Bayes analysis of abridged age specific fertility pattern using parametric models

Abstract

The paper provides a Bayesian alternative to transform the abridged age-specific fertility data into an unabridged one. A model suitable for a binary type of fertility data is considered for the study. The success probabilities of the considered model are assumed to vary in accordance with some established parametric age-specific fertility models. Bayes analysis is done using uniform priors for the unknown parameters of the considered models. Since the posterior analysis involves analytically intractable form of integrals, the paper employs the Gibbs sampler algorithm with intermediate Metropolis-Hastings steps to draw the corresponding posterior samples. Numerical illustration is provided using grouped age-specific fertility rate data. Finally, a few standard Bayesian model comparison tools are used in order to recommend an appropriate model for the data in hand, keeping in view the intended objectives.

Keywords:

• Age-specific fertility rate
• Grouped data
• Non-linear model
• Bayes analysis
• Gibbs sampler
• Metropolis-Hastings algorithm
• Model comparison
• Bayes information criterion
• Predictive loss criterion

Acknowledgements

The authors would like to thank the Editor, and the referees for their valuable comments and suggestions that improved the earlier version of the manuscript.