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The Dispersion of Measures in Population Sciences

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Probability and Social Science

Part of the book series: Methodos Series ((METH,volume 10))

Abstract

The different aspects of probability that played a crucial role in the history of population sciences pertains to the dispersion of measures, either around their main value, or as a function of other characteristics of the population studied. We follow this use from the seventeenth century to nowadays and show how these sciences used, according to their paradigm, epistemic or objectivist probability. The different approaches followed, cross-sectional, longitudinal, event history, contextual and multilevel analyses are illustrated with examples of application. We conclude this chapter with a detailed presentation of the estimation of the age structure of a paleodemographic population for which no age measurements exist but for which proxy estimators are available: only a fully Bayesian method allows a correct estimate of the age structure and its dispersion.

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Notes

  1. 1.

    In modern Greek, the term for variance is diaspora (διασπορά), which brings us back to the dispersion of the Jewish people.

  2. 2.

    binis limitibus conclusam, sed qui tam arcti constitui possunt, quàm quis voulerit.

  3. 3.

    As Moheau (1778) noted, ‘humane mortality is not regulated in the same manner as fertility: there are years that produce a multitude of deaths, there are others that spare our days, whereas the rate of annual newcomers is almost equal and invariable’. That is one of the reasons why eighteenth-century authors preferred to calculate a birth multiplier rather than a death multiplier.

  4. 4.

    It is interesting to note that such a sampling replaces the exhaustive census in France after 1999.

  5. 5.

    The Comté de Nice and Savoie (Savoy) were annexed to France in 1860.

  6. 6.

    For the record, these figures are currently challenged (Brian 2001). However, our purpose here is not an accurate reconstruction of France’s population, but a discussion of Laplace’s estimates. Laplace himself revisited the subject in Théorie analytique des probabilités (1812), using a different approach from the one described here. In this later study, he worked on an enumeration of 1802 and on the average number of births recorded between September 22, 1799, and September 22, 1802. Laplace also introduced the longitudinal analysis of mortality (‘Let us suppose that we have tracked the distribution of mortality among a very large number n of children, from their birth to their total extinction’), and the mean duration of marriages between boys aged a and girls aged \( {a}^{\prime }\). He naturally calculated confidence intervals for all these quantities.

  7. 7.

    Legendre published an application of the least-squares method to a simpler case (1805) before Gauss and claimed precedence for the discovery. However, besides the evidence that Gauss used the method before 1805, the key element of this approach is missing from Legendre’s publication: he fails to present it in a clear probabilistic framework.

  8. 8.

    When the second event has occurred, and consists of the marriage of the surveyed individual, it is useful to incorporate the spouse’s fixed characteristics in addition to those of the individual.

  9. 9.

    It is interesting to note how strongly David Cox criticized the Bayesian approach. For instance, in discussing a later work by Cox and Hinkley (1974), Jaynes (2003) stated that the presentation of Bayesian methods led Cox ‘to repeat all the old, erroneous objections to them, showing no comprehension that these were ancient misunderstandings long since corrected by Jeffreys (1939), Savage (1954) and Lindley (1956).’

  10. 10.

    In this second article, Stephan recognized that the results published in the previous article did not coincide with those given by the least-squares method—as the authors had mistakenly claimed—but he argued that they supplied a proxy solution.

  11. 11.

    For more details on this comparison, see Courgeau (2011).

  12. 12.

    Again, we refer the reader to Courgeau (2011) for fuller details.

  13. 13.

    For more details on this estimation, see Caussinus and Courgeau (2010).

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    Daniel Courgeau

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Courgeau, D. (2012). The Dispersion of Measures in Population Sciences. In: Probability and Social Science. Methodos Series, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2879-0_5

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