An exact version of Hunt's ancestor-descendant directional random walk parameterization

Hunt s ancestor-descendant parameterization for fitting of evolutionary models to empirical paleontological sequences assumes independent log-likelihoods for the transitions between populations (Hunt, 2006). This is not quite correct, as he also pointed out in his paper. The reason is that adjacent trait differences share a trait mean value and its sampling error, and ignorance of this fact may give large errors in the estimated step size. Here, the problem is solved by use of the N-1 dimensional normal density for a random vector, where N is the number of samples. This results in a tridiagonal covariance matrix instead of Hunt s diagonal matrix, and the estimated step sizes, and thus prediction slopes, in cases where the estimated step variance is zero will then be identical to those found by weighted least squares estimation.