Probability density function estimation of laser light scintillation via Bayesian mixtures

A method for probability density function (PDF) estimation using Bayesian mixtures of weighted gamma distributions, called the Dirichlet process gamma mixture model (DP-GaMM), is presented and applied to the analysis of a laser beam in turbulence. The problem is cast in a Bayesian setting, with the mixture model itself treated as random process. A stick-breaking interpretation of the Dirichlet process is employed as the prior distribution over the random mixture model. The number and underlying parameters of the gamma distribution mixture components as well as the associated mixture weights are learned directly from the data during model inference. A hybrid Metropolis-Hastings and Gibbs sampling parameter inference algorithm is developed and presented in its entirety. Results on several sets of controlled data are shown, and comparisons of PDF estimation fidelity are conducted with favorable results.