Understanding how social information is used in human populations is one of the challenges in cultural evolution. Fine-grained individual-level data, detailing who learns from whom, would be most suited to answer this question empirically but this kind of data is difficult to obtain especially in pre-modern contexts. Often, population-level data in form of time-series that describe the dynamics of the frequency change of cultural variants over time, usually comprising sparse samples from the whole population are the only available empirical information. In this talk we develop an inference framework that aims at investigating whether underlying processes of cultural transmission can be inferred from such population-level data. This framework firstly generates theoretical patterns of temporal frequency change conditioned on a specific process of cultural transmission. Secondly, we use statistical comparisons (in form of approximate Bayesian computation (to establish which transmission processes are consistent with observed frequency data and, maybe more importantly, which are not. We demonstrate that there are exist theoretical limits to the inference of underlying processes of cultural transmission from population-level data highlighting the problem of equifnality especially in situations of sparse data. Crucially we show the importance of rare variants for inferential questions. Lastly, we apply our framework to a dataset describing pottery from settlements of some of the first farmers in Europe (the LBK culture) and conclude that the observed frequency dynamic of different types of decorated pottery is consistent with age-dependent selection, a preference for ‘young’ pottery types which is potentially indicative of fashion trends.