Genetic data is often used to understand how populations evolved from past to present. A particularly common example of this type of analysis involves using patterns of neutral variation to estimate past fluctuations in the size of a population, collectively known its "size history". This history can be used to understand various phenomena including migration, admixture, and climate change.
Existing methods for size history estimation are parametric, and require the user to make a number of important model selection and tuning decisions. Usually it is not obvious how to make these choices, or what impact they have on the resulting estimates.
In this work, we provide a new perspective on size history estimation based on survival analysis. Beginning with the simple observation that size history inference amounts to estimating of the rate function of a certain point process, we derive a non-parametric inference procedure based on a suitably modified version of the Nelson-Aalen estimator. The method is fast, optimization-free and self-tuning, and inherits several theoretical guarantees based on known results in survival analysis.