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Reconstructing past populations with uncertainty from fragmentary data. (English) Zbl 06158328

Summary: Current methods for reconstructing human populations of the past by age and sex are deterministic or do not formally account for measurement error. We propose a method for simultaneously estimating age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data that incorporates measurement error. Inference is based on joint posterior probability distributions that yield fully probabilistic interval estimates. It is designed for the kind of data commonly collected in modern demographic surveys and censuses. Population dynamics over the period of reconstruction are modeled by embedding formal demographic accounting relationships in a Bayesian hierarchical model. Informative priors are specified for vital rates, migration rates, population counts at baseline, and their respective measurement error variances. We investigate calibration of central posterior marginal probability intervals by simulation and demonstrate the method by reconstructing the female population of Burkina Faso from 1960 to 2005. Supplementary materials for this article are available online and the method is implemented in the R package “popReconstruct.”

MSC:

62-XX Statistics

Software:

R; popReconstruct; CODA
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[1] Alho J. M., International Journal of Forecasting 8 pp 301– (1992) · doi:10.1016/0169-2070(92)90049-F
[2] Alkema L., Demographic Research 26 pp 331– (2012) · doi:10.4054/DemRes.2012.26.15
[3] DOI: 10.1080/08898480306717 · Zbl 1046.91102 · doi:10.1080/08898480306717
[4] Booth H., International Journal of Forecasting 22 pp 547– (2006) · doi:10.1016/j.ijforecast.2006.04.001
[5] Boyle P. P., Demography 23 pp 543– (1986) · doi:10.2307/2061350
[6] Brass W., Biological Aspects of Demography (1971)
[7] Brooks S. P., Statistical Science 15 pp 357– (2000) · doi:10.1214/ss/1009213003
[8] Brooks S. P., Biometrics 56 pp 951– (2000) · doi:10.1111/j.0006-341X.2000.00951.x
[9] DOI: 10.1080/02664760120108683 · Zbl 1346.62151 · doi:10.1080/02664760120108683
[10] Carlin B. P., Bayesian Methods for Data Analysis, 3. ed. (2009)
[11] Carlin B. P., Canadian Journal of Statistics 19 pp 399– (1991) · Zbl 0850.62285 · doi:10.2307/3315430
[12] Catchpole E. A., Biometrics 57 pp 720– (2001) · Zbl 1209.62350 · doi:10.1111/j.0006-341X.2001.00720.x
[13] DOI: 10.1080/01621459.1979.10481038 · doi:10.1080/01621459.1979.10481038
[14] Cleveland W. S., Statistical Models in S (1992)
[15] Cohen J. E., Encyclopedia of Statistical Sciences (2006)
[16] Condé J., Demographic Aspects of Migration in West Africa (1980)
[17] DOI: 10.1080/01621459.1997.10473647 · doi:10.1080/01621459.1997.10473647
[18] Geman S., Transactions on Pattern Analysis and Machine Intelligence pp 721– (1984)
[19] Givens G. H., Report of the International Whaling Commission 43 pp 495– (1993)
[20] Goodkind D., Population and Development Review 27 pp 219– (2001) · doi:10.1111/j.1728-4457.2001.00219.x
[21] Hastings W. K., Biometrika 57 pp 97– (1970) · Zbl 0219.65008 · doi:10.1093/biomet/57.1.97
[22] DOI: 10.1080/0032472031000150176 · doi:10.1080/0032472031000150176
[23] Keilman N., Population and Development Review 24 pp 15– (1998) · doi:10.2307/2808049
[24] Lee R. D., Econometric Studies of Topics in Demographic History (1971)
[25] DOI: 10.1080/00324728.1974.10405195 · doi:10.1080/00324728.1974.10405195
[26] DOI: 10.1080/0032472031000141466 · doi:10.1080/0032472031000141466
[27] Lee R. D., Old and New Methods in Historical Demography (1993)
[28] Lee R. D., Population and Development Review 24 pp 156– (1998) · doi:10.2307/2808055
[29] Leslie P. H., Biometrika 33 pp 183– (1945) · Zbl 0060.31803 · doi:10.1093/biomet/33.3.183
[30] Leslie P. H., Biometrika 35 pp 213– (1948) · Zbl 0034.23303 · doi:10.1093/biomet/35.3-4.213
[31] Lewis E. G., Sankhyā: The Indian Journal of Statistics (1933–1960) 6 pp 93– (1942)
[32] McAllister M. K., Canadian Journal of Fisheries and Aquatic Sciences 51 pp 2673– (1994) · doi:10.1139/f94-267
[33] McCaa R., Inverse Projection Techniques: Old and New Approaches pp 11– (2004) · doi:10.1007/978-3-662-08016-0_2
[34] Merli M. G., Demography 35 pp 345– (1998) · doi:10.2307/3004042
[35] Metropolis N., Journal of Chemical Physics 21 pp 1087– (1953) · doi:10.1063/1.1699114
[36] DOI: 10.1080/0032472031000146996 · doi:10.1080/0032472031000146996
[37] O’Hagan A., Uncertain Judgements: Eliciting Experts’ Probabilities (2006) · Zbl 1269.62009 · doi:10.1002/0470033312
[38] Plummer M., R News 6 pp 7– (2006)
[39] Plummer M., CODA: Output Analysis and Diagnostics for MCMC (2010)
[40] Pollard J. H., Biometrika 55 pp 589– (1968) · Zbl 0177.45303 · doi:10.1093/biomet/55.3.589
[41] DOI: 10.1080/01621459.2000.10474324 · doi:10.1080/01621459.2000.10474324
[42] Preston S. H., Demography: Measuring and Modeling Population Processes (2001)
[43] Quinn T. J., Quantitative Fish Dynamics (1999)
[44] R Development Core Team, R: A Language and Environment for Statistical Computing (2010)
[45] DOI: 10.1080/01621459.1995.10476529 · doi:10.1080/01621459.1995.10476529
[46] Raftery A. E., Markov Chain Monte Carlo in Practice pp 115– (1996) · doi:10.1007/978-1-4899-4485-6_7
[47] Raymer J., European Journal of Population 27 pp 185– (2011) · doi:10.1007/s10680-011-9230-5
[48] Rosina A., Inverse Projection Techniques: Old and New Approaches pp 29– (2004) · doi:10.1007/978-3-662-08016-0_3
[49] Timæus, I. M. 1999. ”Notes on a Series of Life Table Estimates of Mortality in the Countries of the Sub-Saharan Africa Region,”. unpublished manuscript prepared for the World Health Organization
[50] United Nations, Manual X: Indirect Techniques for Demographic Estimation (1983)
[51] United Nations, World Population Prospects: The 2008 Revision (2009)
[52] United Nations, World Population Prospects: The 2008 Revision (2009)
[53] United Nations, World Population Prospects: The 2008 Revision (2010)
[54] United States Census Bureau, International Data Base: Demographic Indicators, Burkina Faso, 1960–2000 (2008)
[55] Wrigley E. A., The Population History of England, 1541–1871: A Reconstruction (1981)
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