Probability Projection of Total Fertility Rate for Assesing the Replacement Level of Fertility of Selected State Using MCMC Technique under Bayesian Modeling

Abhishek Singh Chauhan¹ , Subhi Srivastava² , Anurag Verma³

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.6 , pp.14-21, Dec-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.1421

Online published on Dec 31, 2019

Copyright © Abhishek Singh Chauhan, Subhi Srivastava, Anurag Verma . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The present paper explains Bayesian methodological approach for projection of Total fertility rate (TFR) for seven states of India taken as (Uttar Pradesh, Bihar, Assam, Madhya Pradesh, Gujarat, Rajasthan, Haryana). The projection has been done by using Gompertz model and the parameters of the model have been estimated using MCMC (Monte Carlo Markove Chain) Technique in Bayesian procedure. Previous year SRS (Sample Registration System) data for TFR is used since 1981 to 2016 for each state. Non-informative prior distribution for estimating parameter in Bayesian approach was used and the entire analysis was done by using WinBUGS (Bayesian Inference using Gibbs Sampling for Windows) software. As a result of our study the projection model shows that Uttar Pradesh will reach to its replacement level in year 2028, Bihar in 2036, Assam in 2018, Gujarat in 2016, Rajasthan in 2025, whereas Haryana has already reached to its replacement level.

Key-Words / Index Term :
Gompertz Curve, Bayesian Methodology, Total Fertility Rate, Non-informative prior, WinBUGS

References :
[1] Census of India. Population Projections for India and States 2001–2026.
[2] Spiegel halter DJ, Thomas A, Best NG, Gilks W, Lunn D. BUGS: Bayesian inference using Gibbs sampling. Version 0.5, (version ii) http://www. mrc-bsu. cam. ac. uk/bugs. 1996 Aug;19.
[3] Gilks WR, Richardson S, Spiegel halter D, editors. Markov chain Monte Carlo in practice. CRC press; 1995 Dec 1.
[4] Gill J., Bayesian Methods: A Social and Behavioral Sciences Approach, Champman and Hall/CRC., (2002).
[5] Gill J., Bayesian Methods: A Social and Behavioral Sciences Approach, Champman and Hall/CRC., (2002).
[6] Rahul GS, Singh OP. Population projection of India using MCMC technique: A WinBUGS implementation. Demography India. 2007 Jan;36(1):145-54.
[7] Rahul GP, Singh OP. using WinBUGS to study logistic growth model with an application to population projection of Uttar Pradesh and Uttaranchal. Indian J. Prev. Soc. Med. 2010;41(1&):2.
[8] Smith BD, Smith GL, Hurria A, Hortobagyi GN, Buchholz TA. Future of cancer incidence in the United States: burdens upon an aging, changing nation. Journal of Clinical Oncology. 2009 Apr 27;27(17):2758-65.
[9] Mari Bhat, P. N. "India`s changing dates with replacement fertility: A review of recent fertility trends and future prospects. Delhi: Institute of Economic Growth, University Enclave." (2010).
[10] Alkema L, Raftery AE, Gerland P, Clark SJ, Pelletier F, Buettner T, Heilig GK. Probabilistic projections of the total fertility rate for all countries. Demography. 2011 Aug 1; 48(3):815-39.
[11] Congdon P. Bayesian statistical modeling. John Wiley & Sons; 2007 Apr 4.
[12] Brooks SP, Gelman A. General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics. 1998 Dec 1;7(4):434-55.
[13] Gill J. Bayesian methods: A social and behavioral sciences approach. CRC press; 2014 Dec 11.