As the use of large-scale radiocarbon datasets becomes more common and applications of Bayesian chronological modeling become a standard aspect of archaeological practice, it is imperative that we grow a community of both effective users and consumers. Indeed, research proposals and publications now routinely employ Bayesian chronological modeling to estimate age ranges such as statistically informed starts, ends, and spans of archaeological phenomena. Although advances in interpretive techniques have been widely adopted, sampling strategies and determinations of appropriate sample sizes for radiocarbon data remain generally underdeveloped. As chronological models are only as robust as the information we feed into them, formal approaches to assessing the validity of model criteria and the appropriate number of radiocarbon dates deserve attention. In this article, through a series of commonly encountered scenarios, we present easy-to-follow instructions for running simulations that should be used to inform the design and construction of chronological models.

Formal models of past human societies informed by archaeological research have a high potential for shaping some of the most topical current debates. Agent-based models, which emphasize how actions by individuals combine to produce global patterns, provide a convenient framework for developing quantitative models of historical social processes. However, being derived from computer science, the method remains largely specialized in archaeology. In this paper and the associated tutorial, we provide a jargon-free introduction to the technique, its potential and limits as well as its diverse applications in archaeology and beyond. We discuss the epistemological rationale of using computational modeling and simulation, classify types of models, and give an overview of the main concepts behind agent-based modeling.

Archaeologists are using spatial data in increasingly sophisticated analyses and invoking more explicit considerations of space in their interpretations. Geographic information systems (GIS) have become standard technology for professional archaeologists in the collection and management of spatial data. Many calls have been made to develop and adapt digital geospatial technologies for interpretation and understanding past social dynamics, but this has been limited to some extent by the static nature of map-oriented GIS approaches. Here, we illustrate how coupling GIS with agent-based modeling (ABM) can assist with more dynamic explorations of past uses of space and geospatial phenomena.

Research on estimation of a psychometric function Ψ has usually focused on comparing alternative algorithms to apply to the data, rarely addressing how best to gather the data themselves (i.e., what sampling plan best deploys the affordable number of trials). Simulation methods were used here to assess the performance of several sampling plans in yes–no and forced-choice tasks, including the QUEST method and several variants of up–down staircases and of the method of constant stimuli (MOCS). We also assessed the efficacy of four parameter estimation methods. Performance comparisons were based on analyses of usability (i.e., the percentage of times that a plan yields usable data for the estimation of all the parameters of Ψ) and of the resultant distributions of parameter estimates. Maximum likelihood turned out to be the best parameter estimation method. As for sampling plans, QUEST never exceeded 80% usability even when 1000 trials were administered and rendered accurate estimates of threshold but misestimated the remaining parameters. MOCS and up–down staircases yielded similar and acceptable usability (above 95% with 400–500 trials) and, although neither type of plan allowed estimating all parameters with optimal precision, each type appeared well suited to estimating a distinct subset of parameters. An analysis of the causes of this differential suitability allowed designing alternative sampling plans (all based on up–down staircases) for yes–no and forced-choice tasks. These alternative plans rendered near optimal distributions of estimates for all parameters. The results just described apply when the fitted Ψ has the same mathematical form as the actual Ψ generating the data; in case of form mismatch, all parameters except threshold were generally misestimated but the relative performance of all the sampling plans remained identical. Detailed practical recommendations are given.

Statistical inference about two binomial parameters implies that they are both estimated by binomial sampling. There are occasions in which one aims at testing the equality of two binomial parameters before and after the occurrence of the first success along a sequence of Bernoulli trials. In these cases, the binomial parameter before the first success is estimated by negative binomial sampling whereas that after the first success is estimated by binomial sampling, and both estimates are related. This paper derives statistical tools to test two hypotheses, namely, that both binomial parameters equal some specified value and that both parameters are equal though unknown. Simulation studies are used to show that in small samples both tests are accurate in keeping the nominal Type-I error rates, and also to determine sample size requirements to detect large, medium, and small effects with adequate power. Additional simulations also show that the tests are sufficiently robust to certain violations of their assumptions.