Section: New Results

Statistical inference for biological systems based on a size-structured population

Participant : Vincent Rivoirard.

The journal paper [21] considers the problem of estimating the division rate of a size-structured population in a nonparametric setting. The size of the system evolves according to a transport-fragmentation equation: each individual grows with a given transport rate, and splits into two offsprings of the same size, following a binary fragmentation process with unknown division rate that depends on its size. In contrast to a deterministic inverse problem approach, this paper takes the perspective of statistical inference: the data consists in a large sample of the size of individuals when the evolution of the system is close to its time-asymptotic behavior, so that it can be related to the eigenproblem of the considered transport-fragmentation equation. By estimating statistically each term of the eigenvalue problem and suitably inverting a certain linear operator, it constructs a more realistic estimator of the division rate that achieves the same optimal error bound as in related deterministic inverse problems. The procedure relies on kernel methods with automatic bandwidth selection. It is inspired by model selection and recent results of Goldenschluger and Lepski.