Statistical Modeling in Biomedical Engineering

Abstract

This article focuses on the histogram and kernel probability density estimation methods for statistical analysis of biomedical data. We first provide the mathematical concepts of the central moments computed from the probability density function. The properties of several typical probability densities, such as uniform distribution, normal distribution, logistic distribution, hyperbolic secant distribution, and Laplace distribution, are described. Then, we present the procedures of constructing a histogram model, along with the different criteria of determining the appropriate number of bins based on the data observations. In addition, we describe the nonparametric probability density estimation method with kernel functions, and discuss the issue of the optimal Gaussian kernel bandwidth selection. Finally, we demonstrate the effectiveness of the histogram and kernel probability density estimation methods in the applications of children's gait maturation characterization and gait variability analysis of patients with Parkinson's disease.