Wright--Fisher Smoothing vs Wright--Fisher Diffusion Bridges in Uncertainty Quantification

We compare one-dimensional Wright--Fisher non-informative smoothing with Wright--Fisher diffusion bridges. We adopt a hidden Markov model setting, where a two-type Wright--Fisher diffusion is an unobserved signal, while binary data are collected at discrete times. We tackle inference at instants different from data collection times, and compare the uncertainty quantification yielded by non-informative smoothing distributions, which were developed elsewhere, with that obtained by running Wright--Fisher diffusion bridges between pairs of true signal values at adjacent data collection times. We suggest how to make the practical implementation computationally efficient, and show that the two methods provide analogous performance, with WF smoothing requiring shorter run time.