  Motivation: Estimating parameters from data is a key stage of the modelling
process, particularly in biological systems where many parameters need to be
estimated from sparse and noisy data sets. Over the years, a variety of
heuristics have been proposed to solve this complex optimisation problem, with
good results in some cases yet with limitations in the biological setting.
  Results: In this work, we develop an algorithm for model parameter fitting
that combines ideas from evolutionary algorithms, sequential Monte Carlo and
direct search optimisation. Our method performs well even when the order of
magnitude and/or the range of the parameters is unknown. The method refines
iteratively a sequence of parameter distributions through local optimisation
combined with partial resampling from a historical prior defined over the
support of all previous iterations. We exemplify our method with biological
models using both simulated and real experimental data and estimate the
parameters efficiently even in the absence of a priori knowledge about the
parameters.
