We give an easy proof of Sch\"utzenberger's Theorem stating that non-commutative formal power series are rational if and only if they are recognisable. A byproduct of this proof is a natural metric on a subgroup of invertible rational non-commutative power series. We describe a few features of this metric group.
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
Bayesian approach remained rather unsuccessful in treating nonparametric problems. This is primarily due to the difficulty in finding workable prior distribution on the parameter space , which in nonparametric problems is taken to be a set of probability distributions on a given sample space. Two Desirable Properties of a Prior 1. The support of the prior should be large. 2. Posterior distribution given a sample of observation should be manageable analytically. These properties are antagonistic : One may be obtained at the expense of other.