  Nonlinear regression analysis is a popular and important tool for scientists
and engineers. In this article, we introduce theories and methods of nonlinear
regression and its statistical inferences using the frequentist and Bayesian
statistical modeling and computation. Least squares with the Gauss-Newton
method is the most widely used approach to parameters estimation. Under the
assumption of normally distributed errors, maximum likelihood estimation is
equivalent to least squares estimation. The Wald confidence regions for
parameters in a nonlinear regression model are affected by the curvatures in
the mean function. Furthermore, we introduce the Newton-Raphson method and the
generalized least squares method to deal with variance heterogeneity. Examples
of simulation data analysis are provided to illustrate important properties of
confidence regions and the statistical inferences using the nonlinear least
squares estimation and Bayesian inference.
