Outlier Models
Rayfo...@aol.com
Dear Christopher,
Can you offer some guidance here?
In OxCal V4.1 Interface build 46 the help file on Outlier analysis notes that SSimple closely follows the model of Christen 1994 i.e.
Outlier_Model("SSimple",N(0,2),0,"s").
This is applied to the Chancay culture dates with the addition of a Fake value of 1400+/-70 to illustrate the outlier analysis and includes late date of 1550 AD. The outlier analysis shifts this Fake date from a prior of 0.1 to a posterior of .39. I have tried to simulate the Christen analysis as follows (SSimple below):
with the following in broad agreement with Christen’s result. ‘Dum’ is the Fake date and is flagged as poor individual agreement of 34% and A model 72%. Posterior probability of ‘Dum’ as an outlier shifts from 10% to 50%
However, Christen also notes that the 13 Chancay determinations on table 1 are all from Charcoal samples (page 493).
If I then repeat the analysis but use the Charcoal outlier model as below (the Charcoal model):
This gives Amodel of 99% and the ‘Dum’ fake an individual agreement of 65%, which, without the knowledge that it was a fake determination, would not suggest it was an outlier.
My take on this is that the 1400+/-70 fake determination is not an outlier when we consider that the other 13 determinations are from charcoal and hence could be residual, but that the 1400+/-70 would be an outlier had the other 13 determinations been non-charcoal.
Treating the 13 determinations simply as a non charcoal phase with ‘Dum’ an outlier (question) gives it a 1% probability of it belonging to the phase.
Was the Fake determination an unfortunate illustration given the circumstances?
Regards Ray Kidd
The SSimple Model
Plot()
{
Outlier_Model("SSimple",N(0,2),0,"s");
Sequence()
{
Boundary("Start 1");
Phase("1")
{
R_Date("Dum", 1400, 70)
{
Outlier("SSimple", .1);
};
R_Date("Gd5824", 1140, 50)
{
Outlier("SSimple", .1);
};
R_Date("Gd6189", 1070, 60)
{
Outlier("SSimple", .1);
};
R_Date("Gd5310", 1000, 50)
{
Outlier("SSimple", .1);
};
R_Date("Gd5307", 970, 50)
{
Outlier("SSimple", .1);
};
R_Date("Gd5309", 910, 35)
{
Outlier("SSimple", .1);
};
R_Date("Gd6197", 900, 70)
{
Outlier("SSimple", .1);
};
R_Date("Gd5672", 830, 50)
{
Outlier("SSimple", .1);
};
R_Date("Gd6196", 810, 70)
{
Outlier("SSimple", .1);
};
R_Date("Gd5823", 670, 40)
{
Outlier("SSimple", .1);
};
R_Date("Gd2818", 520, 60)
{
Outlier("SSimple", .1);
};
R_Date("Gd5304", 460, 50)
{
Outlier("SSimple", .1);
};
R_Date("Gd3396", 430, 30)
{
Outlier("SSimple", .1);
};
R_Date("Gd5312", 390, 45)
{
Outlier("SSimple", .1);
};
};
Boundary("End 1");
Date("T_1550", 1550);
};
};
The Charcoal model
Plot()
{
Outlier_Model("Charcoal",Exp(1,-10,0),U(0,3),"t");
Sequence()
{
Boundary("Start 1");
Phase("1")
{
R_Date("Dum", 1400, 70)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5824", 1140, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd6189", 1070, 60)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5310", 1000, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5307", 970, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5309", 910, 35)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd6197", 900, 70)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5672", 830, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd6196", 810, 70)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5823", 670, 40)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd2818", 520, 60)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5304", 460, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd3396", 430, 30)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5312", 390, 45)
{
Outlier(" Charcoal", 1);
};
};
Boundary("End 1");
Date("T1550", 1550);
};
};
Christopher Ramsey
The charcoal model is very different in nature. In this model it is
assumed that all of the dates are outliers - that is they are all
wrong relative to their deposition date - since wood takes some time
to grow and therefore all charcoal dates should be older than their
context. The difference between the date of growth and deposition for
each piece of charcoal os modelled to be drawn from an exponential
distribution with an unknown time-constant (whose value is a parameter
of the model). So in this case the sample 'Dum' is just a rather
older piece of charcoal than the others.
Christopher
On 24 Jul 2009, at 20:09, Rayfo...@aol.com wrote:
> Dear Christopher,
>
> Can you offer some guidance here?
>
> In OxCal V4.1 Interface build 46 the help file on Outlier analysis
> notes that SSimple closely follows the model of Christen 1994 i.e.
>
> Outlier_Model("SSimple",N(0,2),0,"s").
>
> This is applied to the Chancay culture dates with the addition of a
> Fake value of 1400+/-70 to illustrate the outlier analysis and
> includes late date of 1550 AD. The outlier analysis shifts this
> Fake date from a prior of 0.1 to a posterior of .39. I have tried
> to simulate the Christen analysis as follows (SSimple below):
>
> with the following in broad agreement with Christen’s result. ‘Dum’
> is the Fake date and is flagged as poor individual agreement of 34%
> and A model 72%. Posterior probability of ‘Dum’ as an outlier
> shifts from 10% to 50%
Rayfo...@aol.com
{
Outlier_Model("Charcoal",Exp(1,-10,0),U(0,3),"t");
Sequence()
{
Boundary("Start 1");
Phase("1")
{
{
Outlier(" Charcoal", 1);
};
R_Date("Gd6189", 1070, 60)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5310", 1000, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5307", 970, 50)
{
Outlier(" Charcoal", 1);
};
Boundary("Transition 1/2");
Phase("2")
{
R_Date("Gd5309", 910, 35)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd6197", 900, 70)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5672", 830, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd6196", 810, 70)
{
Outlier(" Charcoal", 1);
};
Boundary("Transition 2/3");
Phase("3")
{
R_Date("Gd5823", 670, 40)
{
Outlier(" Charcoal", 1);
};
Boundary("Transition 3/4");
Phase("4")
{
R_Date("Gd2818", 520, 60)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5304", 460, 50)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd3396", 430, 30)
{
Outlier(" Charcoal", 1);
};
R_Date("Gd5312", 390, 45)
{
Outlier(" Charcoal", 1);
};
};
Date("T_1550", 1550);
};
};
Christopher Ramsey
That is reasonable - I think this is appropriate. The only problem
is, if you accept a model where all dates are expected to be earlier
than the dates of their deposition, the concept of an outlier no
longer applies as they are all outliers in this sense (just by varying
degrees). The important think with this model is that the odd really
early date won't matter at all as it will just be treated as a
terminus post quem - and it is a perfectly good date for that purpose.
There may be merits in using classical statistical methods to sort out
which dates are different from the group (as you have done with
DetSplit - but I think this should be seen as an alternative approach
to Bayesian outlier methods - I think mixing the two very different
approaches is not likely to be productive.
Christopher