Abstract: Here, we propose combining empirical Bayes modeling with recent advances in Markov chain Monte Carlo filters for hidden Markov models. In doing so, we address long-standing problems in the reconstruction of 3D images, with uncertainty quantification, from noisy 2D pixels in cryogenic electron microscopy and other applications, such as brain network development in infants.

Key words and phrases: Change-points, cryogenic electron microscopy, empirical Bayes, hidden Markov models, Markov chain Monte Carlo, particle filters, stem cells, uncertainty quantification.