Archaeology operates under extreme uncertainty. The material record is fragmentary, dating evidence is indirect, and the processes that generated the archaeological record — human behavior, taphonomy, recovery bias — are complex and poorly understood. Bayesian methods have transformed the field by providing a principled framework for combining multiple lines of evidence, incorporating prior knowledge from stratigraphy and typology, and quantifying the uncertainty that is inherent in all archaeological inference.
Bayesian Radiocarbon Calibration
Radiocarbon dating measures the residual ¹⁴C in organic material to estimate when an organism died. But the relationship between radiocarbon age and calendar age is nonlinear due to fluctuations in atmospheric ¹⁴C concentration over time. Calibration — converting a radiocarbon measurement into a calendar date — is inherently probabilistic, and the calibration curve introduces multimodality and asymmetry that make simple confidence intervals meaningless.
Where t = calendar date (the unknown)
r ± σ_r = measured radiocarbon age and lab uncertainty
μ(t) = calibration curve (IntCal20)
π(t) = prior on calendar age
The OxCal and BCal software packages implement Bayesian radiocarbon calibration, producing posterior distributions of calendar dates that capture the full complexity of the calibration curve. These posteriors are often multimodal — a single radiocarbon measurement may be consistent with several calendar date ranges — making the Bayesian approach essential for honest uncertainty quantification.
Chronological Modeling
The real power of Bayesian methods in archaeology emerges when multiple dates are combined with stratigraphic and contextual information. If archaeologists know that Layer A lies below Layer B, the calendar dates must satisfy t_A > t_B (earlier deposits are older). Bayesian chronological models incorporate these ordering constraints as priors, dramatically narrowing the posterior date ranges for individual events.
Christopher Bronk Ramsey's OxCal software, first released in 1995, brought Bayesian chronological modeling to mainstream archaeology. By combining radiocarbon dates with stratigraphic priors — sequences, phases, boundaries, and termini — OxCal can compress century-wide calibrated date ranges into decade-level precision. The software has been cited tens of thousands of times and fundamentally changed how archaeologists construct chronologies. Nearly every major archaeological dating study now uses Bayesian methods.
Phase Modeling and Summed Probability Distributions
Bayesian phase models group dates into archaeological phases (e.g., "Early Bronze Age occupation") and estimate the start and end boundaries of each phase. The posterior distributions of boundary dates answer questions like "When did this settlement begin?" and "How long did this phase last?" with calibrated uncertainty. Kernel density estimation approaches within a Bayesian framework have also improved the analysis of summed probability distributions of radiocarbon dates, which are used as proxies for past population levels.
"Bayesian statistics has done more to improve archaeological chronology in the past thirty years than any advance in laboratory technique. It is not a better measurement — it is a better way of thinking about what measurements mean." — Christopher Bronk Ramsey, University of Oxford
Cultural Transmission and Evolutionary Archaeology
Bayesian methods model cultural evolution — how technologies, styles, and practices spread and change through populations. Approximate Bayesian Computation (ABC) is used when the likelihood function for cultural transmission models is intractable: simulated assemblages are compared to observed artifact frequencies, and parameter values that produce similar assemblages are retained as approximate posterior samples. These methods have been applied to the spread of pottery styles, the diffusion of farming, and the evolution of stone tool technologies.
Spatial Analysis and Settlement Patterns
Bayesian spatial models analyze site distributions, estimating the intensity of human activity across landscapes while accounting for survey coverage and preservation bias. Bayesian approaches to least-cost path analysis incorporate uncertainty in terrain costs and movement models, producing probability surfaces for ancient routes rather than single deterministic paths.