BCal: an introduction for new users

Caitlin E. Buck, J. Andrés Christen and Gary N. James.


The BCal software

BCal is an Internet-based Bayesian radiocarbon calibration service that arises from ten years of collaborative research between archaeologists and statisticians around the world.  All of the techniques used in the computation routines have been published in the references listed in the bibliography section below.  This document is a user introduction to BCal rather than an introduction to Bayesian radiocarbon calibration.  As such, we do not discuss in detail how and why Bayesian radiocarbon calibration works.  We assume that users of BCal are already familiar with the literature in this area and aim here to supply the additional information needed to use the software successfully.

General requirements

BCal may be accessed from any modern (e.g. any version of Firefox, Opera, Safari, or Konqueror, Netscape 2 and above or Internet Explorer 3 and above) World-Wide Web browser.  BCal is entirely HTML based and so requires no special "plug ins" for your browser. All processing takes place on the BCal server and its' clients around the world. All that is required is a reasonably well equipped computer with Internet access. If your computer can read this document, you almost definitely have all you need to use BCal. We make no charge for using BCal for academic research purposes, but you should read our terms and conditions.

Using BCal

Before you start using BCal you must register yourself.  Registering provides you with your own personal BCal account and corresponding work space.  Your work space contains any projects you have created and any customization settings.  Projects contain calibration definitions and (when calibrated) the results of such calibrations.  Your work space is stored on the BCal server.  This means you can access BCal from any computer on the Internet and always have access to your own work space.

You can access the BCal software from the BCal home page.  The software is displayed in a separate window (see the screen shot below).  To access your work space you must enter the user name and PIN that correspond to your account. Once you are logged in, the window will be split into three frames. The BCal menu (in the left frame) is used to gain access to commonly used parts of BCal. The BCal work area (top right frame) is used for most of your interactions with the software.  The BCal help system (bottom right frame) provides assistance while using BCal. Using links available in the three frames you should be able to navigate through the software with relative ease. You should not need to use the standard navigational facilities provided by your browser; using them may cause unpredictable behaviour within BCal.

A typical screen shot from BCal.

Understanding parameters, determinations and groups

To get the most out of BCal it is essential that you understand three important concepts that are at the core of the software.  These are parameters, determinations and groups.  You may also wish to familiarise yourself with other BCal vocabulary.

A parameter represents the calendar date of a temporal event within your chronology.   It is such calendar dates that BCal will help you to learn more about.  The software asks you (one step at a time) to provide as much information as you can about:

  1. the chronological relationships between each parameter (i.e. relative chronological information), and
  2. the true calendar date of each parameter (i.e. absolute chronological information).
BCal calibrates the information you have supplied using mexcal which is written in C++ and utilizes the Bayesian calibration framework described in the publications in the bibliography.  Once calibrated, BCal will provide you with probability distributions for estimates of the calendar dates associated with each parameter.

One type of parameter within BCal corresponds to the calendar date for an event for which we have direct radiocarbon information.  This is called a determination parameter.  Each determination parameter represents the true, but unknown, calendar date of an archaeological event.  Users supply the radiocarbon data relating to each determination parameter in the form of determinations.  A determination is a radiocarbon age and associated error produced by a radiocarbon dating laboratory.  In most cases a determination parameter has only one determination associated with it, but "pooled" determinations are permitted within the BCal software.

BCal represents archaeological phases (and sequences) using groups.  Each group contains an archaeologically coherent collection of determination parameters.  In addition to the determination parameters it contains, a group also has two boundary parameters which relate to a late boundary and an early boundary date for the phase (or sequence).  The values of these parameters are used to bound the determination parameters within a particular group.  The posterior probability distributions for the calendar dates of the group boundary events are computed by BCal along with those for the determination parameters themselves.

User interface tools

The BCal software consists of four tools which are:

Project manager

The project manager allows you to manage the projects within your work space.  This tool provides the functionality to create new projects and to edit, copy, delete, calibrate and view the results of existing projects.  The main page of the project manager can be accessed by selecting "Project Manager" from the BCal menu.  This page also occupies the BCal work area once you are logged into the software.

The main page of the project manager is the project list page.  This page lists all the projects currently contained within your work area.  You may perform actions on each of these projects.  These actions may show other pages of the project manager, such as the copy project page, or launch one of the other BCal tools such as the definition editor tool.

Definition editor

The definition editor is the largest tool within BCal and may be accessed from the project manager by selecting "Edit" for the project you wish to edit, or by choosing "New Project" from the BCal menu.  This tool is used to create a calibration definition for each of your projects.  This definition is elicited via a question- and answer-based approach.  Questions, based upon the information you have submitted, are asked until all the information BCal requires has been elicited.  You should note that, in general, information should be provided in an "earliest first" manner, i.e. you should provide information about the earliest group in your chronology, then the second earliest and so on.

The information you provide is always stored on the BCal server, not on your own computer.  Each time you click the submit button, the information on the page is sent to the BCal server.  This information is then processed and stored (provided it does not contain errors).  Consequently, if you decide to move to another section of BCal, log out out or even turn off your computer, the information is always stored and can be returned to.

The elicitation of information is split into several stages.  At each stage BCal poses questions about a particular aspect of the calibration definition.  Once the information required for a stage has been elicited successfully, the software then moves on to ask questions about the next stage.   A stage bar appears near the top of the BCal work area.   This shows the names of all the stages for which information has been completely elicited, along with the name of the current stage.   By clicking on the stage bar you can move back, at any time, to any preceding stage, to view the elicited information and make changes.

BCal automatically keeps track of your progress through the elicitation process.  You may break this flow at any time to view or make changes to the information elicited at a previous stage, move to another part of BCal or even log out.  When you wish to return to the elicitation process, BCal will always try to take you back to your previous position in the flow of questions.  However, if you make changes to the project definition (like removing or adding a group), BCal may need to ask you further questions before it can return to your previous position.  If you break the flow of questions and wish to return, BCal will attempt to take you to your previous position in the flow of questions any time you:

In many cases you will automatically be returned to the flow of questions after submitting new information.

Calibration tool

The calibration tool is used to calibrate a project and to perform post calibration processing. The tool is split into two parts.  The first part is used to submit the calibration to BCal. This is activated by selecting "Submit" (from the project manager) for the project you wish to calibrate. Before the calibration is submitted you may alter particular settings for the Gibbs sampler used in the calibration process. These settings include the number of samples that should be used in the simulation.

The second part of the calibration tool is used to to monitor and control calibrations currently running on the BCal server.  This tool can be accessed from the BCal menu by selecting "Calibration Tool".  You will be able to view the progress of your calibrations and cancel them if you need to.

Results presentation

The results presentation tool provides you with the means to view (and download) the results of your calibrations.  Results are always expressed as posterior probability distributions of the calendar dates of interest.  You can view such distributions as plots or highest posterior density (HPD) regions.  Currently, BCal allows you to generate these distributions for estimates of the calendar age of individual parameters and also for estimates of the elapsed time between parameters.

The results presentation tool may be accessed from the project manager by selecting "Results" for any project that is already calibrated.  You are given some control over the format of the results produced.  For example, you can change the ranges and the plot style to use for posterior density plots.

Some comments on reliability and reproducibility

BCal and mexcal implement methodologies which are sophisticated and complex from both an archaeological and a statistical perspective.  As a result, it is necessary to raise here some issues that all users of the software must be aware of and should read about before using the software to tackle in interpretation of real archaeological sites.  If you have not already done so, we strongly recommend that you read Litton and Buck (1996) and Buck et al. (1996).

Firstly, translating your archaeological and a priori chronological information into suitable forms for submission to BCal may be time consuming and much more error prone than you first expect.  This software (like most other complex software) suffers badly from the garbage-in garbage-out scenario.  Think very carefully about how you represent your ideas - it will effect the kinds of answers you get and you will need to justify your specific representations when you come to write the results up!!

Secondly, because BCal uses Markov chain Monte Carlo methods to obtain the results you request, no two runs of the code will produce the same answers (unless you fix the seed for the random number generator).  However, provided that the methodology is working well you should find that multiple runs with different random seeds produce results which are very similar and certainly within the tolerance of the other errors inherent in radiocarbon dating.  You MUST check this for each project you work on.  It's easy to do, just resubmit the project for calibration a few times and check that the results are sufficiently similar given your knowledge of the variability of your data and your prior information.   We have done everything we can to assure that this will happen for most sites you are likely to analyse.  However, BCal is very flexible and you may well be trying to do something that no one has done before.  If you do have problems we will do our best to help you overcome them, but we make no promises about this as we are all researchers with our own projects to finish too.

Thirdly, because Bayesian methods are so flexible you can use BCal to define both your archaeological models and your prior information in many different ways.  This means that you have a responsibility to check what effect your specific choices are having on the results you obtain.  We suggest that, for all projects you work on, you should investigate how sensitive your results are to the decisions you have made.  Consider all the group definitions and the prior information.  Ask yourself questions of the sort.  Is it possible that a group you have defined as strictly ordered is in fact only partially ordered?  Is it possible that two groups you have defined as abutting are in fact overlapping?  Is the absolute prior information definitely of the form you specified, or are there other possibilities?  Be honest and if there is any doubt at all recalibrate your project with the alternative conditions and compare the posterior distributions you obtain.  Any reports you submit for publication (and any that you are asked to referee!) should contain reference to sensitivity analysis of this type.

Finally, we have done what we can to make BCal both reliable and robust, but Markov chain Monte Carlo simulation is sensitive, the modelling you are undertaking is complex and things may go wrong.  There are circumstances under which the software will fail.  We have done our best to eliminate these, but if you construct statistical or archaeological scenarios that we have not thought of before you may have problems - we cannot guarantee that everything you try to do will work without problems.  If you do have problems please let us know and we will do what we can, when we can.

Terms and conditions


This software is provided for academic research purposes only.  Individuals, institutions and companies wishing to use this software for commercial purposes should contact the University of Sheffield via Caitlin Buck (c.e.buck@sheffield.ac.uk).

While the University of Sheffield ("the University") has used all reasonable endeavours to ensure the quality of this software, the University makes no warranty, express or implied, as to fitness for purpose and will not be held responsible for any consequence arising out of any inaccuracies or omissions. Individuals, organisations and companies which use this software do so on the understanding that no liability whatsoever either direct or indirect shall rest upon the University for the effects of any act, product, process or method that may be effected, produced or adopted by any party, notwithstanding that the formulation of such act, product, process or method may be based upon use of this software.


Copyright © University of Sheffield, 1999-2014. All rights reserved.

Certain software components embedded within BCal are owned by third parties:

mexcal is Copyright © 1999, 2008, J. A. Christen, CIMAT, MEXICO.
Gnuplot is Copyright © 1986 - 1993, 1998, 2004 Thomas Williams, Colin Kelley.
fly is Copyright © 1995-2009, Martin Gleeson.
The Java(tm) Language Environment is Copyright © 1995, 1996, Sun Microsystems, Inc. All rights reserved.
The Generic Collection Library for Java(tm) is Copyright © 1997 ObjectSpace, Inc. - All Rights Reserved.
R is Copyright © 2014 The R Foundation for Statistical Computing.
CODA is Copyright © 1995-2012 The R Core Team.
Apache Tomcat is copyright © 1999-2013 The Apache Software Foundation.

BCal also incorporates:

available at the website of the journal Radiocarbon as supplementary material to the 2013 Calibration Special Issue (Volume 55, nr 4, 2013). available at the website of the journal Radiocarbon as supplementary material to the 2004 Calibration Special Issue (Volume 46, nr 3, 2004). provided by the Quaternary Isotope Laboratory, University of Washington; see (Stuiver 1998).


C. E. Buck (1994) Towards Bayesian Archaeology, PhD thesis University of Nottingham, Nottingham, UK.

C. E. Buck (1995) Radiocarbon dating: problem definition and sample selection, Science and Site, J. Beavis and K. Barker (eds.), 1-11.

C. E. Buck, W. G. Cavanagh and C. D. Litton (1996) The Bayesian Approach to Interpreting Archaeological Data, Wiley, Chichester.

C. E. Buck and J. A. Christen (1998) A novel approach to selecting samples for radiocarbon dating, Journal of Archaeological Science, 25, 303-310.

C. E. Buck, J. A. Christen, J. B. Kenworthy and C. D. Litton (1994) Estimating the duration of archaeological activity using 14C determinations, Oxford Journal of Archaeology, 13(2), 229-240.

C. E. Buck, J. B. Kenworthy, C. D. Litton and A. F. M. Smith (1991) Combining archaeological and radiocarbon information: a Bayesian approach to calibration, Antiquity, 65, 808-821.

C. E. Buck and C. D. Litton (1995) The radiocarbon chronology: further consideration of the Danebury dataset, in Danebury: an iron age hillfort in Hampshire, Volume 6, A hillfort community in Hampshire, B. Cunliffe (ed.), Council for British Archaeology, Report Number 102, 130-136.

C. E. Buck, C. D. Litton and E. M. Scott (1994) Making the most of radiocarbon dating: some statistical considerations, Antiquity, 68(259), 252-263.

C. E. Buck, C. D. Litton and S. J. Shennan (1994) A case study in combining radiocarbon and archaeological information: the early Bronze Age settlement of St. Veit-Klinglberg, Land Salzburg, Austria, Germania, 72, 427-447.

C. E. Buck, C. D. Litton and A. F. M. Smith (1992) Calibration of radiocarbon results pertaining to related archaeological events, Journal of Archaeological Science, 19, 497-512.

J. A. Christen (1994) Bayesian interpretation of 14C results, PhD thesis University of Nottingham, Nottingham, UK.

J. A. Christen (1994) Summarizing a set of radiocarbon determinations: a robust approach, Applied Statistics, 43(3), 489-503.

J. A. Christen and C. E. Buck (1998) Sample selection in radiocarbon dating, Applied Statistics, 47(4), 543-557.

J. A. Christen, R. S. Clymo and C. D. Litton (1995) A Bayesian approach to the use of 14C dates in the estimation of the age of peat, Radiocarbon, 37(2), 431-441.

J. A. Christen and C. D. Litton (1995) A Bayesian approach to wiggle-matching, Journal of Archaeological Science, 22(6), 719-725.

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

K. A. Hughen, M. G. L. Baillie, E. Bard, J. W. Beck, C. J. H. Bertrand, P. G. Blackwell, C. E. Buck, G. S. Burr, K. B. Cutler, P. E. Damon, R. L. Edwards, R. G. Fairbanks, M. Friedrich, T. P. Guilderson, B. Kromer, G. McCormac, S. Manning, C. B. Ramsey, P. J. Reimer, R. W. Reimer, S. Remmele, J. R. Southon, M. Stuiver, S. Talamo, F. W. Taylor, J. van der Plicht and C. E. Weyhenmeyer (2004). Marine04 - marine radiocarbon age calibration, 0 − 26 kyr BP. Radiocarbon, 46(3), 1059-1086.

C. D. Litton and C. E. Buck (1996) An archaeological example: radiocarbon dating, in Markov Chain Monte Carlo in Practice, W. Gilks, S. Richardson and D. Spiegelhalter (eds.), Chapman and Hall, London, 465-480.

C. D. Litton and M. N. Leese (1991) Some statistical problems arising in radiocarbon calibration, in Computer Applications and Quantitative Methods in Archaeology, 1990 K. Lockyear and S. Rahtz (eds.), BAR International Series 565, 101-109.

F. G. McCormac, A. G. Hogg, P. G. Blackwell, C. E. Buck, T. F. G. Higham and P. J. Reimer (2004). SHCal04 - Southern Hemisphere calibration, 0 − 11.0 cal kyr BP. Radiocarbon, 46(3), 1087-1092.

P. J. Reimer, M. G. L. Baillie, E. Bard, A. Bayliss, J. W. Beck, C. J. H. Bertrand, P. G. Blackwell, C. E. Buck, G. S. Burr, K. B. Cutler, P. E. Damon, R. L. Edwards, R. G. Fairbanks, M. Friedrich, T. P. Guilderson, A. G. Hogg, K. A. Hughen, B. Kromer, G. McCormac, S. Manning, C. B. Ramsey, R. W. Reimer, S. Remmele, J. R. Southon, M. Stuiver, S. Talamo, F. W. Taylor, J, van der Plicht and C. E. Weyhenmeyer (2004). IntCal04 - terrestrial radiocarbon age calibration, 0 − 26 cal kyr BP. Radiocarbon, 46(3), 1029-1058.

P. J. Reimer, E. Bard, A. Bayliss, J. W. Beck, P. G. Blackwell, C. Bronk Ramsey, C. E. Buck, H. Cheng, R. L. Edwards, M. Friedrich, P. M. Grootes, T. P. Guilderson, H. Haflidason, I. Hajdas, C. Hatté, T. J. Heaton, D. L. Hoffmann, A. G. Hogg, K. A. Hughen, K. F. Kaiser, B. Kromer, S. W. Manning, M. Niu, R. W. Reimer, D. A. Richards, E. M. Scott, J. R. Southon, R. A. Staff, C. S. M. Turney, J. van der Plicht (2013). IntCal13 and Marine13 radiocarbon age calibration curves 0 − 50,000 years cal BP. Radiocarbon 55(4), 1869-1887.

M. Stuiver, P. J. Reimer, E. Bard, J. W. Beck, G. S. Burr, K. A. Hughen, B. Kromer, F. G. McCormac, J. Plicht, and M. Spurk (1998) INTCAL98 Radiocarbon age calibration 24,000 - 0 cal BP, Radiocarbon, 40, 1041-1083.

J. A. Zeidler, C. E. Buck and C. D. Litton (1998) The integration of archaeological phase information and radiocarbon results from the Jama River Valley, Ecuador: a Bayesian approach, Latin American Antiquity, 9(2), 160-179.