We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be
observed directly. Instead, at times t1 < t2 < . . ., the observations y(ti)
are such that, given the process (x(t)), the random variables (y(ti)) are
independent and the conditional distribution of y(ti) only depends on x(ti).
When this conditional distribution has a specific form, we prove that the model
((x(ti), y(ti)), i 1) is a computable filter in the sense that all
distributions involved in filtering, prediction and smoothing are exactly
computable. These distributions are expressed as finite mixtures of parametric
distributions. Thus, the number of statistics to compute at each iteration is
finite, but this number may vary along iterations.Comment: 24 page
