Data assimilation combines numerical models and data. The model and data define a posterior probability density function which describes the model conditioned on the data. Numerical methods for data assimilation approximate this posterior. 

I will present a weighted sampling method, implicit sampling, and apply it to data assimilation. The idea is to sample in two steps: one first finds the region of large posterior probability by numerical optimization and then generates samples in this region by solving algebraic equations with a stochastic right-hand-side. The result is a collection of samples, where each sample carries significant posterior probability.

I apply implicit sampling for studying reversals of the dipole component of the geomagnetic field using a low-order chaotic model and paleomagnetic data. The model is calibrated to the paleomagnetic record of the past 2 million years and then used for predicting dipole reversals.