Non-informative priors in Wright–Fisher smoothing

We consider a hidden Markov model for discretely observed binary data, with underlying unobserved dynamic probabilities driven by a one-dimensional Wright–Fisher diffusion. We leverage on recent results on the posterior distribution of the diffusion state given data collected at two time points, to investigate a non-informative prior specification for inference at an intermediate time. Our findings describe explicitly the probability distribution of the data points retention for inference at this intermediate time.