Wiggle-match dating and the use of outlier analysis

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Rowan McBride

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Mar 1, 2022, 11:15:28 AM3/1/22
to OxCal

Hi All, 

My name is Rowan McBride and I am a PhD Student at the University of Waikato, New Zealand. My thesis aims are to apply radiocarbon wiggle-match dating to preserved palisade posts excavated from Māori pā sites (fortified villages), using the age the tree was felled to infer various construction phases of the palisade defences. 

 

My question is regarding the use of outlier analysis within the tree-ring sequence model (D_Sequence), and specifically how I prove a successful model: 

 

  • When using the tree-ring sequence model, and outlier analysis (Outlier Model ("SSimple",N(0,2),0,"s")) can the agreement indices be utilised to indicate a successful model? i.e. how else can we know the model uncertainty is reliable?

 

To illustrate the relevance of this question, I have included the models from two palisade posts from the same pa site: MA2P152 (Date of outside ring = AD1805 ± 9) and MA2P161 (Date of outside ring = AD1736 ± 3). These two posts are 69 ± 9.5 years apart in cal age, which suggests the palisade was constructed in at least two phases - but this interpretation depends upon the accuracy of the uncertainties. Please note that although in the models below I have used SHCal20, we have additional known tree-ring age data that indicates the SHCal20 is inaccurate in places. Although using a new curve with better data improves the agreement indices for both posts, MA2P161 still has a significantly higher agreement index than MA2P152.

 

Many thanks for any help or advice you can give.

 

_________________________________________________________________________________

MA2P152

Date of outside ring = AD1805 ± 9

N=5; Acomb=6.5% (An=31.6%)

N=5; df=4; T=17.3 (5% 9.5)

 

 MA2P152

Options()

 {

  Resolution=1;

  kIterations=3000;

 };

 Plot()

 {

  Curve("SHCal20.14c","SHCal20.14c")

  {

   color="red";

  };

  Outlier_Model("SSimple",N(0,2),0,"s");

  D_Sequence()

  {

   R_Date("53_MA2P152 (1-5)",234,17)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(11);

   R_Date("54_MA2P152 (12-16)",273,17)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(14);

   R_Date("55_MA2P152 (26-30)",250,15)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(21);

   R_Date("56_MA2P152 (47-51)",222,17)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(22);

   R_Date("57_MA2P152 (69-73)",241,19)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(2.5);

   Date ("Date of outside ring of tree MA2P152");

  };

  Axis(calBP(750), calBP(0));

 };

 

MA2P161

Date of outside ring = AD1736 ± 3

N=5; Acomb=49.0% (An=31.6%)

N=5; df=4; T=7.0 (5% 9.5)

 

Options()

 {

  Resolution=1;

  kIterations=3000;

 };

 Plot()

 {

  Curve("SHCal20.14c","SHCal20.14c")

  {

   color="red";

  };

  Outlier_Model("SSimple",N(0,2),0,"s");

  D_Sequence()

  {

   R_Date("64_MA2P161 (1-5)",307,17)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(19);

   R_Date("65_MA2P161 (20-24)",213,17)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(19);

   R_Date("66_MA2P161 (39-43)",198,16)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(19);

   R_Date("67_MA2P161 (58-62)",158,16)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(22);

   R_Date("68_MA2P161 (80-84)",225,16)

   {

    color="black";

    Outlier(0.05);

   };

   Gap(2.5);

   Date ("Date of outside ring of tree MA2P161");

  };

  Axis(calBP(750), calBP(0));

 };

 

 

Bayliss, Alex

unread,
Mar 1, 2022, 11:53:18 AM3/1/22
to ox...@googlegroups.com

See below in red:

 

From: 'Rowan McBride' via OxCal <ox...@googlegroups.com>
Sent: 25 February 2022 01:02
To: OxCal <ox...@googlegroups.com>
Subject: Wiggle-match dating and the use of outlier analysis

 

THIS IS AN EXTERNAL EMAIL: do not click any links or open any attachments unless you trust the sender and were expecting the content to be sent to you

Hi All, 

My name is Rowan McBride and I am a PhD Student at the University of Waikato, New Zealand. My thesis aims are to apply radiocarbon wiggle-match dating to preserved palisade posts excavated from Māori pā sites (fortified villages), using the age the tree was felled to infer various construction phases of the palisade defences. 

 

My question is regarding the use of outlier analysis within the tree-ring sequence model (D_Sequence), and specifically how I prove a successful model: 

 

  • When using the tree-ring sequence model, and outlier analysis (Outlier Model ("SSimple",N(0,2),0,"s")) can the agreement indices be utilised to indicate a successful model? i.e. how else can we know the model uncertainty is reliable?

No. Outlier analysis is a model averaging technique, so you can’t use agreement indices. You can tell if the quoted lab uncertainty is reliable by inspecting the posterior outlier values. Personally, I would run a model without outlier analysis and look at the agreement indices, and then one with your SSimple outlier model and look at the posterior outliers, and then compare the two. In practice, they almost always tell the same story (especially in something like wiggle-matching where the informative prior information in your model is correct).

To illustrate the relevance of this question, I have included the models from two palisade posts from the same pa site: MA2P152 (Date of outside ring = AD1805 ± 9) and MA2P161 (Date of outside ring = AD1736 ± 3). These two posts are 69 ± 9.5 years apart in cal age, which suggests the palisade was constructed in at least two phases - but this interpretation depends upon the accuracy of the uncertainties. Please note that although in the models below I have used SHCal20, we have additional known tree-ring age data that indicates the SHCal20 is inaccurate in places. Although using a new curve with better data improves the agreement indices for both posts, MA2P161 still has a significantly higher agreement index than MA2P152.

 I don’t understand what (e.g.) AD 1805 ± 9 is. Is this the posterior from your model? Is it really normally distributed? HPD intervals are generally safer.

It doesn’t really matter whether one post has a higher (Acomb?) index of agreement than the other, as long as both pass the An threshold of your wiggle-match. In practice, the size of the index of agreement (if the lab errors are perfectly correct) varies depending on how constrained the wiggle-match sequence is by the shape of the calibration curve. But a low index of agreement can mean your lab is under-quoting its errors, or a high index of agreement can mean your lab is over-quoting its errors. Both are possible (see Wacker et al 2020; https://doi.org/10.1017/RDC.2020.49).

But I agree with you that the calibration curve is as much of an issue as laboratory accuracy. I spent 10 years trying to do this kind of wiggle-matching on standing buildings in England, and it was not until we got single-year calibration for the northern hemisphere in the period that I was interested in that it worked consistently (and by worked I mean C14 wiggle-matching got the same answer as dendrochronology, consistently and blind). In my opinion, you need single-year calibration and a laboratory that is falling in the green zone of Wacker et al. 2020.

This is asking a lot. But not impossible.

Good luck!

Alex

 

 

Many thanks for any help or advice you can give.

 


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