A Bayesian Approach for Nonlinear Regression Models with Continuous Errors

Abstract

In this paper we develop a Bayesian analysis for the nonlinear regression model with errors that follow a continuous autoregressive process. In this way, unequally spaced observations do not present a problem in the analysis. We employ the Gibbs sampler, (see Gelfand, A., Smith, A. (1990). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85:398–409.), as the foundation for making Bayesian inferences. We illustrate these Bayesian inferences with an analysis of a real data-set. Using these same data, we contrast the Bayesian approach with a generalized least squares technique.

Keywords:

• Continuous autoregressive process
• Gibbs sampler
• Metropolis-Hastings algorithm within Gibbs sampler
• Nonlinear models

Acknowledgments

We would like to thank the referee for comments that improved the presentation of this paper. This paper was partially funded by the Sciences and Technology Foundation of Chile; grant number: Fondecyt 1010958.