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Particle swarm optimization is a popular method for solving difficultoptimization problems. There have been attempts to formulate the method informal probabilistic or stochastic terms (e.g. bare bones particle swarm) withthe aim to achieve more generality and explain the practical behavior of themethod. Here we present a Bayesian interpretation of the particle swarmoptimization. This interpretation provides a formal framework for incorporationof prior knowledge about the problem that is being solved. Furthermore, it alsoallows to extend the particle optimization method through the use of kernelfunctions that represent the intermediary transformation of the data into adifferent space where the optimization problem is expected to be easier to beresolved, such transformation can be seen as a form of prior knowledge aboutthe nature of the optimization problem. We derive from the general Bayesianformulation the commonly used particle swarm methods as particular cases.

A Bayesian Interpretation of the Particle Swarm Optimization and Its Kernel Extension