<figure><img src="image_181.png" /><figcaption>**Figure 97:** Example of Posterior Distribution drawing for an Event item</figcaption></figure>

## 12.5 Marginal Posterior Distributions

In ChronoModel, the MCMC results are displayed as marginal posterior densities on the time scale (horizontal axis).

### 12.5.1 Graphs for Data, Events, Phases

The posterior densities are estimated by using a FFTW process with controllable settings in **Distrib. Options** >> **Density Options** (see section 12.3.2).

* For the Data: If the item is a Data result, the distribution curve obtained from the FFTW process is displayed with the same color as the parent Event. Under it, the solid area is limited by the HPD region. If you have ticked the **Unfold Data** >> **Individual Calib. Date**, the individual Calibration distribution without model constraints (see section 5.6) is displayed in grey outline.

If you have ticked the **Unfold Data** >> **Wiggle shifted** (see Figure 81 and Figure 83, one more curve is displayed in a grey dashed line).

If you checked **Density Options** >> **Show confidence Bar** (see section 12.3.2), the credibility interval is plotted as a horizontal bar above the curves.

<figure><img src="image_182.png" /><figcaption>**Figure 98:** Example of Posterior Distribution graph for a Data item</figcaption></figure>

* For the Event: In the same way as for the Data curve, the Event date's marginal posterior distribution is displayed with a continuous line, and the HPD region is a solid area under the curve.

Like the Data Credibility interval, the credibility interval for the Event date is displayed in the form of a bar.

The color of the graph is the color of the Event item in the Events Scene.
<figure><img src="image_180.png" /><figcaption>**Figure 97:** Example of Posterior Distribution drawing for an Event item</figcaption></figure>

## 12.5 Marginal Posterior Distributions

In ChronoModel, the MCMC results are displayed as marginal posterior densities on the time scale (horizontal axis).

### 12.5.1 Graphs for Data, Events, Phases

The posterior densities are estimated by using a FFTW process with controllable settings in **Distrib. Options** >> **Density Options** (see section 12.3.2).

* For the Data: If the item is a Data result, the distribution curve obtained from the FFTW process is displayed with the same color as the parent Event. Under it, the solid area is limited by the HPD region. If you have ticked the **Unfold Data** >> **Individual Calib. Date**, the individual Calibration distribution without model constraints (see section 5.6) is displayed in grey outline.

If you have ticked the **Unfold Data** >> **Wiggle shifted** (see Figure 81 and Figure 83, one more curve is displayed in a grey dashed line).

If you checked **Density Options** >> **Show confidence Bar** (see section 12.3.2), the credibility interval is plotted as a horizontal bar above the curves.

<figure><img src="image_181.png" /><figcaption>**Figure 98:** Example of Posterior Distribution graph for a Data item</figcaption></figure>

* For the Event: In the same way as for the Data curve, the Event date's marginal posterior distribution is displayed with a continuous line, and the HPD region is a solid area under the curve.

Like the Data Credibility interval, the credibility interval for the Event date is displayed in the form of a bar.

The color of the graph is the color of the Event item in the Events Scene.
<figure><img src="image_183.png" /><figcaption>**Figure 99:** Example of a Posterior Distribution graph for an Event item</figcaption></figure>

* For the Phase: If the item is a Phase, you can see the beginning (with dotted line) and the end posterior distributions (with dashed line) on the same graph. Under both curves, the solid area is limited by the HPD region.

At the top of the graph, there is the "Time Phase Range" bar obtained from the calculus of the same name.

This bar is shown if you ticked the [Density Options] >> [Show confidence Bar] (see section 12.3.2).

The color of the graph is the color of the Phase item in the Phases Scene.

<figure><img src="image_184.png" /><figcaption>**Figure 100:** Example of a Posterior Distribution drawing for a Phase item</figcaption></figure>

## 12.5.2 Statistics view

In the Main Results Option, click on **Show Stat.** or **Show Tempo Stat.**. A box appears on the right of each graph, with the classical statistical parameters which summarize the posterior density with the **Posterior Distrib.**.

This summary includes: MAP (posterior mode), Mean, Std Deviation, quartiles Q1, Q2 (Median), Q3, HPD Region and Credibility Interval at a given confidence level in the [Distrib. Options] >> [Density Options] >> [Confidence Level (%)].
<figure><img src="image_182.png" /><figcaption>**Figure 99:** Example of a Posterior Distribution graph for an Event item</figcaption></figure>

* For the Phase: If the item is a Phase, you can see the beginning (with dotted line) and the end posterior distributions (with dashed line) on the same graph. Under both curves, the solid area is limited by the HPD region.

At the top of the graph, there is the "Time Phase Range" bar obtained from the calculus of the same name.

This bar is shown if you ticked the [Density Options] >> [Show confidence Bar] (see section 12.3.2).

The color of the graph is the color of the Phase item in the Phases Scene.

<figure><img src="image_183.png" /><figcaption>**Figure 100:** Example of a Posterior Distribution drawing for a Phase item</figcaption></figure>

## 12.5.2 Statistics view

In the Main Results Option, click on **Show Stat.** or **Show Tempo Stat.**. A box appears on the right of each graph, with the classical statistical parameters which summarize the posterior density with the **Posterior Distrib.**.

This summary includes: MAP (posterior mode), Mean, Std Deviation, quartiles Q1, Q2 (Median), Q3, HPD Region and Credibility Interval at a given confidence level in the [Distrib. Options] >> [Density Options] >> [Confidence Level (%)].
### 12.5.3 History plot

The tab **History Plot** shows the values sampled during the MCMC process. This is a good view to check whether the model has reached a stationary state. This plot is called the trace. At the top, the ruler recalls the different steps of the MCMC process: in red the burn-in process, in orange the adapting process and in green the acquisition process. On the Phase graph, there are two traces, one for the beginning and one for the end.

The green lines are the values of the quartiles Q1 and Q3 and the red line is the value of Q2. These quartiles are computed with the acquired part which corresponds to the concatenation of all the chains.

<figure><img src="image_185.png" /><figcaption>Figure 101: Example of traces for Phase, Event and Data</figcaption></figure>

### 12.5.4 Acceptance rate

The acceptance rate is available only for Data and for Events. If you choose the Method "MH: Proposal = adapt. Gaussian Random Walk" in the Event's properties, then the expected theoretical value for the acceptance rate is 44%. This value is represented by a red dashed line on the history plot.
### 12.5.3 History plot

The tab **History Plot** shows the values sampled during the MCMC process. This is a good view to check whether the model has reached a stationary state. This plot is called the trace. At the top, the ruler recalls the different steps of the MCMC process: in red the burn-in process, in orange the adapting process and in green the acquisition process. On the Phase graph, there are two traces, one for the beginning and one for the end.

The green lines are the values of the quartiles Q1 and Q3 and the red line is the value of Q2. These quartiles are computed with the acquired part which corresponds to the concatenation of all the chains.

<figure><img src="image_184.png" /><figcaption>Figure 101: Example of traces for Phase, Event and Data</figcaption></figure>

### 12.5.4 Acceptance rate

The acceptance rate is available only for Data and for Events. If you choose the Method "MH: Proposal = adapt. Gaussian Random Walk" in the Event's properties, then the expected theoretical value for the acceptance rate is 44%. This value is represented by a red dashed line on the history plot.
<figure><img src="image_186.png" /><figcaption>Figure 102: Example of Acceptance rate for Event and Data</figcaption></figure>

12.5.5 Autocorrelation

The Y axis is always between 0 and 40.

The red dashed line has the value of 0. The autocorrelation must quickly reach 0, the best would be from the 1st iteration.

<figure><img src="image_187.png" /><figcaption>Figure 103: Example of an autocorrelation plot for Event and Data</figcaption></figure>
<figure><img src="image_185.png" /><figcaption>Figure 102: Example of Acceptance rate for Event and Data</figcaption></figure>

12.5.5 Autocorrelation

The Y axis is always between 0 and 40.

The red dashed line has the value of 0. The autocorrelation must quickly reach 0, the best would be from the 1st iteration.

<figure><img src="image_186.png" /><figcaption>Figure 103: Example of an autocorrelation plot for Event and Data</figcaption></figure>
# 13 Log

On the **Log** tab, a list of summaries is displayed.

<figure><img src="image_188.png" /></figure>

Under **Model Description** is a summary of the model structure along with the type of measurement, age, standard deviation, reference curve for the calibration process, MCMC method, stratigraphic constraints, and so on.

Under **MCMC Initialisation** is the list of the initial values used in the MCMC process and for each chain. This text is created at the first step of MCMC in the Initialization process. The information stacked on this panel is produced with the application settings which are used at the beginning of the run. So, the date format and the decimal separator cannot be changed after the run process.

Under **MCMC Adaptation**, the MCMC parameter values are displayed after the adaptation step has been completed.

Under **Posterior Distrib. Stats** are all the statistical results according for all the posterior distributions.

If you remember when you saved all the results in CSV files (see 94, these three tabs are saved in a html format. Indeed, this is useful to read results without having to open ChronoModel.

## 13.1 Model description

The first line recalls the study period set in the model. A color is defined by item type: Data in black, Events in blue, Bounds in red, Phases in orange and in green for curve parameters The main organization is: The description of each Event with the description of each of the Data included. The description of each Phase with a reminder of the name of the Event included. The description of the constraint between Phases named "Succession".
# 13 Log

On the **Log** tab, a list of summaries is displayed.

Under **Model Description** is a summary of the model structure along with the type of measurement, age, standard deviation, reference curve for the calibration process, MCMC method, stratigraphic constraints, and so on.

Under **MCMC Initialisation** is the list of the initial values used in the MCMC process and for each chain. This text is created at the first step of MCMC in the Initialization process. The information stacked on this panel is produced with the application settings which are used at the beginning of the run. So, the date format and the decimal separator cannot be changed after the run process.

Under **MCMC Adaptation**, the MCMC parameter values are displayed after the adaptation step has been completed.

Under **Posterior Distrib. Stats** are all the statistical results according for all the posterior distributions.

If you remember when you saved all the results in CSV files (see 94, these three tabs are saved in a html format. Indeed, this is useful to read results without having to open ChronoModel.

## 13.1 Model description

The first line recalls the study period set in the model. A color is defined by item type: Data in black, Events in blue, Bounds in red, Phases in orange and in green for curve parameters The main organization is: The description of each Event with the description of each of the Data included. The description of each Phase with a reminder of the name of the Event included. The description of the constraint between Phases named "Succession".
<figure><img src="image_189.png" /><figcaption>Figure 104: Description</figcaption></figure>

## 13.2 MCMC initialisation

These comments are recorded in an internal memory along the way. It means that the format date value cannot be changed after the MCMC process. The first line is the date and the hour at which the MCMC process started. This is followed by the seed of each MCMC cycle. A text indicates the list of the seeds used in the MCMC Settings to redo the same calculus. Here in the example:

List of used chains seeds (to be copied for re-use in MCMC Settings) : 703;832;32
So, if you want to redo the same process set 703;832;32

After the MCMC process initialization, for each chain there are the values of all the parameters: the Bounds in red, the Events in blue, with their Data in black and at the end the Phases and the order constraints.

The header is a reminder of the model's sampling parameters, with the seed value of each chain.
<figure><img src="image_187.png" /><figcaption>Figure 104: Description</figcaption></figure>

## 13.2 MCMC initialisation

These comments are recorded in an internal memory along the way. It means that the format date value cannot be changed after the MCMC process. The first line is the date and the hour at which the MCMC process started. This is followed by the seed of each MCMC cycle. A text indicates the list of the seeds used in the MCMC Settings to redo the same calculus. Here in the example:

List of used chains seeds (to be copied for re-use in MCMC Settings) : 703;832;32
So, if you want to redo the same process set 703;832;32

After the MCMC process initialization, for each chain there are the values of all the parameters: the Bounds in red, the Events in blue, with their Data in black and at the end the Phases and the order constraints.

The header is a reminder of the model's sampling parameters, with the seed value of each chain.
<figure><img src="image_190.png" /><figcaption>Figure 105: Log Initialisation</figcaption></figure>
<figure><img src="image_188.png" /><figcaption>Figure 105: Log Initialisation</figcaption></figure>
13.3 MCMC Adaptation

After the MCMC process Adaptation, for each chain there are the values of all the
parameters: the Bounds in red, the Events in blue, with their Data in black and at
the end the Phases and the order constraints. And gives the acceptance rate obtained
at the end of the adaptation stage. For information, when the rate is below 44%, it
is shown in red.

<figure><img src="image_191.png" /><figcaption>Figure 106: Log adaptation</figcaption></figure>

13.4 Posterior Distrib. Stats

On this tab you find all the classical statistics summaries for each item of your model.
The date format is defined in the **Application Settings** > **Time Scale** and the threshold for
HPD region and credibility is set in the **Results** > **Density Options** > **Confidence Level (%)**
Unlike the **Model Description**, if you change the threshold or the date format, all
the results are recalculated. The list starts with the Phases results in orange, next
## 13.3 MCMC Adaptation

After the MCMC process Adaptation, for each chain there are the values of all the parameters: the Bounds in red, the Events in blue, with their Data in black and at the end the Phases and the order constraints. And gives the acceptance rate obtained at the end of the adaptation stage. For information, when the rate is below 44%, it is shown in red.

<figure><img src="image_189.png" /><figcaption>Figure 106: Log adaptation</figcaption></figure>

## 13.4 Posterior Distrib. Stats

On this tab you find all the classical statistics summaries for each item of your model. The date format is defined in the **Application Settings** > **Time Scale** and the threshold for HPD region and credibility is set in the **Results** > **Density Options** > **Confidence Level (%)**. Unlike the **Model Description**, if you change the threshold or the date format, all the results are recalculated. The list starts with the Phases results in orange, next
Phases constraints (named Succession) in green and next Bounds results and finishes
with the Events results including Data and Std. Deviation results.

<figure><img src="image_192.png" /><figcaption>Figure 107: Log Posterior Distribution</figcaption></figure>
Phases constraints (named Succession) in green and next Bounds results and finishes
with the Events results including Data and Std. Deviation results.

<figure><img src="image_190.png" /><figcaption>Figure 107: Log Posterior Distribution</figcaption></figure>
# 14 Citing ChronoModel

## 14.1 Cite ChronoModel 3

When writing up results arising from CM 3, please cite our work by giving the reference with the URL for the software:

Lanos Ph. and Dufresne Ph. (2023). ChronoModel version 3: Software for Chronological Modeling of Archaeological Data using Bayesian Statistics. Available from: https://chronomodel.com

Citing the User manual:

Lanos Ph. and Dufresne Ph. (2024). ChronoModel version 3: User manual. Available from: https://chronomodel.com

## 14.2 LATEX code for BIBTEX

```bibtex
@Manual{chronomodelSoftwareV3-2024,
  title = {ChronoModel version 3: Software for Chronological Modeling of Archaeological Data using Bayesian Statistics.},
  author = {Lanos, Philippe and Dufresne, Philippe},
  year = {2024},
  url = {https://chronomodel.com},
}
```

```bibtex
@Manual{chronomodelManualV3-2024,
  title = {ChronoModel version 3: User manual},
  author = {Lanos, Philippe and Dufresne, Philippe},
  year = {2024},
  url = {https://chronomodel.com},
}
```
# 14 Citing ChronoModel

## 14.1 Cite ChronoModel 3

When writing up results arising from CM 3, please cite our work by giving the reference with the URL for the software:

Lanos Ph. and Dufresne Ph. (2023). ChronoModel version 3: Software for Chronological Modeling of Archaeological Data using Bayesian Statistics. Available from: https://chronomodel.com

Citing the User manual:

Lanos Ph. and Dufresne Ph. (2024). ChronoModel version 3: User manual. Available from: https://chronomodel.com

## 14.2 LATEX code for BIBTEX

```bibtex
@Manual{chronomodelSoftwareV3-2024,
  title = {ChronoModel version 3: Software for Chronological Modeling of Archaeological Data using Bayesian Statistics.},
  author = {Lanos, Philippe and Dufresne, Philippe},
  year = {2024},
  url = {https://chronomodel.com},
}
```

```bibtex
@Manual{chronomodelManualV3-2024,
  title = {ChronoModel version 3: User manual},
  author = {Lanos, Philippe and Dufresne, Philippe},
  year = {2024},
  url = {https://chronomodel.com},
}
```
References

Andrews, A. H., Siciliano, D., Potts, D. C., DeMartini, E. E., and Covarrubias, S. (2016). Bomb Radiocarbon and the Hawaiian Archipelago: Coral, Otoliths, and Seawater. *Radiocarbon*, 58(3):531–548.

Dye, T. (2016). Long-term rhythms in the development of Hawaiian social stratification. *Journal of Archaeological Science*, 71:1–9.

Green, P. J. and Silverman, B. W. (1994). *Nonparametric regression and generalized linear models: a roughness penalty approach*. Number 58 in Monographs on statistics and applied probability. Chapman & Hall, London ; New York, 1st ed edition.

Heaton, T. J., Köhler, P., Butzin, M., Bard, E., Reimer, R. W., Austin, W. E. N., Bronk Ramsey, C., Grootes, P. M., Hughen, K. A., Kromer, B., Reimer, P. J., Adkins, J., Burke, A., Cook, M. S., Olsen, J., and Skinner, L. C. (2020). Marine20—The Marine Radiocarbon Age Calibration Curve (0–55,000 cal BP). *Radiocarbon*, 62(4):779–820.

Hervé, G., Chauvin, A., and Lanos, P. (2013a). Geomagnetic field variations in Western Europe from 1500BC to 200AD. Part I: Directional secular variation curve. *Physics of the Earth and Planetary Interiors*, 218:1–13.

Hervé, G., Chauvin, A., and Lanos, P. (2013b). Geomagnetic field variations in western Europe from 1500bc to 200ad. part ii: New intensity secular variation curve. *Physics of the Earth and Planetary Interiors*, 218:51–65.

Hogg, A. G., Heaton, T. J., Hua, Q., Palmer, J. G., Turney, C. S., Southon, J., Bayliss, A., Blackwell, P. G., Boswijk, G., Bronk Ramsey, C., Pearson, C., Petchey, F., Reimer, P., Reimer, R., and Wacker, L. (2020). SHCal20 Southern Hemisphere Calibration, 0–55,000 Years cal BP. *Radiocarbon*, 62(4):759–778.

Hogg, A. G., Hua, Q., Blackwell, P. G., Niu, M., Buck, C. E., Guilderson, T. P., Heaton, T. J., Palmer, J. G., Reimer, P. J., Reimer, R. W., Turney, C. S. M., and Zimmerman, S. R. H. (2013). SHCal13 Southern Hemisphere Calibration, 0–50,000 Years cal BP. *Radiocarbon*, 55(4):1889–1903.

Hua, Q., Barbetti, M., and Rakowski, A. Z. (2013). Atmospheric Radiocarbon for the Period 1950–2010. *Radiocarbon*, 55(4):2059–2072.
References

Andrews, A. H., Siciliano, D., Potts, D. C., DeMartini, E. E., and Covarrubias, S. (2016). Bomb Radiocarbon and the Hawaiian Archipelago: Coral, Otoliths, and Seawater. *Radiocarbon*, 58(3):531–548.

Dye, T. (2016). Long-term rhythms in the development of Hawaiian social stratification. *Journal of Archaeological Science*, 71:1–9.

Green, P. J. and Silverman, B. W. (1994). *Nonparametric regression and generalized linear models: a roughness penalty approach*. Number 58 in Monographs on statistics and applied probability. Chapman & Hall, London ; New York, 1st ed edition.

Heaton, T. J., Köhler, P., Butzin, M., Bard, E., Reimer, R. W., Austin, W. E. N., Bronk Ramsey, C., Grootes, P. M., Hughen, K. A., Kromer, B., Reimer, P. J., Adkins, J., Burke, A., Cook, M. S., Olsen, J., and Skinner, L. C. (2020). Marine20—The Marine Radiocarbon Age Calibration Curve (0–55,000 cal BP). *Radiocarbon*, 62(4):779–820.

Hervé, G., Chauvin, A., and Lanos, P. (2013a). Geomagnetic field variations in Western Europe from 1500BC to 200AD. Part I: Directional secular variation curve. *Physics of the Earth and Planetary Interiors*, 218:1–13.

Hervé, G., Chauvin, A., and Lanos, P. (2013b). Geomagnetic field variations in western Europe from 1500bc to 200ad. part ii: New intensity secular variation curve. *Physics of the Earth and Planetary Interiors*, 218:51–65.

Hogg, A. G., Heaton, T. J., Hua, Q., Palmer, J. G., Turney, C. S., Southon, J., Bayliss, A., Blackwell, P. G., Boswijk, G., Bronk Ramsey, C., Pearson, C., Petchey, F., Reimer, P., Reimer, R., and Wacker, L. (2020). SHCal20 Southern Hemisphere Calibration, 0–55,000 Years cal BP. *Radiocarbon*, 62(4):759–778.

Hogg, A. G., Hua, Q., Blackwell, P. G., Niu, M., Buck, C. E., Guilderson, T. P., Heaton, T. J., Palmer, J. G., Reimer, P. J., Reimer, R. W., Turney, C. S. M., and Zimmerman, S. R. H. (2013). SHCal13 Southern Hemisphere Calibration, 0–50,000 Years cal BP. *Radiocarbon*, 55(4):1889–1903.

Hua, Q., Barbetti, M., and Rakowski, A. Z. (2013). Atmospheric Radiocarbon for the Period 1950–2010. *Radiocarbon*, 55(4):2059–2072.
Hua, Q., Barbetti, M., and Zoppi, U. (2004). Radiocarbon in Annual Tree Rings from Thailand During the Pre-Bomb Period, Ad 1938–1954. *Radiocarbon*, 46(2):925–932.

Hua, Q., Turnbull, J. C., Santos, G. M., Rakowski, A. Z., Ancapichún, S., De Pol-Holz, R., Hammer, S., Lehman, S. J., Levin, I., Miller, J. B., Palmer, J. G., and Turney, C. S. M. (2021). Atmospheric radiocarbon for the period 1950-2019. *Radiocarbon*, pages 1–23.

Hughen, K. A., Baillie, M. G. L., Bard, E., Warren Beck, J., Bertrand, C. J. H., Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon, P. E., Edwards, R. L., Fairbanks, R. G., Friedrich, M., Guilderson, T. P., Kromer, B., McCormac, G., Manning, S., Bronk Ramsey, C., Reimer, P. J., Reimer, R. W., Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor, F. W., VAN der Plicht, J., and Weyhenmeyer, C. E. (2004). Marine04 Marine Radiocarbon Age Calibration, 0–26 Cal Kyr Bp. *Radiocarbon*, 46(3):1059–1086.

Kovacheva, M., Kostadinova-Avramova, M., Jordanova, N., Lanos, P., and Boyadzhiev, Y. (2014). Extended and revised archaeomagnetic database and secular variation curves from bulgaria for the last eight millennia. *Physics of the Earth and Planetary Interiors*, 236:79 – 94.

Kueppers, L. M., Southon, J., Baer, P., and Harte, J. (2004). Dead wood biomass and turnover time, measured by radiocarbon, along a subalpine elevation gradient. *Oecologia*, 141(4):641–651.

Lanos, P. and Dufresne, P. (2019a). *Chronomodel version 2.0: Software for Chronological Modelling of Archaeological Data using Bayesian Statistics*.

Lanos, P. and Dufresne, P. (2019b). *Chronomodel version 2.0: User manual*.

Lanos, P. and Philippe, A. (2017). Hierarchical bayesian modeling for combining dates in archaeological context. *Journal de la Société Française de Statistique*, 158(2):72–88.

Lanos, P. and Philippe, A. (2018). Event date model: a robust bayesian tool for chronology building. *Communications for Statistical Applications and Methods*, 25(2):131–157.

Lanos, P., Philippe, A., Lanos, H., and Dufresne, P. (2016). *Chronomodel: Chronological Modelling of Archaeological Data using Bayesian Statistics (Version 1.5)*.
Hua, Q., Barbetti, M., and Zoppi, U. (2004). Radiocarbon in Annual Tree Rings from Thailand During the Pre-Bomb Period, Ad 1938–1954. *Radiocarbon*, 46(2):925–932.

Hua, Q., Turnbull, J. C., Santos, G. M., Rakowski, A. Z., Ancapichún, S., De Pol-Holz, R., Hammer, S., Lehman, S. J., Levin, I., Miller, J. B., Palmer, J. G., and Turney, C. S. M. (2021). Atmospheric radiocarbon for the period 1950-2019. *Radiocarbon*, pages 1–23.

Hughen, K. A., Baillie, M. G. L., Bard, E., Warren Beck, J., Bertrand, C. J. H., Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon, P. E., Edwards, R. L., Fairbanks, R. G., Friedrich, M., Guilderson, T. P., Kromer, B., McCormac, G., Manning, S., Bronk Ramsey, C., Reimer, P. J., Reimer, R. W., Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor, F. W., VAN der Plicht, J., and Weyhenmeyer, C. E. (2004). Marine04 Marine Radiocarbon Age Calibration, 0–26 Cal Kyr Bp. *Radiocarbon*, 46(3):1059–1086.

Kovacheva, M., Kostadinova-Avramova, M., Jordanova, N., Lanos, P., and Boyadzhiev, Y. (2014). Extended and revised archaeomagnetic database and secular variation curves from bulgaria for the last eight millennia. *Physics of the Earth and Planetary Interiors*, 236:79 – 94.

Kueppers, L. M., Southon, J., Baer, P., and Harte, J. (2004). Dead wood biomass and turnover time, measured by radiocarbon, along a subalpine elevation gradient. *Oecologia*, 141(4):641–651.

Lanos, P. and Dufresne, P. (2019a). *Chronomodel version 2.0: Software for Chronological Modelling of Archaeological Data using Bayesian Statistics*.

Lanos, P. and Dufresne, P. (2019b). *Chronomodel version 2.0: User manual*.

Lanos, P. and Philippe, A. (2017). Hierarchical bayesian modeling for combining dates in archaeological context. *Journal de la Société Française de Statistique*, 158(2):72–88.

Lanos, P. and Philippe, A. (2018). Event date model: a robust bayesian tool for chronology building. *Communications for Statistical Applications and Methods*, 25(2):131–157.

Lanos, P., Philippe, A., Lanos, H., and Dufresne, P. (2016). *Chronomodel: Chronological Modelling of Archaeological Data using Bayesian Statistics (Version 1.5)*.
Levin, I. and Kromer, B. (2004). The Tropospheric 14CO2 Level in Mid-Latitudes of the Northern Hemisphere (1959–2003). *Radiocarbon*, 46(3):1261–1272.

McCormac, F. G., Hogg, A. G., Blackwell, P. G., Buck, C. E., Higham, T. F. G., and Reimer, P. J. (2004). Shcal04 Southern Hemisphere Calibration, 0–11.0 Cal Kyr BP. *Radiocarbon*, 46(3):1087–1092.

Reimer, P. J., Austin, W. E. N., Bard, E., Bayliss, A., Blackwell, P. G., Bronk Ramsey, C., Butzin, M., Cheng, H., Edwards, R. L., Friedrich, M., Grootes, P. M., Guilderson, T. P., Hajdas, I., Heaton, T. J., Hogg, A. G., Hughen, K. A., Kromer, B., Manning, S. W., Muscheler, R., Palmer, J. G., Pearson, C., van der Plicht, J., Reimer, R. W., Richards, D. A., Scott, E. M., Southon, J. R., Turney, C. S. M., Wacker, L., Adolphi, F., Büntgen, U., Capano, M., Fahrni, S. M., Fogtmann-Schulz, A., Friedrich, R., Köhler, P., Kudsk, S., Miyake, F., Olsen, J., Reinig, F., Sakamoto, M., Sookdeo, A., and Talamo, S. (2020). The intcal20 northern hemisphere radiocarbon age calibration curve (0–55 cal kbp). *Radiocarbon*, pages 1–33.

Reimer, P. J., Baillie, M. G. L., Bard, E., Bayliss, A., Beck, J. W., Bertran, C. J. H., Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon, P. E., Edwards, R. L., Fairbanks, R. G., Friedrich, M., Guilderson, T. P., Hogg, A. G., Hughen, K. A., Kromer, B., McCormac, G., Manning, S. W., Bronk Ramsey, C., Reimer, R. W., Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor, F. W., van der Plicht, J., and Weyhenmeyer, C. E. (2004). Intcal04 Terrestrial Radiocarbon Age Calibration, 0–26 Cal Kyr BP. *Radiocarbon*, 46(3):1029–1058.

Reimer, P. J., Baillie, M. G. L., Bard, E., Bayliss, A., Beck, J. W., Blackwell, P. G., Bronk Ramsey, C., Buck, C. E., Burr, G. S., Edwards, R. L., Friedrich, M., Grootes, P. M., Guilderson, T. P., Hajdas, I., Heaton, T. J., Hogg, A. G., Hughen, K. A., Kaiser, K. F., Kromer, B., McCormac, F. G., Manning, S. W., Reimer, R. W., Richards, D. A., Southon, J. R., Talamo, S., Turney, C. S. M., van der Plicht, J., and Weyhenmeyer, C. E. (2009). IntCal09 and Marine09 Radiocarbon Age Calibration Curves, 0–50,000 Years cal BP. *Radiocarbon*, 51(4):1111–1150.

Reimer, P. J., Bard, E., Bayliss, A., Beck, J. W., Blackwell, P. G., Ramsey, C. B., Buck, C. E., Cheng, H., Edwards, R. L., Friedrich, M., Grootes, P. M., Guilderson, T. P., Haflidason, H., Hajdas, I., Hatté, C., Heaton, T. J., Hoffmann, D. L., Hogg, A. G., Hughen, K. A., Kaiser, K. F., Kromer, B., Manning, S. W., Niu, M., Reimer, R. W., Richards, D. A., Scott, E. M., Southon, J. R., Staff, R. A., Turney, C. S. M., and van der Plicht, J. (2013). IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP. *Radiocarbon*, 55(4):1869–1887.
Levin, I. and Kromer, B. (2004). The Tropospheric 14CO2 Level in Mid-Latitudes of the Northern Hemisphere (1959–2003). *Radiocarbon*, 46(3):1261–1272.

McCormac, F. G., Hogg, A. G., Blackwell, P. G., Buck, C. E., Higham, T. F. G., and Reimer, P. J. (2004). Shcal04 Southern Hemisphere Calibration, 0–11.0 Cal Kyr BP. *Radiocarbon*, 46(3):1087–1092.

Reimer, P. J., Austin, W. E. N., Bard, E., Bayliss, A., Blackwell, P. G., Bronk Ramsey, C., Butzin, M., Cheng, H., Edwards, R. L., Friedrich, M., Grootes, P. M., Guilderson, T. P., Hajdas, I., Heaton, T. J., Hogg, A. G., Hughen, K. A., Kromer, B., Manning, S. W., Muscheler, R., Palmer, J. G., Pearson, C., van der Plicht, J., Reimer, R. W., Richards, D. A., Scott, E. M., Southon, J. R., Turney, C. S. M., Wacker, L., Adolphi, F., Büntgen, U., Capano, M., Fahrni, S. M., Fogtmann-Schulz, A., Friedrich, R., Köhler, P., Kudsk, S., Miyake, F., Olsen, J., Reinig, F., Sakamoto, M., Sookdeo, A., and Talamo, S. (2020). The intcal20 northern hemisphere radiocarbon age calibration curve (0–55 cal kbp). *Radiocarbon*, pages 1–33.

Reimer, P. J., Baillie, M. G. L., Bard, E., Bayliss, A., Beck, J. W., Bertran, C. J. H., Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon, P. E., Edwards, R. L., Fairbanks, R. G., Friedrich, M., Guilderson, T. P., Hogg, A. G., Hughen, K. A., Kromer, B., McCormac, G., Manning, S. W., Bronk Ramsey, C., Reimer, R. W., Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor, F. W., van der Plicht, J., and Weyhenmeyer, C. E. (2004). Intcal04 Terrestrial Radiocarbon Age Calibration, 0–26 Cal Kyr BP. *Radiocarbon*, 46(3):1029–1058.

Reimer, P. J., Baillie, M. G. L., Bard, E., Bayliss, A., Beck, J. W., Blackwell, P. G., Bronk Ramsey, C., Buck, C. E., Burr, G. S., Edwards, R. L., Friedrich, M., Grootes, P. M., Guilderson, T. P., Hajdas, I., Heaton, T. J., Hogg, A. G., Hughen, K. A., Kaiser, K. F., Kromer, B., McCormac, F. G., Manning, S. W., Reimer, R. W., Richards, D. A., Southon, J. R., Talamo, S., Turney, C. S. M., van der Plicht, J., and Weyhenmeyer, C. E. (2009). IntCal09 and Marine09 Radiocarbon Age Calibration Curves, 0–50,000 Years cal BP. *Radiocarbon*, 51(4):1111–1150.

Reimer, P. J., Bard, E., Bayliss, A., Beck, J. W., Blackwell, P. G., Ramsey, C. B., Buck, C. E., Cheng, H., Edwards, R. L., Friedrich, M., Grootes, P. M., Guilderson, T. P., Haflidason, H., Hajdas, I., Hatté, C., Heaton, T. J., Hoffmann, D. L., Hogg, A. G., Hughen, K. A., Kaiser, K. F., Kromer, B., Manning, S. W., Niu, M., Reimer, R. W., Richards, D. A., Scott, E. M., Southon, J. R., Staff, R. A., Turney, C. S. M., and van der Plicht, J. (2013). IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP. *Radiocarbon*, 55(4):1869–1887.
Stuiver, M., Reimer, P. J., Bard, E., Beck, J. W., Burr, G. S., Hughen, K. A., Kromer, B., McCormac, G., Van Der Plicht, J., and Spurk, M. (1998). INTCAL98 Radiocarbon Age Calibration, 24,000–0 cal BP. *Radiocarbon*, 40(3):1041–1083.

Vibet, M.-A., Philippe, A., Lanos, P., and Dufresne, P. (2016). *ChronoModel V1.5 User's manual*.

Wu, Y., Fallon, S. J., Cantin, N. E., and Lough, J. M. (2021). Surface ocean radiocarbon from a porites coral record in the great barrier reef : 1945–2017. *Radiocarbon*, 63(4):1193–1203.
Stuiver, M., Reimer, P. J., Bard, E., Beck, J. W., Burr, G. S., Hughen, K. A., Kromer, B., McCormac, G., Van Der Plicht, J., and Spurk, M. (1998). INTCAL98 Radiocarbon Age Calibration, 24,000–0 cal BP. *Radiocarbon*, 40(3):1041–1083.

Vibet, M.-A., Philippe, A., Lanos, P., and Dufresne, P. (2016). *ChronoModel V1.5 User's manual*.

Wu, Y., Fallon, S. J., Cantin, N. E., and Lough, J. M. (2021). Surface ocean radiocarbon from a porites coral record in the great barrier reef : 1945–2017. *Radiocarbon*, 63(4):1193–1203.