Abstract
We contend that Bayesian accounts of evidence are inadequate, and that in this sense a complete theory of hypothesis testing must go beyond belief adjustment. Some prominent Bayesians disagree. To make our case, we will discuss and then provide reasons for rejecting the accounts of David Christensen, James Joyce, and Alan Hàjek. The main theme and final conclusions are straightforward: first, that no purely subjective account of evidence, in terms of belief alone, is adequate and second, that evidence is a comparative notion, applicable only when two hypotheses are confronted with the same data, as has been suggested in the literature on “crucial experiments” from Francis Bacon on.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Christensen has shown that another measure, S*(D/H) = Pr(H/D) - Pr(H), is equivalent to S(D, H). Joyce arrived at the same measure independently, and Hájek and Joyce (2008) later called it “probative evidence,” denoting it by q(,).
- 2.
Christensen’s own candor needs to be acknowledged at the outset. What he has provided, he says (Christensen 1999, p. 460), is not an “account of confirmation”, but a way of understanding certain features of it. Shedding even a little light is better than shedding no light at all.
- 3.
Joyce (1999) handles the case where Pr(D) reaches its highest value by considering a Reyni-Popper measure, on which (as against the standard Kolmogorov definition), Pr(H│ ̴ D) is defined when Pr(D) = 1. Joyce finds it quite counter-intuitive that when the agent’s value for D changes continuously and ultimately attains value 1, due to her learning new information, the confirmational value of D for her will stop suddenly. The intuitive way to approach the case where Pr(D) reaches 1, according to him, is to consider a specific sense in which D could still be counted as evidence for H even when the agent is certain about D. On his interpretation, D is evidence for H in that H is more likely to be the case given D (whatever its probability) than not-D. He thinks that this sort of intuition underlies the confirming power of “old evidence (see Chap. 9 for a discussion of the “old evidence” paradox). Fitelson (1999) notes, however, that if one incorporates a Reyni-Popper measure in q(,) or its equivalents, then q(,) differs not only from the conventional quantitative Bayesian measure of confirmation (as they do not on the Kolmogorov definition), but also from the purely qualitative measure. Indeed, Fitelson argues that if one incorporates the Reyni-Popper measure, there are many possible qualitative “Bayesian” measures of confirmation, and just as many “old evidence problems” (only one of which the Christensen-Joyce measure addresses). Since a principal motive of the C-J account is to resolve “the” old evidence problem, this is a serious difficulty for it. In trying to close one door, many others appear to have opened.
- 4.
A functional is a “function” of an entire distribution such as the mean, variance, or proportion in a category.
- 5.
See particularly the discussion of the Focused Information Criterion (FIC) in Claeskens and Hjort (2008).
- 6.
Even though prediction is involved, this is an evidential question as soon as the researcher asks the comparative questions, “which model has the greatest predictive power?”
- 7.
- 8.
See our earlier discussion of this assumption in Chap. 2.
- 9.
Our reconstruction is based mainly on Christensen (1999).
- 10.
Although not necessarily endorsing the “woodscraft” expressed.
- 11.
For a brief summary, see Brumfiel (2012).
- 12.
See Christensen (1999): “It [i.e., probability theory] provides a basis for conditionalization principles regulating change of belief—a topic about which traditional logic had little to say; it offers a quantitative analysis of our notion of confirmation, or evidential support”. See also Joyce (1999): “all Bayesians agree that the degree to which D counts as evidence for or against H for a given person is a matter of the extent to which learning D would increase or decrease her confidence” (we have replaced Joyce’s “X” by “H” and “C” by “D” in the quote to square with our usage), or again, “Relative to q(q,)…the extent to which D counts as evidence in favor of H for a given person depends on that person’s degree of belief for H” (same letter replacement). As already noted in the text, Joyce uses “confirmational power” and “evidential relevance” interchangeably.
- 13.
Joyce (2004) might well question whether there is any worth to this objection because he denies that there is any issue. He would like to say that the various measures represent distinct, but complimentary notions of evidential support. Our response to his attempt to bring confirmation and evidence under the encompassing rubric of “evidential support” is, first, that these notions are intuitively distinct, second that the distinction exposes the motive for the scientific need to distinguish hypotheses (recall the global warming example) and, third, that blurring the line between them is the root cause of important epistemological problems.
- 14.
Likelihoods and evidence can of course depend on observation order if there is correlated observation error or some of the hypotheses represent conditional data-generating mechanisms.
References
Bozdogan, H. (1987). Model selection and akaike information criterion (AIC)—the general theory and its analytical extensions. Psychometrika, 52, 345–370.
Brumfield, G. (2012). Neutrinos not faster than light. Nature, 16 (March 16). doi:10.1038/nature.2012.10249.
Christensen, D. (1999). Measuring confirmation. Journal of Philosophy, 99(9), 437–461.
Claeskens, G., & Hjort, N. (2008). Model Selection and Model Averaging. Cambridge: Cambridge University Press.
Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science, PSA, 66(1), 362–378.
Hájek, A., & Joyce, J. (2008). Confirmation. In S. Psillos & M. Curd (Eds.), The Routledge Companion to Philosophy of Science. New York: Routledge.
Joyce, J. (1999). The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.
Joyce, J. (2004). Bayes theorem. In Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/bayes-theorem/.
Lele, S. (2004). Evidence function and the optimality of the law of likelihood. In (Taper and Lele, 2004).
Taper, M., & Gogan, P. (2002). The northern yellowstone Elk: density dependence and climate conditions. Journal of Wildlife Management, 66(1), 106–122.
Taper, M., et al. (2008). Model structure adequacy analysis: selecting models on the basis of their ability to answer scientific questions. Synthèse , 163, 357–370.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 The Author(s)
About this chapter
Cite this chapter
Bandyopadhyay, P.S., Brittan, G., Taper, M.L. (2016). A Subjective Bayesian Surrogate for Evidence. In: Belief, Evidence, and Uncertainty. SpringerBriefs in Philosophy(). Springer, Cham. https://doi.org/10.1007/978-3-319-27772-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-27772-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27770-7
Online ISBN: 978-3-319-27772-1
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)