  The Van Allen radiation belts in the magnetosphere have been extensively
studied using models based on radial diffusion theory, which is based on a
quasi-linear approach with prescribed inner and outer boundary conditions. The
1-d diffusion model requires the knowledge of a diffusion coefficient and an
electron loss timescale, which are typically parameterized in terms of various
quantities such as the spatial ($L$) coordinate or a geomagnetic index (for
example, $Kp$). These terms are empirically derived, not directly measurable,
and hence are not known precisely, due to the inherent non-linearity of the
process and the variable boundary conditions. In this work, we demonstrate a
probabilistic approach by inferring the values of the diffusion and loss term
parameters, along with their uncertainty, in a Bayesian framework, where
identification is obtained using the Van Allen Probe measurements. Our results
show that the probabilistic approach statistically improves the performance of
the model, compared to the parameterization employed in the literature.
