  Particle swarm optimization is a popular method for solving difficult
optimization problems. There have been attempts to formulate the method in
formal probabilistic or stochastic terms (e.g. bare bones particle swarm) with
the aim to achieve more generality and explain the practical behavior of the
method. Here we present a Bayesian interpretation of the particle swarm
optimization. This interpretation provides a formal framework for incorporation
of prior knowledge about the problem that is being solved. Furthermore, it also
allows to extend the particle optimization method through the use of kernel
functions that represent the intermediary transformation of the data into a
different space where the optimization problem is expected to be easier to be
resolved, such transformation can be seen as a form of prior knowledge about
the nature of the optimization problem. We derive from the general Bayesian
formulation the commonly used particle swarm methods as particular cases.
