Over the course of the last half-century, archaeological demographers have increasingly recognized the potential value of temporal distributions of archaeological samples as proxy population abundance time series. This framework for demographic inference is premised on the assumption that such distributions are either proportional to or - minimally - statistically dependent on the population abundance curve N(t). If we are to draw compelling census-like inferences from such distributions, several potential confounders must be mitigated, including both random and temporally dependent variability in (a) per capita creation rates of archaeological materials over time, (b) the survival of deposits against destructive geological forces, and (c) practices intrinsic to the archaeological investigation itself. Even if we take for granted that these confounders have either been mitigated or are not important in particular cases, even the simple act of describing the temporal distributions of archaeological data is far less straightforward than we might wish. Consequently, statistical inference is necessary not only to characterize the generative processes underlying such sample distributions, but even more basically to quantify our uncertainty surrounding the timestamps required to anchor samples to the timeline. The distinct motivations separating these two inferential activities has not always been fully recognized, leading to contested best-practice protocols for producing meaningful distributional constructs. In this presentation, I illustrate how finite mixture models may be used to model the generative processes underlying temporal distributions of archaeological data, in a way that fully accommodates probabilistic timestamp estimation in a Bayesian framework. Data from the archaeological record of the Kuril Archipelago, in the Northwest Pacific Rim, are used as an illustration.