Making use of Continuous Evidence Through Kernel Density Estimation

This chapter discusses kernel density estimation, a density estimation technique for continuous variables, which is nonparametric. The main advantage of kernel density estimation is that it naturally follows the shape of the data and can adequately model the distributions regardless of the shape taken. The chapter discusses many important aspects of kernel density estimation, including performance relative to discrete methods, how to obtain the critically important bandwidth parameter, and how to reduce dimensionality. It considers two main schemes: independence assumptions and independent component analysis (ICA). For the discrete case, Bayesian marginalization and the estimation algorithms (EM) are typically the most popular solutions. For missing values in kernel density estimates, kernel density regression for the missing values is an effective and popular solution. The Nadaraya-Watson method is a fairly popular method of nonparametric, or kernel density, regression.