  Parameter estimation is a major challenge in computational modeling of
biological processes. This is especially the case in image-based modeling where
the inherently quantitative output of the model is measured against image data,
which is typically noisy and non-quantitative. In addition, these models can
have a high computational cost, limiting the number of feasible simulations,
and therefore rendering most traditional parameter estimation methods
unsuitable. In this paper, we present a pipeline that uses Gaussian process
learning to estimate biological parameters from noisy, non-quantitative image
data when the model has a high computational cost. This approach is first
successfully tested on a parametric function with the goal of retrieving the
original parameters. We then apply it to estimating parameters in a biological
setting by fitting artificial in-situ hybridization (ISH) data of the
developing murine limb bud. We expect that this method will be of use in a
variety of modeling scenarios where quantitative data is missing and the use of
standard parameter estimation approaches in biological modeling is prohibited
by the computational cost of the model.
