  We generalize a stochastic model of DNA replication to the case where
replication-origin-initiation rates vary locally along the genome and with
time. Using this generalized model, we address the inverse problem of inferring
initiation rates from experimental data concerning replication in cell
populations. Previous work based on curve fitting depended on arbitrarily
chosen functional forms for the initiation rate, with free parameters that were
constrained by the data. We introduce a non-parametric method of inference that
is based on Gaussian process regression. The method replaces specific
assumptions about the functional form of initiation rate with more general
prior expectations about the smoothness of variation of this rate, along the
genome and in time. Using this inference method, we recover, with high
precision, simulated replication schemes from noisy data that are typical of
current experiments.
