Network applications commonly maintain local copies of remote data sources in order to provide caching, indexing, and data-mining services to their clients. Modeling performance of these systems and predicting future updates usually requires knowledge of the inter-update distribution at the source, which can only be estimated through blind sampling-periodic downloads and comparison against previous copies. In this paper, we first introduce a stochastic modeling framework for this problem, where updates and sampling follow independent point processes. We then show that all previous approaches are biased unless the observation rate tends to infinity or the update process is Poisson. To overcome these issues, we propose four new algorithms that achieve various levels of consistency, which depend on the amount of temporal information revealed by the source and capabilities of the download process.