Bayesian analysis of radiocarbon dates is a statistical method used to calibrate radiocarbon measurements and determine the chronological order of events. This approach uses both the information from new measurements and the 14C calibration curve to provide a coherent framework for analysis. It is becoming a core element in many 14C dating projects. The article provides an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together in a modular fashion from simple elements with defined constraints and groupings. In other cases, the commonly used "uniform phase" models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able to run simulations on synthetic data. Methods for performing such tests are discussed along with other methods of diagnosing possible problems with statistical models of this kind. The article discusses the use of Bayesian statistics in radiocarbon dating, emphasizing the need for statistical analysis to interpret 14C dates as calendar dates. It explains that 14C dates are not calendar dates but measurements of an isotope ratio, requiring calibration. Once calibrated, 14C dates have probability density functions that are not normally distributed, so many standard statistical methods cannot be applied. The development of probabilistic methods for calibration and the creation of a new statistical framework for dealing with multiple 14C dates have been important in promoting the adoption of Bayesian analysis. The article also discusses the use of probability density functions to express the likelihood of events and the importance of defining a timescale for calendar age information. It explains that different dating techniques provide different types of information, and Bayesian analysis combines these to provide a more accurate chronological framework. The article highlights the importance of defining a prior, which is the information about the parameters we have apart from the measurements. It also discusses the use of different distributions for modeling events, such as uniform, ramped, exponential, or normal distributions, depending on the nature of the events. The article provides examples of how Bayesian analysis can be applied in practice, using the OxCal software. It discusses the use of different models for different types of events and the importance of considering the constraints on the order of events. It also discusses the use of cross-referencing between models to synchronize events across different sites or cultures. The article concludes by emphasizing the importance of using Bayesian analysis in radiocarbon dating to provide a more accurate and reliable chronological framework.Bayesian analysis of radiocarbon dates is a statistical method used to calibrate radiocarbon measurements and determine the chronological order of events. This approach uses both the information from new measurements and the 14C calibration curve to provide a coherent framework for analysis. It is becoming a core element in many 14C dating projects. The article provides an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together in a modular fashion from simple elements with defined constraints and groupings. In other cases, the commonly used "uniform phase" models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able to run simulations on synthetic data. Methods for performing such tests are discussed along with other methods of diagnosing possible problems with statistical models of this kind. The article discusses the use of Bayesian statistics in radiocarbon dating, emphasizing the need for statistical analysis to interpret 14C dates as calendar dates. It explains that 14C dates are not calendar dates but measurements of an isotope ratio, requiring calibration. Once calibrated, 14C dates have probability density functions that are not normally distributed, so many standard statistical methods cannot be applied. The development of probabilistic methods for calibration and the creation of a new statistical framework for dealing with multiple 14C dates have been important in promoting the adoption of Bayesian analysis. The article also discusses the use of probability density functions to express the likelihood of events and the importance of defining a timescale for calendar age information. It explains that different dating techniques provide different types of information, and Bayesian analysis combines these to provide a more accurate chronological framework. The article highlights the importance of defining a prior, which is the information about the parameters we have apart from the measurements. It also discusses the use of different distributions for modeling events, such as uniform, ramped, exponential, or normal distributions, depending on the nature of the events. The article provides examples of how Bayesian analysis can be applied in practice, using the OxCal software. It discusses the use of different models for different types of events and the importance of considering the constraints on the order of events. It also discusses the use of cross-referencing between models to synchronize events across different sites or cultures. The article concludes by emphasizing the importance of using Bayesian analysis in radiocarbon dating to provide a more accurate and reliable chronological framework.