Heteroscedastic nonlinear regression models. (English) Zbl 1183.62045

Cuervo, Edilberto Cepeda; Achcar, Jorge Alberto

Commun. Stat., Simulation Comput. 39, No. 2, 405-419 (2010).

Summary: We present a generalization of the Bayesian methodology introduced by E. Cepeda and D. Gamerman [Braz. J. Probab. Stat. 14, No. 2, 207–221 (2000; Zbl 0983.62013)] for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm.

MSC:

62F15	Bayesian inference
62J02	General nonlinear regression
62H12	Estimation in multivariate analysis
62J12	Generalized linear models (logistic models)
65C40	Numerical analysis or methods applied to Markov chains

Keywords:

Bayesian analysis; heteroscedasticity; MCMC algorithm; nonlinear regression; parameter estimation

Citations:

Zbl 0983.62013