Online Probability Density Estimation of Nonstationary Random Signal using Dynamic Bayesian Networks 109 Online Probability Density Estimation of Nonstationary Random Signal using Dynamic Bayesian Networks

We present two estimators for discrete non-Gaussian and nonstationary probability density estimation based on a dynamic Bayesian network (DBN). The first estimator is for offline computation and consists of a DBN whose transition distribution is represented in terms of kernel functions. The estimator parameters are the weights and shifts of the kernel functions. The parameters are determined through a recursive learning algorithm using maximum likelihood (ML) estimation. The second estimator is a DBN whose parameters form the transition probabilities. We use an asymptotically convergent, recursive, on-line algorithm to update the parameters using observation data. The DBN calculates the state probabilities using the estimated parameters. We provide examples that demonstrate the usefulness and simplicity of the two proposed estimators.