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Rémi DAVID 1, Chantal LEROYER 2, Philippe LANOS 3, Philippe DUFRESNE 3, Gisèle ALLENET DE RIBEMONT 4
1 PhD - UMR 6566 CReAAH – University Rennes 12 MCC - UMR 6566 CReAAH - University Rennes 1
3 CNRS - UMR 5060 IRAMAT-CRP2A – University Bordeaux 34 INRAP - UMR 6566 CReAAH Rennes 1
Context of the studyBayesian statistic
Application of Bayesian method
LinksThese age models will allow to apply various modeling methods: LANDCLIM (with
Florence Mazier), modern analogues (with Odile Peyron).
Our final objective will then be to better understand the climatic changes that
influenced, since the Neolithic, the evolution of the Paris Basin, in order to compare them
with the cultural changes that took place in this geographical area during the same periods
and thus try to distinguish climatic and anthropogenic determinisms on the environment.
Contribution of Bayesian statisticto characterize the chronological limits
of the Paris Basin palynozones
These regional pollen
assemblages zones (RPAZ) are
dated by 197 radiocarbon datings,
obtained on different analyzed cores,
supplemented by archaeological and
dendrochronological datings.
To determine the precise
chronological boundaries of these
palynozones, 14C dates have been
treated by Bayesian statistics. To do
this, we used the RenDateModel
software, developed by Ph. Lanos
and Ph. Dufresne.
Based on 91 cores (about 2000 pollen samples), the
palynological synthesis established by Ch.Leroyer in paleochannels of
flood plains of the Paris Basin summarizes the Holocene vegetation
history by the individualization of 7 regional palynozones (IV to X).
Download RenDateModel software→ https://sourcesup.cru.fr/projects/rendatemodel/
Download RenGraph software → http://sourcesup.cru.fr/projects/rengraph/
The calculation allows to obtain three probability distributions for each palynozone. The first (white background)
describes the extent of the phase itself. The two others (gray background) represent, for one, the uncertainty about the
start of this phase and, for the other, the uncertainty about its end.
These three distributions result from the integration of all 14C measures ( green background) relating to the RPAZ
considered. The Bayesian treatment of the data is very "robust" in the sense that distant 14C (outliers) in a RPAZ did not
influence significantly the calculation. Indeed, they will be assigned a high variance that will underestimate their impact
in the final equation.
For each of these distributions, we can determine a time interval with a confidence level of 95% (represented by
rectangles). We obtain four dates for each RPAZ, a start date and an end date for each distribution of start and end.
ProspectsThe definition of temporal limits for the various PAZ of the Paris Basin is
a major source of chronological information. All of the pollen sequences, whose
interpretation is based on the history of regional vegetation, can benefit from it.
This allows the construction of more accurate age models for these cores.
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Fresnes Gord V C1-2
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Fresnes Noues V
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Lesches V C2
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Lesches V C3
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Neuilly V
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Vignely V a
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Vignely V b
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Warluis V b C3
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
Warluis V a C3
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
95%
Boreal V
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
95%
Begin
-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000
95%
End
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Bazoches IX Cant
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Bazoches IX Cant
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Bazoches IX Cant
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Fresnes Gord IXb C3
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Beaurains IX C1
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Houdancourt IX Tr9
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Houdancourt IX Tr9
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Houdancourt IX C2
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Jouars IX Tr41 a
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Chatenay IXa P1
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Jouars IX Tr41 b
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
Sacy IXa C2
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
95%Ancient SubAtlantic IX
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
95%
Begin
-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500
95%
End
We can thus
represent all the results
obtained with RenDateModel
for the RPAZ of the Paris
basin during the Holocene,
and confront them to the
boundaries established in
the literature for the RPAZ
and the various cultural
phases.
2000
2000
-10000 -9000 -8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000 0 1000
Preboreal IV
Boreal V
Ancient Atlantic VI
Recent Atlantic VII
SubBoreal VIII
Ancient SubAtlantic IX
-9000 -8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000 0 1000
Recent SubAtlantic X
-10000
We obtain after
calculation some probability
densities for the RPAZ which are
in succession all over the
Holocene.
In our case, the major interest is
the possibility of characterizing
successions of regional RPAZ
and to consider them as
"stratigraphic" entities that can be
used as references on all the
studied sites.
Annet Jablines IV
Beaurains IV C1 Fontainebleau IVa BEL Fresnes Gord IV C3
Fresnes Gord IVb C1-2
Fresnes Gord IVa C1-2 Joinville IV S3Neuilly IV
Noyen IV MN C23
Noyen IV MN C23 Sacy IV C2
Sevre IVWarluis IV C3
Fresnes Gord V C1-2Fresnes Noues V
Lesches V C2
Lesches V C3
Neuilly VVignely V a
Vignely V bWarluis V b C3
Warluis V a C3
Annet Jablines VI
Chatenay VI P2Fontvanne VI C3
Noyen VI a CXV
Noyen VI a CXV
Noyen VI e L196
Noyen VI d L196
Noyen VI c L196
Noyen VI b L196
Noyen VI a L196Sacy VI a C2
Sacy VI b C2
Verrieres Champs VI C7
Verrieres Cœurs VI P1
Verrieres Cœurs VI P1 b
Verrieres Cœurs VI P1 a Vignely VI
Annet Beuvronne VII C1
Annet Jablines VII
Armancourt VIIFresnes Noues VII a
Fresnes Noues VII b
Joinville VII S3 Lesches VII C3Noyen VIIa U211 a
Noyen VIIa L196 b
Noyen VIIa U211 c
Noyen VIIb MN
Noyen VIIb
Noyen VIIb
Noyen VIIb
Noyen VIIb
Bercy VIIb QS C21
Bercy VIIb QS C21
Bercy VIIb QS C21
Bercy VIIb QS C21
Bercy VIIb QS Struc7
Bercy VIIb Cap9
Bercy VIIa pirog1 Cap7
Bercy VIIb QS7
Bercy VIIb QS7Paris Harley VII
Pont St Max VII b
Pont St Max VII a
Verrieres Champs VIIa C7Verrieres Cœurs VIIa P1
Verrieres Cœurs VIIa P1
Annet Beuvronne VIII C1
Annet Jablines VIII
Armancourt VIII
Bazoches VIIIa BM
Bazoches VIIIa Csud
Champagne VIII
Champagne VIII
Champagne VIII
Champagne VIII
Champagne VIII
Chatenay VIII P3
Fresnes Noues VIIIb
Fresnes Gord VIIIa C1-2
Croix St Ouen VIIIa S2
Lesches VIII C3
Bercy VIIIa pirog3 cap6
Bercy VIIIa pirog3 cap6
Bercy VIIIa pirog3 Cap6
Bercy VIIIa pirog12 QS KIX
Bercy VIIIa pirog2 Cap7
Bercy VIIIa pirog2 Cap7
Bercy VIII QS6
Paris Harley VIII
Rueil VIII C6 a
Rueil VIII C6 a
Rueil VIII C6 b
Rueil VIII C6 c
Rueil VIII C6 c
Sacy VIIIb C2
Saint Pouange VIIIa C3 Vignely VIII a
Vignely VIII b
Bazoches IX Cant
Bazoches IX Cant
Bazoches IX Cant
Beaurains IX C1Chatenay IXa P1
Fresnes Gord IXb C3
Houdancourt IX Tr9
Houdancourt IX Tr9
Houdancourt IX C2Jouars IX Tr41 a
Jouars IX Tr41 b
Sacy IXa C2
Annet Beuvronne X C1
Baloy Xb C2
Baloy Xa C2
Beaurains X C1
Dourdan X c C12
Dourdan X b C12
Dourdan X a C12
Dourdan X c C13
Dourdan X b C13Dourdan X b C13
Dourdan X a C13
Estissac X
Fontainebleau X c BEL
Fontainebleau X b BEL
Fontainebleau X a BEL
Fontainebleau X c FRA
Fontainebleau X b FRA
Fontainebleau X a FRA
Fontainebleau X b COU
Fontainebleau X a COU
Fontainebleau X c MAJ
Fontainebleau X b MAJ
Fontainebleau X a MAJ
Fontvanne X C1Hirson X
Jouars X Tr41Lailly X c
Lailly X b
Lailly X a
Moussey XBranly X Branly XBranly X
Neauphles X a C3
Neauphles X b C3
Neauphles X C26
Neauphles X C13
Bercy X QS4
Senart X
Senart X
Senart X c
Senart X b
Senart X a
Septeuil Xb C2
Ann Jab IV
Beau IV Fonta IVa Fre Gord IV
Fre Gord IVb
Fre Gord IVa Join IVNeui IV
Noy IV
Sacy IV
Sev IVWar IV
Fre Gord VFre Noues V
Les V
Neui VVign V a
Vign V bWar V b
War V a
Ann Jab VI
Cha VIFontva VI
Noy VI a
Noy VI e L196
Noy VI d L196
Noy VI c L196
Noy VI b L196
Noy VI a L196Sacy VI a
Sacy VI b
Ver Ch VI
Ver Co VI
Ver Co VI b
Ver Co VI a Vign VI
Ann Beuv VII
Ann Jab VII
Arm VIIFre Noues VII a
Fre Noues VII b
Join VII Les VIINoy VIIa a
Noy VIIa b
Noy VIIa c
Noy VIIb
Ber VIIb
Ber VIIa
Harl VII
Pt St Max VII b
Pt St Max VII a
Ver Ch VIIa
Ver Co VIIa
Ann Beuv VIII
Ann Jab VIII
Arm VIII
Baz VIIIa
Champ VIII
Chat VIII
Fre Noues VIIIb
Fre Gord VIIIa
Cx St Ouen VIIIa
Les VIII
Ber VIIIa
Ber VIII
Harl VIII
Rue VIII a
Rue VIII b
Rue VIII c
Sacy VIIIb
St Pou VIIIa Vig VIII a
Vig VIII b
Baz IX Cant
Beau IXChat IXa
Fre Gord IXb
Houd IX
Jou IX a
Jou IX b
Sacy IXa
Ann Beuv X
Bal Xb
Bal Xa
Beau X
Dou X a
Dou X b
Dou X c
Est X
Fonta X a BEL
Fonta X b BEL
Fonta X c BELFonta X c FRA
Fonta X b FRA
Fonta X a FRA
Fonta X b COU
Fonta X a COU
Fonta X c MAJ
Fonta X b MAJ
Fonta X a MAJ
Fontva XHir X
Jou X
Lai X a
Lai X c
Lai X b
Mou XBran X
Neau X a
Neau X b
Neau X
Ber X
Sen X
Sen X a
Sen X c
Sen X b
Sept Xb
Preboreal IV
Boreal V
Ancient Atlantic VI
Recent Atlantic VII
SubBoreal VIII
Ancient SubAtlantic IX
Recent SubAtlantic X
Until then applied to a single sequence, the Bayesian approach combines 14C dates with a priori informations of
stratigraphic and palynologic type (see dashed arrows), and so to redefine new probability densities (also called distributions)
a posteriori to these dates. The originality of the calculation is to allow the determination of distributions over time for each of
the RPAZ, and also distributions for the begin and the end of these RPAZ.
Bayesian statistics (named after the mathematician Thomas Bayes,
1702-1761) rests on two basic elements:
1 - time series data X (these are the observations: for example 14C
ages with standard deviations) are expressed in the form of random variables
that follow a sampling f(X) depending on parameters ;
2 - parameters (eg calendar time) are unknown but we have prior
knowledge (eg a stratigraphic constraint, or a constraint of belonging to a
period), called a priori, expressed in the form of a probability distribution ().
Bayes' formula allows then to express the probability distribution of ,
called a posteriori, conditionally to the observed data is (X) = f(X) . ().
In our modeling, 14C are encapsulated in Facts (or events) themselves
encapsulated in Phases (or periods). Stratigraphic constraints may exist
between certain facts. Finally, the phases which must be in succession, are
constrained by start and end boundaries that we try to estimate. The
calculation of a posteriori distributions based on numerical methods MCMC
(Markov Chain Monte Carlo), and in this case on the algorithm of Gibbs.
Legend :
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