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Gebremeskel, Haftu Gebrehiwot (2016) Implementing hierarchical bayesian model to fertility data: the case of Ethiopia. [Tesi di dottorato]

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Abstract (inglese)

Background: Ethiopia is a country with 9 ethnically-based administrative regions and 2 city administrations, often cited, among other things, with high fertility rates and rapid population growth rate. Despite the country’s effort in their reduction, they still remain high, especially at regional-level. To this end, the study of fertility in Ethiopia, particularly on its regions, where fertility variation and its repercussion are at boiling point, is paramount important. An easy way of finding different characteristics of a fertility distribution is to build a suitable model of fertility pattern through different mathematical curves. ASFR is worthwhile in this regard. In general, the age-specific fertility pattern is said to have a typical shape common to all human populations through years though many countries some from Africa has already started showing a deviation from this classical bell shaped curve. Some of existing models are therefore inadequate to describe patterns of many of the African countries including Ethiopia. In order to describe this shape (ASF curve), a number of parametric and non-parametric functions have been exploited in the developed world though fitting these models to curves of Africa in general and that of Ethiopian in particular data has not been undertaken yet. To accurately model fertility
patterns in Ethiopia, a new mathematical model that is both easily used, and provides good fit for the data is required. Objective: The principal goals of this thesis are therefore fourfold: (1). to examine the pattern of ASFRs at country and regional level,in Ethiopia; (2). to propose a model that best captures various shapes of ASFRs at both country and regional level, and then compare the performance of the model with some existing ones; (3). to fit the proposed model using Hierarchical Bayesian techniques and show that this method is flexible enough for local estimates vis-´a-vis traditional formula, where the estimates might be very imprecise, due to low sample size; and (4). to compare the resulting estimates obtained with the non-hierarchical procedures, such as Bayesian and Maximum likelihood counterparts.
Methodology: In this study, we proposed a four parametric parametric model, Skew Normal model, to fit the fertility schedules, and showed that it is flexible enough in capturing fertility patterns shown at country level and most regions of Ethiopia. In order to determine the performance of this proposed model, we conducted a preliminary analysis along with ten other commonly used parametric and non-parametric models in demographic literature, namely: Quadratic Spline function, Cubic Splines, Coale-Trussell function, Beta, Gamma, Hadwiger distribution, Polynomial models, the Adjusted Error Model, Gompertz curve, Skew Normal, and Peristera & Kostaki Model. The criterion followed in fitting these models was Nonlinear Regression with nonlinear least squares (nls) estimation. We used Akaike Information Criterion (AIC) as model selecction criterion. For many demographers, however, estimating regional-specific ASFR model and the associated uncertainty introduced due those factors can be difficult, especially in a situation where we have extremely varying sample size among different regions. Recently, it has been proposed that Hierarchical procedures might provide more reliable parameter estimates than Non-Hierarchical procedures, such as complete pooling and independence to make local/regional-level analyses. In this study, a Hierarchical Bayesian procedure was, therefore, formulated to explore the posterior distribution of model parameters (for
generation of region-specific ASFR point estimates and uncertainty bound). Besides, other non-hierarchical approaches, namely Bayesian and the maximum likelihood methods, were also instrumented to estimate parameters and compare the result obtained using these approaches with Hierarchical Bayesian counterparts. Gibbs sampling along with MetropolisHastings argorithm in R (Development Core Team, 2005) was applied to draw the posterior samples for each parameter. Data augmentation method was also implemented to ease the sampling process. Sensitivity analysis, convergence diagnosis and model checking were also thoroughly conducted to ensure how robust our results are. In all cases, non-informative prior distributions for all regional vectors (parameters) were used in order to real the lack
of knowledge about these random variables. Result: The results obtained from this preliminary analysis testified that the values of the Akaike Information criterion(AIC) for the proposed model, Skew Normal (SN), is lowest:
in the capital, Addis Ababa, Dire Dawa, Harari, Affar, Gambela, Benshangul-Gumuz, and country level data as well. On the contrary, its value was also higher some of the models and lower the rest on the remain regions, namely: Tigray, Oromiya, Amhara, Somali and SNNP. This tells us that the proposed model was able to capturing the pattern of fertility at the empirical fertility data of Ethiopia and its regions better than the other existing models considered in 6 of the 11 regions. The result from the HBA indicates that most of the posterior means were much closer to the true fixed fertility values. They were also more precise and have lower uncertainty with narrower credible interval vis-´a-vis the other approaches, ML and Bayesian estimate analogues. Conclusion: From the preliminary analysis, it can be concluded that the proposed model was better to capture ASFR pattern at national level and its regions than the other existing common models considered. Following this result, we conducted inference and prediction on the model parameters using these three approaches: HBA, BA and ML methods. The overall result suggested several points. One such is that HBA was the best approach to implement for such a data as it gave more consistent, precise (the low uncertainty) than the other approaches. Generally, both ML method and Bayesian method can be used to analyze our model, but they can be applicable to different conditions. ML method can be applied when precise values of model parameters have been known, large sample size can be obtained in the test; and similarly, Bayesian method can be applied when uncertainties
on the model parameters exist, prior knowledge on the model parameters are available, and few data is available in the study.

Abstract (italiano)

Background: L’Etiopia è una nazione divisa in 9 regioni amministrative (definite su base etnica) e due città. Si tratta di una nazione citata spesso come esempio di alta fecondità e rapida crescita demografica. Nonostante gli sforzi del governo, fecondità e cresita della popolazione rimangono elevati, specialmente a livello regionale. Pertanto, lo studio della fecondità in Etiopia e nelle sue regioni – caraterizzate da un’alta variabilità – è di vitale importanza. Un modo semplice di rilevare le diverse caratteristiche della distribuzione della feconditàè quello di costruire in modello adatto, specificando diverse funzioni matematiche. In questo senso, vale la pena concentrarsi sui tassi specifici di fecondità, i quali mostrano una precisa forma comune a tutte le popolazioni. Tuttavia, molti paesi mostrano una “simmetrizzazione” che molti modelli non riescono a cogliere adeguatamente. Pertanto, per cogliere questa la forma dei tassi specifici, sono stati utilizzati alcuni modelli parametrici ma l’uso di tali modelliè ancora molto limitato in Africa ed in Etiopia in particolare.
Obiettivo: In questo lavoro si utilizza un nuovo modello per modellare la fecondità in Etiopia con quattro obiettivi specifici: (1). esaminare la forma dei tassi specifici per età dell’Etiopia a livello nazionale e regionale; (2). proporre un modello che colga al meglio le varie forme dei tassi specifici sia a livello nazionale che regionale. La performance del modello proposto verrà confrontata con quella di altri modelli esistenti; (3). adattare la funzione di fecondità proposta attraverso un modello gerarchico Bayesiano e mostrare che tale modelloè sufficientemente flessibile per stimare la fecondità delle singole regioni – dove le stime possono essere imprecise a causa di una bassa numerosità campionaria; (4). confrontare le stime ottenute con quelle fornite da metodi non gerarchici (massima verosimiglianza o Bayesiana semplice) Metodologia: In questo studio, proponiamo un modello a 4 parametri, la Normale Asimmetrica, per modellare i tassi specifici di fecondità. Si mostra che questo modello è sufficientemente flessibile per cogliere adeguatamente le forme dei tassi specifici a livello sia nazionale che regionale. Per valutare la performance del modello, si è condotta un’analisi preliminare confrontandolo con altri dieci modelli parametrici e non parametrici usati nella letteratura demografica: la funzione splie quadratica, la Cubic-Spline, i modelli di Coale e Trussel, Beta, Gamma, Hadwiger, polinomiale, Gompertz, Peristera-Kostaki e l’Adjustment Error Model. I modelli sono stati stimati usando i minimi quadrati non lineari (nls) e il Criterio d’Informazione di Akaike viene usato per determinarne la performance. Tuttavia, la stima per le singole regioni pu‘o risultare difficile in situazioni dove abbiamo un’alta variabilità della numerosità campionaria. Si propone, quindi di usare procedure gerarchiche che permettono di ottenere stime più affidabili rispetto ai modelli non gerarchici (“pooling” completo o “unpooling”) per l’analisi a livello regionale. In questo studia si formula un modello Bayesiano gerarchico ottenendo la distribuzione a posteriori dei parametri per i tassi di fecnodità specifici a livello regionale e relativa stima dell’incertezza. Altri metodi non gerarchici (Bayesiano semplice e massima verosimiglianza) vengono anch’essi usati per confronto. Gli algoritmi Gibbs Sampling e Metropolis-Hastings vengono usati per campionare dalla distribuzione a posteriori di ogni parametro. Anche il metodo del “Data Augmentation” viene utilizzato per ottenere le stime. La robustezza dei risultati viene controllata attraverso un’analisi di sensibilità e l’opportuna diagnostica della convergenza degli algoritmi viene riportata nel testo. In tutti i casi, si sono usate distribuzioni a priori non-informative.
Risultati: I risutlati ottenuti dall’analisi preliminare mostrano che il modello Skew Normal ha il pi`u basso AIC nelle regioni Addis Ababa, Dire Dawa, Harari, Affar, Gambela, Benshangul-Gumuz e anche per le stime nazionali. Nelle altre regioni (Tigray, Oromiya, Amhara, Somali e SNNP) il modello Skew Normal non risulta il milgiore, ma comunque mostra un buon adattamento ai dati. Dunque, il modello Skew Normal risulta il migliore in 6 regioni su 11 e sui tassi specifici di tutto il paese. Conclusioni: Dunque, il modello Skew Normal risulta globalmente il migliore. Da questo risultato iniziale, siè partiti per costruire i modelli Gerachico Bayesiano, Bayesiano semplice e di massima verosimiglianza. Il risultato del confronto tra questi tre approcci è che il modello gerarchico fornisce stime più preciso rispetto agli altri.

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Tipo di EPrint:Tesi di dottorato
Relatore:Nicola , Sartori
Correlatore:Stefano , Mazzuco
Dottorato (corsi e scuole):Ciclo 28 > Scuole 28 > SCIENZE STATISTICHE
Data di deposito della tesi:31 Gennaio 2016
Anno di Pubblicazione:31 Gennaio 2016
Informazioni aggiuntive:The pdf file attached herewith is my PhD thesis in the Department of Statistics, University of Padova. I would, therefore, like to be deemed that way.
Parole chiave (italiano / inglese):ASFR, fertility pattern, fertility rate, Skew Normal model,Unified Skew Normal Model, parametric fertility model, non-parametric fertility models, AIC, Hierarchical Bayesian Analysis, MCMC, Latent variables , Data Augmentation, Maximum Likelihood Estimator, Gibbs Sampling, MH Algorithm
Settori scientifico-disciplinari MIUR:Area 13 - Scienze economiche e statistiche > SECS-P/13 Scienze merceologiche
Struttura di riferimento:Dipartimenti > Dipartimento di Scienze Statistiche
Codice ID:9438
Depositato il:10 Ott 2016 10:47
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Bibliografia

I riferimenti della bibliografia possono essere cercati con Cerca la citazione di AIRE, copiando il titolo dell'articolo (o del libro) e la rivista (se presente) nei campi appositi di "Cerca la Citazione di AIRE".
Le url contenute in alcuni riferimenti sono raggiungibili cliccando sul link alla fine della citazione (Vai!) e tramite Google (Ricerca con Google). Il risultato dipende dalla formattazione della citazione.

Hirotugu Akaike. Canonical correlation analysis of time series and the use of an information criterion. Mathematics in Science and Engineering, 126:27–96, 1976. (page 21) Cerca con Google

James H Albert and Siddhartha Chib. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88:160–170, 1993. (page 8, 55, 65, 67) Cerca con Google

Tewodros Alemayehu, Jemal Haider, and Dereje Habte. Determinants of adolescent fertility in ethiopia. Ethiopian Journal of Health Development, 24(1), 2010. (page 17) Cerca con Google

Getu D Alene and Alemayehu Worku. Differentials of fertility in north and south gondar zones, northwest ethiopia: A comparative cross-sectional study. BMC Public Health, 8 (1):397, 2008. (page 17) Cerca con Google

Reinaldo B Arellano-Valle and Adelchi Azzalini. On the unification of families of skewnormal distributions. Scandinavian Journal of Statistics, pages 561–574, 2006. (page 30) Cerca con Google

Reinaldo B Arellano-Valle and Adelchi Azzalini. The centred parametrization for the multivariate skew-normal distribution. Journal of Multivariate Analysis, 99(7):1362– 1382, 2008. (page 29) Cerca con Google

V GOPALAKRISHNAN Asari and C John. Determinants of desired family size in kerala. Demography India, 27(2):369–381, 1998. (page 17) Cerca con Google

Greg Atkinson and Alan M Nevill. Statistical methods for assessing measurement error (reliability) in variables relevant to sports medicine. Sports medicine, 26(4):217–238, 1998. (page 68) Cerca con Google

Azzalini. Further results on a class of distributions which includes the normal ones. Biometrika, 46(2):199–208, 1986. (page 29) Cerca con Google

A Azzalini and A Capitanio. The skew-normal and related families. Cambridge University Press, IMS Monographs series, 2014. (page 27) Cerca con Google

Adelchi Azzalini. A class of distributions which includes the normal ones. Scandinavian journal of statistics, pages 171–178, 1985. (page 15, 27, 100, 101) Cerca con Google

Adelchi Azzalini and Alessandra Dalla Valle. The multivariate skew-normal distribution. Biometrika, 83(4):715–726, 1996. (page 100) Cerca con Google

Radheshyam Bairagi. Effects of sex preference on contraceptive use, abortion and fertility in matlab, bangladesh. International Family Planning Perspectives, pages 137–143, 2001. (page 3) Cerca con Google

James O Berger. Statistical decision theory and bayesian analysis, 1985. (page 40) Jane T Bertrand, Janet Rice, Tara M Sullivan, and James Shelton. Skewed method mix: a measure of quality in family planning programs. Citeseer, 2000. (page 3) Cerca con Google

Julian Besag. Markov chain monte carlo for statistical inference. Center for Statistics and the Social Sciences, 2001. (page 35) Cerca con Google

Julian Besag, Peter Green, David Higdon, and Kerrie Mengersen. Bayesian computation and stochastic systems. Statistical science, pages 3–41, 1995. (page 35) Cerca con Google

MK Bhasin and Shampa Nag. A demographic profile of the people of jammu and kashmir: Estimates, trends and differentials in fertility. Journal of Human Ecology, 13(1-2):57–112, 2002. (page 17) Cerca con Google

Veena Bhasin and MK Bhasin. Habitat, habitation, and health in the Himalayas. KamlaRaj Enterprises, 1990. (page 17) Cerca con Google

JC Bhatia. Prevalent knowledge and attitude of males towards family planning in a punjab village. Journal of Family Welfare, 16(3):3–14, 1970. (page 17) Cerca con Google

William Brass. The graduation of fertility distributions by polynomial functions. Population Studies, 14(2):148–162, 1960. (page 101) Cerca con Google

William Brass. The use of the gompertz relational model to estimate fertility. 1981.(page 15) Cerca con Google

Stephen P Brooks and Andrew Gelman. General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4):434–455, 1998. (page ) Cerca con Google

Emery N Brown, Robert E Kass, and Partha P Mitra. Multiple neural spike train data analysis: state-of-the-art and future challenges. Nature neuroscience, 7(5):456–461, 2004. (page 93) Cerca con Google

Scott Brown and Andrew Heathcote. Averaging learning curves across and within participants. Behavior Research Methods, Instruments, & Computers, 35(1):11–21, 2003. (page 64) Cerca con Google

John C. Caldwell. Theory of Fertility Decline. New York: Academic Press, 1982. (page 3) John C Caldwell, Israel O Orubuloye, and Pat Caldwell. Fertility decline in africa: A new type of transition? Population and development review, pages 211–242, 1992. (page 2) Cerca con Google

Antonio Canale and Bruno Scarpa. Informative bayesian inference for the skew-normal distribution. arXiv preprint arXiv:1305.3080, 2013. (page 41, 48, 49, 50, 80, 81, 84) Cerca con Google

Antonio Canale and Bruno Scarpa. Age-specific probability of childbirth. smoothing via bayesian nonparametric mixture of rounded kernels. Statistica, 75(1):101–110, 2015. (page 69) Cerca con Google

John B Casterline and RT Lazarus. Determinants and consequences of high fertility: a synopsis of the evidence. Addressing the Neglected MDG: World Bank Review of Population and High Fertility, World Bank publications, 2010. (page 4) Cerca con Google

Eduardo A Castro, Zhen Zhang, Arnab Bhattacharjee, Jos´e M Martins, and Tapabrata Maiti. Regional fertility data analysis: A small area bayesian approach. Current Trends in Bayesian Methodology with Applications, page 203, 2015. (page 25) Cerca con Google

S Paul Chachra and MK Bhasin. Anthropo-demographic study among the caste and tribal groups of central himalayas: fertility differentials and determinants. Journal of HumanEcology, 9:417–429, 1998. (page 17) Cerca con Google

T Chandola, DA Coleman, and RW Hiorns. Recent european fertility patterns: Fitting curves to distorteddistributions. Population Studies, 53(3):317–329, 1999. (page 13, 14) Cerca con Google

Y Chen and D Fournier. Impacts of atypical data on bayesian inference and robust bayesian approach in fisheries. Canadian Journal of Fisheries and Aquatic Sciences, 56(9):1525–1533, 1999. (page 26) Cerca con Google

James S Clark. Why environmental scientists are becoming bayesians. Ecology letters, 8 (1):2–14, 2005. (page 69) Cerca con Google

James S Clark and Alan E Gelfand. Hierarchical Modelling for the Environmental Sciences: Statistical methods and applications: Statistical methods and applications. Oxford University Press, 2006. (page 69) Cerca con Google

James Samuel Clark. Models for ecological data: an introduction, volume 11. Princeton university press Princeton, New Jersey, USA, 2007. (page 69) Cerca con Google

Ansley J Coale and T James Trussell. Technical note: Finding the two parameters that specify a model schedule of marital fertility. Population Index, pages 203–213, 1978. (page 101) Cerca con Google

A Clifford Cohen. Maximum likelihood estimation in the weibull distribution based on complete and on censored samples. Technometrics, 7(4):579–588, 1965. (page 87) Cerca con Google

Peter Congdon. Applied bayesian modelling. John Wiley & Sons, 2003. (page 31) Mary Kathryn Cowles and Bradley P Carlin. Markov chain monte carlo convergence diagnostics: a comparative review. Journal of the American Statistical Association, 91 (434):883–904, 1996. (page 55, 57, 93) Cerca con Google

Noel Cressie, Catherine A Calder, James S Clark, Jay M Ver Hoef, and Christopher K Wikle. Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling. Ecological Applications, 19(3):553–570, 2009. (page 69) Cerca con Google

CSA and G ICF International. Central Statistical Agency, ORC Macro. Ethiopia 2011 Demographic and Heath Survey. Addis Ababa, Ethiopia ; Calverton, Maryland 2011. Preliminary report, 2012. (page 4) Cerca con Google

JAA de Beer. A new relational method for smoothing and projecting age specific fertility rates: Topals. Demographic Research, 24, 2011. (page 16) Cerca con Google

K Desta and G Seyoum. Family system in ethiopia. Hand Book on Population and for Secondary School Teachers in Ethiopia. Edited by Seyoum Gebreselassie and Markos Ezra DTRC and ICDR, Addis Ababa. Family line Education, 1998. (page 4) Cerca con Google

R Development Core Team. Development core team. 2005. r: A language and environment for statistical computing. the r foundation for statistical computing, vienna, austria, 2005. (page iii, 90) Cerca con Google

Debarshi Dey. Estimation of the parameters of skew normal distribution by approximating the ratio of the normal density and distribution functions. 2010. (page 27) Cerca con Google

Dipak K Dey, Sujit K Ghosh, and Bani K Mallick. Generalized linear models: A Bayesian perspective. CRC Press, 2000. (page 68) Cerca con Google

J Dominguez-Molina, G Gonz´alez-Far´ıas, and AK Gupta. The multivariate closed skew normal distribution. Technical report, Technical report, 2003. (page 30) Cerca con Google

Jean Dreze and Mamta Murthi. Fertility, education and development: Further evidence from india. Vol, 2000. (page 5) Cerca con Google

W Eshetu and A Habtamu. The influence of selected social and demographic factors on fertility: the case of bahirdar town. Ethiopian Journal of Development Research, 20(1): 1–21, 1998. (page 17) Cerca con Google

Ethiopian Society of Population Studies[ESPS] ESPS. Levels, Trends and Determinants of Lifetime and Desired Fertility in Ethiopia:Findings from EDHS 2005. In-depth Analysis of the Ethiopian Demographic and Health Survey 2005, 2008. (page 4) Cerca con Google

William K Estes and W Todd Maddox. Risks of drawing inferences about cognitive processes from model fits to individual versus average performance. Psychonomic Bulletin & Review, 12(3):403–408, 2005. (page 64) Cerca con Google

WK Estes. Traps in the route to models of memory and decision. Psychonomic bulletin & review, 9(1):3–25, 2002. (page 64) Cerca con Google

Eleanor R Fapohunda and Michael P Todaro. Family structure, implicit contracts, and the demand for children in southern nigeria. Population and Development Review, pages 571–594, 1988. (page 3) Cerca con Google

SM Farid. On the pattern of cohort fertility. Population Studies, 27(1):159–168, 1973. (page 15) Cerca con Google

Patrizia Farina, Eshetu Gurmu, Abdulahi Hasen, and Dionisia Maffioli. Fertility and Family Change in Ethiopia. Central Statistical Authority, 2001. (page 2, 9) Cerca con Google

C Fernandez, S Cervino, N Perez, and E Jardim. Stock assessment and projections incorporating discard estimates in some years: an application to the hake stock in ices divisions viiic and ixa. ICES Journal of Marine Science: Journal du Conseil, 67(6): 1185–1197, 2010. (page 26) Cerca con Google

Carmen Fernandez, Eduardo Ley, and Mark FJ Steel. Bayesian modelling of catch in a north-west atlantic fishery. Journal of the Royal Statistical Society: Series C (Applied Statistics), 51(3):257–280, 2002. (page 26) Cerca con Google

Yohannes Fitaw, Yemane Berhane, and Alemayehu Worku. Impact of child mortality and fertility preferences on fertility status in rural ethiopia. East African medical journal, 81 (6):300–306, 2004. (page 17) Cerca con Google

Yohannis Fitaw, Yemane Berhane, and Alemayehu Worku. Differentials of fertility in rural butajira. Ethiopian Journal of health development, 17(1):17–25, 2003. (page 17) Cerca con Google

Cedric Flecher, Ph Naveau, and Denis Allard. Estimating the closed skew-normal distribution parameters using weighted moments. Statistics & Probability Letters, 79(19): 1977–1984, 2009. (page 101) Cerca con Google

John Fox. Nonparametric simple regression: smoothing scatterplots. Number 130. Sage, 2000. (page 16) Cerca con Google

Sylvia Fr¨uhwirth-Schnatter. Finite mixture and Markov switching models. Springer Science & Business Media, 2006. (page 41) Cerca con Google

Dani Gamerman. Markov chain monte carlo: stochastic simulation for bayesian inference. 1997. London: Chapman Hall. (page 35) Cerca con Google

Ezra Gayawan, Samson B Adebayo, Reuben A Ipinyomi, Benjamin A Oyejola, et al. Modeling fertility curves in africa. Demographic Research, 22(10):211–236, 2010. (page 101) Cerca con Google

Samson Gebremedhin. Level and Differentials of Fertility in Awassa Town. PhD thesis, Addis Ababa University, 2006. (page 17) Cerca con Google

Samson Gebremedhin and Mulugeta Betre. Level and differentials of fertility in awassa town, southern ethiopia: original research article. African journal of reproductive health, 13(1):93–112, 2009. (page 17) Cerca con Google

Alan E Gelfand. Bayesian methods and modeling. Encyclopedia of Environmetrics, 2014. (page 43) Cerca con Google

Alan E Gelfand and Adrian FM Smith. Sampling-based approaches to calculating marginal densities. Journal of the American statistical association, 85(410):398–409, Cerca con Google

1990. (page 35) A Gelman and J Hill. Missing-data imputation. Behavior research methods, 43(2):310–30, 2007. (page 65, 66, 68, 69) Cerca con Google

A Gelman, JB Carlin, HS Stern, and D Rubin. Bayesian data analysis/’chapman & hall, new york. 1995. (page 85) Cerca con Google

Andrew Gelman and Xiao-Li Meng. Model checking and model improvement. In Markov chain Monte Carlo in practice, pages 189–201. Springer, 1996. (page 91) Cerca con Google

Andrew Gelman and Donald B Rubin. Inference from iterative simulation using multiple sequences. Statistical science, pages 457–472, 1992. (page ) Cerca con Google

Andrew Gelman, John B Carlin, Hal S Stern, and Donald B Rubin. Bayesian data analysis, (chapman & hall/crc texts in statistical science). 2003. (page 35, 75) Cerca con Google

Andrew Gelman, John B Carlin, Hal S Stern, and Donald B Rubin. Bayesian data analysis, volume 2. Taylor & Francis, 2014. (page 26, 33, 34, 54, 67) Cerca con Google

J Geweke. Evaluating the accuracy of sampling0based approaches to the calculation of posterior moments, bayesian statistics 4, ed. JM Bernardo, JO Berger, AP David, and AFM Smith, 1690193, 1992. (page 55, 90) Cerca con Google

John Geweke, Michael Keane, and David Runkle. Alternative computational approaches to inference in the multinomial probit model. The review of economics and statistics, pages 609–632, 1994. (page 44) Cerca con Google

Tewodros Tsegaye Gezahegn. Cross sectional study of women employment and fertility in ethiopia. 2011. (page 3) Cerca con Google

E Gilje. Fitting curves to age-specific fertility rates: Some examples. Statistical Review of the Swedish National Central Bureau of Statistics III, 7:118–134, 1972. (page 13) Cerca con Google

Walter R Gilks. The relationship between birth history and current fertility in developing countries. Population Studies, 40(3):437–455, 1986. (page 16, 71) Cerca con Google

Andreas Gl¨ockner and Thorsten Pachur. Cognitive models of risky choice: Parameter stability and predictive accuracy of prospect theory. Cognition, 123(1):21–32, 2012. (page ) Cerca con Google

Benjamin Gompertz. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical transactions of the Royal Society of London, pages 513–583, 1825. (page 15) Cerca con Google

William E Griffiths, R Carter Hill, and Peter J Pope. Small sample properties of probit model estimators. Journal of the American Statistical Association, 82(399):929–937, 1987. (page 6, 18, 25) Cerca con Google

Riccardo Griggio. Tassi di fecondit´a per et´a del costa rica.unanalisi bayesiana. 2013/2014. (page 48, 69, 102) Cerca con Google

Arjun K Gupta and John T Chen. A class of multivariate skew-normal models. Annals of the Institute of Statistical Mathematics, 56(2):305–315, 2004. (page 101) Cerca con Google

Arjun K Gupta, Truc T Nguyen, and Jose Almer T Sanqui. Characterization of the skewnormal distribution. Annals of the Institute of Statistical Mathematics, 56(2):351–360, 2004. (page 101) Cerca con Google

Eshetu Gurmu. Fertility transition driven by poverty: the case of Addis Ababa (Ethiopia). PhD thesis, University of London, 2005. (page 17) Cerca con Google

Eshetu Gurmu and Ruth Mace. Fertility decline driven by poverty: the case of Addis Ababa, Ethiopia. Journal of biosocial science, 40(03):339–358, 2008. (page 17) Cerca con Google

Hugo Hadwiger. Eine analytische reproduktionsfunktion f¨ur biologische gesamtheiten. Scandinavian Actuarial Journal, 1940(3-4):101–113, 1940. (page 13, 101) Cerca con Google

Hilde Haider and Peter A Frensch. Why aggregated learning follows the power law of practice when individual learning does not: Comment on rickard (1997, 1999), delaney et al.(1998), and palmeri (1999). 2002. (page 64) Cerca con Google

H Leon Harter and Albert H Moore. Point and interval estimators, based on m order statistics, for the scale parameter of a weibull population with known shape parameter. Technometrics, 7(3):405–422, 1965. (page 87) Cerca con Google

W Keith Hastings. Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1):97–109, 1970. (page 36, 44) Cerca con Google

Andrew Heathcote, Scott Brown, and DJK Mewhort. The power law repealed: The case for an exponential law of practice. Psychonomic bulletin & review, 7(2):185–207, 2000. (page 64) Cerca con Google

Philip Heidelberger and Peter D Welch. Simulation run length control in the presence of an initial transient. Operations Research, 31(6):1109–1144, 1983. (page 55, 90) Cerca con Google

Norbert Henze. A probabilistic representation of the’skew-normal’distribution. Scandinavian journal of statistics, pages 271–275, 1986. (page 29, 48, 79) Cerca con Google

Jan M Hoem and Bo Rennermalm. On the statistical theory of graduation by Splines. Laboratory of Actuarial Mathematics, University of Copenhagen, 1977. (page 101) Cerca con Google

Jan M Hoem, Dan Madien, Jørgen Løgreen Nielsen, Else-Marie Ohlsen, Hans Oluf Hansen, and Bo Rennermalm. Experiments in modelling recent danish fertility curves. Demography, 18(2):231–244, 1981. (page 13, 14, 16, 101) Cerca con Google

C Jennison. Contribution to the discussion of paper by richardson and green (1997). Journal of the Royal Statistical Society, series B, 59:778–779, 1997. (page 41) Cerca con Google

Robert E Kass and Larry Wasserman. The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91(435):1343–1370, 1996. (page 40) Cerca con Google

Y Kinfu. The quiet revolution: An analysis of change toward below-replacement level fertility in Addis Ababa. PhD thesis, PhD Thesis, Australian National University, 2001. (page 3, 17) Cerca con Google

Ruth King, Byron Morgan, Olivier Gimenez, and Steve Brooks. Bayesian analysis for population ecology. CRC Press, 2009. (page 89) Cerca con Google

Anne B Koehler and Emily S Murphree. A comparison of results from state space forecasting with forecasts from the makridakis competition. International Journal of Forecasting, 4(1):45–55, 1988. (page 21) Cerca con Google

Heemun Kwok and Roger J Lewis. Bayesian hierarchical modeling and the integration of heterogeneous information on the effectiveness of cardiovascular therapies. Circulation: Cardiovascular Quality and Outcomes, 4(6):657–666, 2011. (page 69) Cerca con Google

Wallace E Larimore and Raman K Mehra. Problem of overfitting data. Byte, 10(10): 167–178, 1985. (page 21) Cerca con Google

AM Latimer, S Banerjee, H Sang Jr, ES Mosher, and JA Silander Jr. Hierarchical models facilitate spatial analysis of large data sets: a case study on invasive plant species in the northeastern united states. Ecology Letters, 12(2):144–154, 2009. (page 26) Cerca con Google

Michael D Lee and Michael R Webb. Modeling individual differences in cognition. Psychonomic Bulletin & Review, 12(4):605–621, 2005. (page 69) Cerca con Google

Sik-Yum Lee. Structural equation modeling: A Bayesian approach, volume 711. John Wiley & Sons, 2007. (page 19) Cerca con Google

Tsung I Lin. Maximum likelihood estimation for multivariate skew normal mixture models. Journal of Multivariate Analysis, 100(2):257–265, 2009. (page 100) Cerca con Google

Tsung I Lin, Jack C Lee, Shu Y Yen, et al. Finite mixture modelling using the skew normal distribution. Statistica Sinica, 17(3):909, 2007. (page 101) Cerca con Google

David P Lindstrom and Zewdu Woubalem. The demographic components of fertility decline in addis ababa, ethiopia: a decomposition analysis. Genus, pages 147–158, 2003. (page 17) Cerca con Google

Brunero Liseo and Nicola Loperfido. A bayesian interpretation of the multivariate skewnormal distribution. Statistics & probability letters, 61(4):395–401, 2003. (page 30, 101) Cerca con Google

David J Lunn, Andrew Thomas, Nicky Best, and David Spiegelhalter. Winbugs-a bayesian modelling framework: concepts, structure, and extensibility. Statistics and computing, 10(4):325–337, 2000. (page 26) Cerca con Google

Scott M Lynch. Introduction to applied Bayesian statistics and estimation for social scientists. Springer Science & Business Media, 2007. (page 32) Cerca con Google

E Mumbi Machera. Social, economic and cultural barriers to family planning among rural women in kenya: A comparative case study of the divisions in embu district. 1997. (page 3) Cerca con Google

Kuttan Mahadevan. Sociology of fertility: Determinants of fertility differentials in South India. Sterling, 1979. (page 17) 136 Cerca con Google

Peter Martin. Une application des fonctions de gompertz a l’etude de la fecondite d’une cohorte. Population, 22(6):1085–1096, 1967. (page 15) Cerca con Google

Stefano Mazzuco and Bruno Scarpa. Fitting age-specific fertility rates by a skew-symmetric probability density function. 2011. (page 6, 100, 101) Cerca con Google

Stefano Mazzuco and Bruno Scarpa. Fitting age-specific fertility rates by a flexible generalized skew normal probability density function. Journal of the Royal Statistical Society: Series A (Statistics in Society), 178(1):187–203, 2015. (page 6, 15, 16, 18, 25, 26, 29, 44, 88, 102) Cerca con Google

Michael A McCarthy. Bayesian methods for ecology. Cambridge University Press, 2007. (page 26) Cerca con Google

Donald R McNeil, T Jamel Trullell, and John C Turner. Spline interpolation of demographic oata. Demography, 14(2):245–252, 1977. (page 16) Cerca con Google

Demena Melake. Population and Development: Lecture note. HaramayaUniversity in collaboration with the Ethiopia Public Health Training Initiative, The Carter Center, the Ethiopia Ministry of Health, and the Ethiopia Ministry of Education, 2005. (page 1) Cerca con Google

Nicholas Metropolis, Arianna W Rosenbluth, Marshall N Rosenbluth, Augusta H Teller, and Edward Teller. Equation of state calculations by fast computing machines. The journal of chemical physics, 21(6):1087–1092, 1953. (page 36, 44) Cerca con Google

Russell B Millar. Reference priors for bayesian fisheries models. Canadian Journal of Fisheries and Aquatic Sciences, 59(9):1492–1502, 2002. (page 26) Cerca con Google

Marco Minozzo and Laura Ferracuti. On the existence of some skew-normal stationary processes. Chilean Journal of Statistics, 3:157–170, 2012. (page 101) Cerca con Google

Anteneh Mulugeta Eyasu. Multilevel Modeling of Determinants of Fertility Status of Married Women in Ethiopia. American Journal of Theoretical and Applied Statistics, 4 (1):19–25, 2015. (page 4) Cerca con Google

Edmund M Murphy and Dhruva N Nagnur. A gompertz fit that fits: applications to canadian fertility patterns. Demography, 9(1):35–50, 1972. (page 15) Cerca con Google

H˚akan Nilsson, J¨org Rieskamp, and Eric-Jan Wagenmakers. Hierarchical bayesian parameter estimation for cumulative prospect theory. Journal of Mathematical Psychology, 55 (1):84–93, 2011. (page 8, 63, 66, 67, 68, 69, 89) Cerca con Google

NOP. National Population Office. National Population Policy of Ethiopia, Addis Ababa. Office of the Prime Minister, 1993. (page 100)137 Cerca con Google

T Ozaki. On the order determination of arima models. Applied Statistics, pages 290–301, 1977. (page 21) Cerca con Google

Samba SR Pasupuleti and Prasanta Pathak. Special form of gompertz model and its application. Genus, 66(2):95–125, 2010. (page 13, 101) Cerca con Google

Paraskevi Peristera and Anastasia Kostaki. Modeling fertility in modern populations. Demographic Research, 16(6):141–194, 2007. (page 14, 16, 101) Cerca con Google

Adrian E Raftery, Steven Lewis, et al. How many iterations in the gibbs sampler. Bayesian statistics, 4(2):763–773, 1992. (page 55, 90) Cerca con Google

Christian P Robert. The bayesian choice: From decision-theoretic foundations to computational implementation (springer texts in statistics) by. 2001. (page 69) Cerca con Google

Jeffrey N Rouder and Jun Lu. An introduction to bayesian hierarchical models with an application in the theory of signal detection. Psychonomic Bulletin & Review, 12(4): 573–604, 2005. (page 68) Cerca con Google

Jeffrey N Rouder, Jun Lu, Richard D Morey, Dongchu Sun, and Paul L Speckman. A hierarchical process-dissociation model. Journal of Experimental Psychology: General, 137(2):370, 2008. (page 68) Cerca con Google

J Andrew Royle, K Ullas Karanth, Arjun M Gopalaswamy, and N Samba Kumar. Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. Ecology, 90(11):3233–3244, 2009. (page 93) Cerca con Google

M Schaub and M K´ery. Combining information in hierarchical models improves inferences in population ecology and demographic population analyses. Animal Conservation, 15 (2):125–126, 2012. (page 67) Cerca con Google

Benjamin Scheibehenne and Thorsten Pachur. Hierarchical bayesian modeling: Does it improve parameter stability? In CogSci 2013: 35th Annual Conference of the Cognitive Science Society, pages 1277–1282. Cognitive Science Society, 2013. (page 65, 68) Cerca con Google

Benjamin Scheibehenne and Bettina Studer. A hierarchical bayesian model of the influence of run length on sequential predictions. Psychonomic bulletin & review, 21(1):211–217, 2014. (page 68) Cerca con Google

Carl P Schmertmann. A system of model fertility schedules with graphically intuitive parameters. Demographic Research, 9(5):81–110, 2003. (page 16, 101) Cerca con Google

Rajendra K Sharma. Demography and population problems. Atlantic Publishers & Dist, 2004. (page 1) 138 Cerca con Google

Richard M Shiffrin, Michael D Lee, Woojae Kim, and Eric-Jan Wagenmakers. A survey of model evaluation approaches with a tutorial on hierarchical bayesian methods. Cognitive Science, 32(8):1248–1284, 2008. (page 66, 68) Cerca con Google

Susan E Short and Gebre-Egziabher Kiros. Husbands, wives, sons, and daughters: Fertility preferences and the demand for contraception in ethiopia. Population Research and Policy Review, 21(5):377–402, 2002. (page 17) Cerca con Google

Amson Sibanda, Zewdu Woubalem, Dennis P Hogan, and David P Lindstrom. The proximate determinants of the decline to below-replacement fertility in addis ababa, ethiopia. Studies in family planning, 34(1):1–7, 2003. (page 17) Cerca con Google

Brijesh P Singh, Kushagra Gupta, and KK Singh. Analysis of fertility pattern through mathematical curves. American Journal of Theoretical and Applied Statistics, 4(2):64–70, 2015. (page 17) Cerca con Google

Brian J Smith. Bayesian output analysis program (boa) for mcmc. R package version, 1 (5), 2005. (page 90) Cerca con Google

Tom AB Snijders and Roel Bosker. J. 1999: Multilevel analysis. an introduction to basic and advanced multilevel modeling. (page 26) Cerca con Google

David J Spiegelhalter, Keith R Abrams, and Jonathan P Myles. Bayesian approaches to clinical trials and health-care evaluation, volume 13. John Wiley & Sons, 2004. (page 26, 75) Cerca con Google

Martin A Tanner and Wing Hung Wong. The calculation of posterior distributions by data augmentation. Journal of the American statistical Association, 82(398):528–540, 1987. (page 44) Cerca con Google

Hailemariam Teklu, Alula Sebhatu and Tesfayi Gebreselassie. Components of Fertility Change in Ethiopia. Further Analysis of the 2000, 2005 and 2011 Demographic and Health Surveys. DHS Further Analysis Reports.No. 80. Calverton, Maryland, USA: ICF International, 2013. (page 2) Cerca con Google

Charles Teller and Assefa Hailemariam. The Demographic Transition and Development in Africa. Springer, 2011. (page 4) Cerca con Google

y The World Factbook. https://www.cia.gov/Library/publications/ the-world-factbook/geos/print/country/countrypdf_et.pdf. 2014. (page 2) Vai! Cerca con Google

Howell Tong. Some comments on the canadian lynx data. Journal of the Royal Statistical Society. Series A (General), pages 432–436, 1977. (page 21) 139 Cerca con Google

Don van Ravenzwaaij, Gilles Dutilh, and Eric-Jan Wagenmakers. Cognitive model decomposition of the bart: assessment and application. Journal of Mathematical Psychology, 55(1):94–105, 2011. (page 68, 69) Cerca con Google

John Von Neumann. 13. various techniques used in connection with random digits. 1951. (page 33) Cerca con Google

Christopher K Wikle. Hierarchical models in environmental science. International Statistical Review, 71(2):181–199, 2003. (page 69) Cerca con Google

Guillaume Wunsch. Courbes de gompertz et perspectives de f´econdit´e. Recherches Economiques de Louvain/Louvain Economic Review ´ , pages 457–468, 1966. (page 15) Cerca con Google

Arnold Zellner and Peter E Rossi. Bayesian analysis of dichotomous quantal response models. Journal of Econometrics, 25(3):365–393, 1984. (page 18) Cerca con Google

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