Abstract
Rev. Bayes and his friend Richard Price created a new way to deal with the philosophical and theological problems on induction as were explained by Hume. This mathematical formula included the notion of subjective probabilities and, consequently, opened a debate on its validity. French mathematician Pierre-Simon Laplace applied it successfully to astronomical calculations just before starting to change his mind over the correctness of Bayes’ formula. Several objections and practical challenges made the general implementation of Bayes’ ideas impossible.
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Notes
- 1.
Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731) and An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst (published anonymously in 1736).
- 2.
Price was even a beneficiary of Bayes’ inheritance. Bayes left £200 to be divided between John Hoyle and Richard Price (Dale 1999: 26). Hoyle was the minister at Stoke Newington from 1748 to 1756. When Hoyle left Stoke Newington to take up a position in Norwich (Browne 1877), Richard Price became the pastor at Stoke Newington. Both chapels eventually became Unitarian churches, and both Hoyle and Price were known Arians, (Bellhouse 2004: 11). It was a complete religious environment.
- 3.
Although Price himself expressed his role as simple transmitter of the ideas of Bayes, some reluctance could be expressed about his complete respect of the original manuscript. Following some remarks of Prof. Bellhouse (2002), it might be very probable that Mr. Price made some “adjustments” to the final redaction, although he respected the main ideas (see Earman (1992) for a technical analysis).
- 4.
Following Gillies (1987, as well as by personal correspondence), we must say that Bayes made the mathematical contributions and Price the philosophical arrangement of it. Though the papers do not explicitly cite Hume, there is evidence that the authors were trying to solve Hume’s problems about induction.
- 5.
The original essay can be freely downloaded as a PDF file from http://www.stat.ucla.edu/history/essay.pdf.
- 6.
Downloadable from the Royal Society at http://rstl.royalsocietypublishing.org/content/53/370.
- 7.
There is a different possibility that Laplace knew about the Bayes–Price ideas through a common friend, Condorcet. Unfortunately, this is only a possibility that cannot be confirmed empirically.
- 8.
Dealing with large amounts of complex data was a problem that emerged at the end of the eighteenth century and became a true problem for nineteenth-century scientists. New evidences and calculations in Astronomy, huge amounts of natural collected biological data required a fundamentally new way of thinking. It was provided by statistical thinking. Was the universe stable thanks to a Newtonian God? Besides the lack of knowledge about the real mechanistical cause of gravitatory, then still a dark force (the Higgs boson that justified gravity as undiscovered until 2013, at the European LHC), the gravitatori calculations were so complex that their calculation power was not able then to do it. As a consequence, statistical approximations were the only rational solution to that problem, and it’s what Laplace understood (Bertsch McGrayne 2011: 19).
- 9.
This attitude can be labeled as “infidel mathematics” and was run by the free thinkers of the Enlightenment. On the other side, religious reformists that were considered Dissenters were interested in using mathematics to do the opposite: use mathematics to justify the existence of God (Bertsch McGrayne 2011: 3–5).
- 10.
Newton, opposed Laplace in this point, claimed against hypotheses: just remember his “hypotheses non fingo,” but at the same time was not able to explain gravity and the necessity of a God as a Watchmaker inside a clock-universe. Clearly, eighteenth-century rationalism is not a unified intellectual project, nor a true naturalist rationalism. Anyhow, Laplace was accused by radical revolutionaries as “Newtonian idolator” and he was arrested on suspicion of disloyalty to the French Revolution. Science under politics debates. Some centuries later, the Lysenko case repeated this situation under the communism of the URSS.
- 11.
Even in that case only to uniform priors following the insightful suggestions of Stigler (2012, from personal electronic epistolary talk). As he wisely points out, before Galton there was no real multivariate analysis, so the modern practice of starting with a prior and likelihood then getting the multivariate and then the conditional (posterior) distribution could not be done before the 1880s.
- 12.
Translated as “We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”
- 13.
There is also the contrary question of scale invariance and dilation, but this is a different question to be analyzed in a different place. We have neither space here to analyze the problem of connecting the gap between quantum microphysics with macrophysics (through mesophysics). Quantum paradoxes are also a crucial challenge for contemporary thinkers and scientists. For an attempt to unify quantum microphysics with macrophysics see Sewell (2002).
- 14.
According to Efron (2012: 133), Objective Bayes is the contemporary name for Bayesian analysis carried out in the Laplace–Jeffreys manner. According to Gillies (2000), Chap. 3, the interpretation of probability as degree of rational belief by Objective Bayesians has never been resolved and has even given rise to several paradoxes. But as far as I can see paradoxes never stopped scientists or theory-users in their activities. Conceptual paradigms are very flexible as well as resistant to internal or external criticisms.
- 15.
Very surprisingly, the military swiftly accepted Bayesian techniques during the Second World War and Cold War, as well as related agencies such as NASA. And this is valid for American and European efforts: In 1979, NATO organization held a symposium to encourage Bayesian application for real conflicts.
- 16.
Curiously, Lindley gave the name to a paradox, called Lindley’s paradox, that put Bayesian and fequentists into the same bottleneck regarding a hypothesis testing problem that gives different results for certain choices of the prior distribution.
- 17.
I thank to Prof. D. Gillies his generous and detailed conceptual suggestions about this section of the book.
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Vallverdú, J. (2016). The Bayesian Approach and Its Evolution Until the Beginning of the Twentieth Century. In: Bayesians Versus Frequentists. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48638-2_3
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