Information geometric similarity measurement for near-random stochastic processes

We outline the information-theoretic differential geometry of gamma distributions, which contain exponential distributions as a special case, and log-gamma distributions. Our arguments support the opinion that these distributions have a natural role in representing departures from randomness, uniformity and Gaussian behaviour in stochastic processes. We show also how the information geometry provides a surprisingly tractable Riemannian manifold and product spaces thereof, on which may be represented the evolution of a stochastic process or the comparison of different processes, by means of wellfounded maximum likelihood parameter estimation. Our model incorporates possible correlations among parameters. We discuss applications and provide some illustrations from a recent study of amino acid self-clustering in protein sequences; we provide also some results from simulations for multi-symbol sequences.