erik,

 

As I said, I don't wish to interfere with anything Alex may have to say, but it strikes me that the spikes are appearing at opposite ends of the two plots, so the medians will probably be biased accordingly.  I think you need to get  plots without the spikes before deciding if there is something to address.

 

regards

 

Ray

 

--

[MILLARD A.R.]

To me these spikes look very much like MCMC convergence problems, so the idea of doing longer runs is definitely a good one. Like every other measure of convergence, OxCal's measure is not perfect and the results can occasionally pass the test while actually not being converged.

On the fact that the median of the first is earlier than the median of the start, this is perfectly possible. In every iteration of the MCMC the start will be earlier than the first, and so the means of the two distributions are guaranteed to be in that order, but with two skewed or multimodal distributions it is possible that the medians do not show the same ordering as the means.


Best wishes

Andrew
--
 Dr. Andrew Millard 
e: A.R.M...@durham.ac.uk | t: +44 191 334 1147
 w: http://www.dur.ac.uk/archaeology/staff/?id=160
 Senior Lecturer in Archaeology, Durham University, UK

> -----Original Message-----
> From: ox...@googlegroups.com [mailto:ox...@googlegroups.com] On Behalf

[Erik]

The additional iterations fixed the spikes - these are good results, I think.

Incidentally, the Last date is just slightly before than the Ending Boundary, as expected, but strongly overlapping.

However, the First date remains earlier than the Starting Boundary (means and medians), and the distributions don't overlap much - see attached.

I understand this is perfectly possible... but the question remains how to interpret it.

Erik

[MILLARD A.R.]

There's definitely something wrong there. Start must be earlier than First by the model definition, and as that is true for every iteration of the MCMC it must be true for the means. More worryingly you have hardly any probability for First after -1440 and a clearly visible probability for Start in that period. I also wonder why Start has a fairly sharp cut-off of probability at -1400. Unless you have some very precise dates in there I would have expected at least a small tail to later dates.

Can you produce a Correlation plot or Difference calculation for the First and Start? Does it show that Start is always earlier than First?

Best wishes

Andrew
--
 Dr. Andrew Millard 
e: A.R.M...@durham.ac.uk | t: +44 191 334 1147
 w: http://www.dur.ac.uk/archaeology/staff/?id=160
 Senior Lecturer in Archaeology, Durham University, UK

[Erik]

Yes, something is amiss. I ran the difference calculation (First - Start), and got:

median: -87

sigma: 70

ranges: -160 to 3 (68.2%), -215 to 3 (95.4%), -285 to 3 (99.7%).

I haven't tried the correlation plot, but I don't know what new information it would offer.

It is clear that while very unlikely, it is possible that First is later (by 3 years), even at the 99.7% range.

The phase is made up of 15 starting boundaries - most actually have fairly wide sigmas themselves, but all include the same period.

It's a short phase (median span of 226 years), but that doesn't seem to explain my first vs. starting boundary issue.

Additionally, I tried to run the Order command, but it doesn't seem to accept a First query (as it's a query, not an event, that kind of makes sense) - what would the syntax be to do that? I tried the following but it doesn't do anything.

Order()

{

First("=First All Sites");

Boundary("=Start All Sites");

};

Erik

[Bayliss, Alex]

Hi Erik,

Can you post the code, as I agree with Andrew something must be wrong?

I think the order function doesn't work because you have the same parameter names in twice (in the main model, and then again in the order function). Can you try:

Order()
{
Date("=First All Sites");
Date("=Start All Sites");
};

Best wishes,

Alex

________________________________________
From: ox...@googlegroups.com [ox...@googlegroups.com] On Behalf Of Erik [erik....@gmail.com]
Sent: Wednesday, October 23, 2013 6:13 PM

To: ox...@googlegroups.com
Subject: Re: Follow up: First earlier than Starting Boundary

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[Erik]

Problem solved. Turned out it was my incorrect syntax for the Order query. I can't explain why, but this created the confusion, and seems to have moved the First date to be much earlier than it should have been. When I corrected the Order query as Alex suggested, everything worked fine. The Starting boundary wasn't affected at all, still 3490 BP, sigma 73 - and now the First date is what I would expect, 3480 BP, sigma 61.

That, and Ray's additional iterations option, have made for a much cleaner model.

Thanks as usual for the conversation. Very helpful.

Erik