期刊
JOURNAL OF APPLIED STATISTICS
卷 49, 期 10, 页码 2612-2628出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/02664763.2021.1913105
关键词
Bayesian analysis; beta regression; default prior distributions; MCMC; ruminal degradation kinetics
资金
- Seneca Foundation Programme for the Generation of Excellence Scientific Knowledge [20862/PI/18]
This article proposes a beta nonlinear model and Bayesian perspective to solve the issue of parameter estimation in ruminal degradation kinetics models. Through simulation studies and applications to real data, the effectiveness of this method has been validated, solving the problem of unacceptable predictions caused by using least squares for parameter estimation.
The models used to describe the kinetics of ruminal degradation are usually nonlinear models where the dependent variable is the proportion of degraded food. The method of least squares is the standard approach used to estimate the unknown parameters but this method can lead to unacceptable predictions. To solve this issue, a beta nonlinear model and the Bayesian perspective is proposed in this article. The application of standard methodologies to obtain prior distributions, such as the Jeffreys prior or the reference priors, involves serious difficulties here because this model is a nonlinear non-normal regression model, and the constrained parameters appear in the log-likelihood function through the Gamma function. This paper proposes an objective method to obtain the prior distribution, which can be applied to other models with similar complexity, can be easily implemented in OpenBUGS, and solves the problem of unacceptable predictions. The model is generalized to a larger class of models. The methodology was applied to real data with three models that were compared using the Deviance Information Criterion and the root mean square prediction error. A simulation study was performed to evaluate the coverage of the credible intervals.
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