Abstract
In the current chapter, four issues are briefly addressed, which are vital to the further discussion, yet not sufficiently within the scope of the topic of this book to be presented in full. Firstly, the problems with migration data are dealt with, focusing on the diversity of definitions, measurement errors, and possible ways to overcome the inconsistencies within the statistical information. Secondly, the issues concerning uncertainty, subjectivity and expert judgement are discussed, together with their role in migration forecasting. Thirdly, general remarks on the Bayesian statistical inference are presented, with the aim of serving as reference throughout the remaining parts of the book. Finally, numerical algorithms used in Bayesian computations are briefly discussed, based on the example of Markov chain Monte Carlo simulations.
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Notes
- 1.
Such matrices were first published in the demographic yearbook of the United Nations (1978) and are often used in the analysis of migration data by origin and destination (Kupiszewska & Nowok, 2005).
- 2.
Shortcomings of this approach are discussed in Kupiszewska and Nowok (2005). An alternative statistical methodology of estimating the magnitude of migration flows on the basis of two sources is proposed by Brierley, Forster, MacDonald, and Smith (2008), notably also within the Bayesian framework. Their approach is under further development in the research project ‘IMEM’ (‘Integrated Modelling of European Migration’), financed by the NORFACE network. For more details, see http://www.norface.org/migration12.html (accessed on 6 March 2010).
- 3.
A discussion of advantages and disadvantages of using migration rates can be found for example in McDonald and Kippen (2002), yet limited to the demographic reality of Australia, in that case visibly differing from Europe.
- 4.
Credits to Marek Kupiszewski. Notably, a recent Eurostat-funded research project ‘MIMOSA: Modelling of statistical data on migration and migrant populations’ (website: mimosa.gedap.be, accessed on 17 November 2009), aims at producing coherent estimates of population stocks and flows for the European Union and EFTA. The final results, concerning the period 2001–2008, were made available in late 2010.
- 5.
In the current study, ‘deterministic’ is thus understood as ‘not allowing for randomness or uncertainty’, in contrast to the dictionary-based definition, describing ‘determinism’ as ‘a theory or doctrine that […] social phenomena are causally determined by preceding events or natural laws’ (Merriam Webster Online Dictionary, http://www.m-w.com, accessed on 25 April 2006). Notably, determinism in the latter interpretation may refer to stochastic explanations of the phenomena under study, provided that the ‘natural laws’ involved contain an element of randomness, as, for example, in many areas of contemporary theoretical physics. A discussion on uncertainty and (in-)determinism is also offered further in Chapter 5.
- 6.
The subsequent four paragraphs are inspired by the History of Economic Thought website (cepa.newschool.edu/het, accessed on 3 June 2005), which includes comprehensive essays onvarious topics concerning the economic theory developments. The website author, Gonçalo L. Fonseca, deserves credit for stimulating ideas and general views on the philosophy of probability, and for providing very useful references to primary sources.
- 7.
A history of the idea of risk, as well as of the attempts to accommodate it in human life has been provided for example in Bernstein (1996/1997).
- 8.
Popper (1982/1996, p. 26), quoting a 1954 paper of the British philosopher P. H. Nowell Smith in Mind, labelled determinism as a somewhat outdated concept – an ‘eighteenth-century bogey’.
- 9.
To preserve coherence with notation prevailing in the Bayesian literature, although somewhat ambiguously in terms of mathematical precision, p(.) can denote different functions, depending on the argument (θ or x).
- 10.
As noted by Jacek Osiewalski, in the orthodox Bayesian approach, these elements should be sufficient for any inference, ‘for whatsoever is more than these, cometh of evil’ (personal communication, English citation after the King James Bible, Mt 5:37, http://www.kingjamesbibleonline.org, accessed on 6 March 2010).
- 11.
DeGroot (1970/1981) provides a comprehensive discussion on the theory of statistical games and the decision approach. Interestingly, a decision-theory approach to demographic forecasting, involving the presence of a loss function, has been advocated by Lee (1998), as well as by Alho and Spencer (2005) as one of the possibilities of methodological improvements of stochastic population predictions (see also Chapter 11).
- 12.
After the International Statistical Institute (ISI) Multilingual Glossary of Statistical Terms (isi.cbs.nl/glossary.htm, accessed on 10 June 2005).
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Bijak, J. (2011). Preliminaries. In: Forecasting International Migration in Europe: A Bayesian View. The Springer Series on Demographic Methods and Population Analysis, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8897-0_2
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