On the Bayesian analysis of species sampling mixture models for density estimation

The mixture of normals model has been extensively applied to density estimation problems. This paper proposes an alternative parameterisation that naturally leads to new forms of prior distribution. The parameters can be interpreted as the location, scale and smoothness of the density. Priors on these parameters are often easier to specify. Alternatively, improper and default choices lead to automatic Bayesian density estimation. The ideas are extended to multivariate density estimation

Aspects of Non-commutative Function Theory

We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable

Algebraic pairs of isometries

We consider pairs of commuting isometries that are annihilated by a polynomial. We show that the polynomial must be inner toral, which is a geometric condition on its zero set. We show that cyclic pairs of commuting isometries are nearly unitarily equivalent if they are annihilated by the same minimal polynomial

Non-commutative holomorphic functions on Operator domains

We characterize functions of $d$-tuples of bounded operators on a Hilbert space that are uniformly approximable by free polynomials on balanced open sets