Bayesian
Reasoning

An Annotated Bibliography Compiled by Timothy McGrew

This brief annotated
bibliography is intended to help students get started with their research. It is
not a substitute for personal investigation of the literature, and it is not a
comprehensive bibliography on the subject. For those just beginning to study
Bayesian reasoning, I suggest the starred items as good places to start your
reading.

L. Jonathan Cohen, *An
Introduction to the Philosophy of Induction and Probability* (Oxford: Oxford
University Press, 1989).

Full of interesting historical
information and challenging suggestions. Cohen contrasts two major concepts of
confirmation, which he terms "Baconian" and "Pascalian."
The latter is the common probabilistic concept, but Cohen argues vigorously
that Pascalian probability cannot be the whole story about the logic of
confirmation.

J. Earman, ed., *Testing
Scientific Theories*, vol. 10, *Minnesota Studies in the Philosophy of
Science* (Minneapolis: University of Minnesota Press, 1983).

An excellent collection of essays,
many pertaining to Glymour's work.

__________, *Bayes
or Bust?* (Cambridge, MA: MIT Press, 1992).

A sympathetic but critical survey
of the state of the art by a self-professed "lapsed Bayesian." Parts
of this are fairly technical.

Clark Glymour, *Theory
and Evidence* (Princeton: Princeton University Press, 1980).

Glymour's book caused quite a stir,
largely because of two features: his novel "bootstrapping" approach
(which can look circular at first glance) and his trenchant essay "Why I
am not a Bayesian."

C. Howson and P.
Urbach, *Scientific Reasoning: the Bayesian Approach* (La Salle, IL: Open
Court, 1989).

The standard reference work for
Subjective Bayesians. Howson and Urbach go well beyond presenting their
position, giving detailed criticisms of alternatives. They are particularly
critical of the classical tradition in statistical inference.

*P. Horwich, *Probability
and Evidence* (Cambridge: Cambridge University Press, 1982).

An elegant and highly readable
elementary treatment of the Bayesian approach to scientific reasoning. Horwich
advocates a "degree of belief" approach to probability, but he
rejects Subjective Bayesianism in favor of a "rationalist" construal
in which an individual's probability assignments are subject to stronger
constraints than mere coherence. He then applies the Bayesian methodology to
many puzzles and problems and demonstrates its power. This one is well worth
reading even if you don't accept all of his solutions.

R. Jeffrey, *The
Logic of Decision*, 2nd ed. (Chicago: University of Chicago Press, 1983).

A standard textbook on Bayesian
inference and decision theory from a Subjectivist or "Personalist"
point of view. This book contains Jeffrey's own explication of "Jeffrey
conditioning," a general probabilistic updating rule of which the standard
Bayesian conditioning is merely a special case.

__________, *Probability
and the Art of Judgment* (Cambridge: Cambridge University Press, 1992).

A collection of Jeffrey's essays
applying and extending Subjective Bayesian methods. Some of the essays are
technical: others are readable without a strong mathematical background so long
as one has mastered the basic probability calculus.

H. Jeffreys, *Scientific
Inference* (Cambridge: Cambridge University Press, 1937).

An early and forceful presentation
of the Objective Bayesian point of view. Though Jeffreys is a high-powered
writer and does not hesitate to invoke mathematics when it is required, there
is much here that can be understood even by readers who lack strong
mathematical preparation. The discussion of simplicity is particularly
important.

__________, *Theory
of Probability*, 2nd ed. (Oxford: Oxford University Press, 1948).

A historically important
formulation of Objective Bayesianism. Jeffreys insists that in situations of
complete ignorance, we must select a prior probability in such a way as to give
experience the maximum impact on our posterior probabilities. In some cases
this leads him to endorse "improper" priors that cannot be
normalized. Often challenging reading, but rewarding.

H. Kyburg, *Epistemology
and Inference* (Minneapolis: University of Minnesota Press, 1983).

Kyburg has long been one of the
most vocal critics of Subjectivism in probability. This collection of his
essays is indispensible for anyone who wants to see what can be said against
Subjectivism. The essay on "Subjective Probability" is a classic.
(Scan the subtitle for acronyms.)

James Logue, *Projective
Probability* (Oxford: Oxford University Press, 1995).

Logue’s book develops a version of
personalism and claims that it captures the univocal meaning of
"probability." He is skeptical, however, about the attempt to resolve
all questions about scientific inference by appealing to Bayesian
conditionalization. The book contains a very interesting discussion of the
problem of probabilistic "weight."

R. Miller, *Fact
and Method* (Princeton: Princeton University Press, 1987).

Miller is deeply critical of
Bayesian approaches to scientific reasoning. His exposition of Subjective
Bayesianism is a model of clarity, and his criticisms, though uneven in
quality, are sometimes exceedingly shrewd.

R. Rosenkrantz, *Inference,
Method and Decision: Towards a Bayesian Philosophy of Science* (Dordrecht:
D. Reidel, 1977).

The definitive treatise on
Objective Bayesianism. Rosenkrantz advocates a the use of "maximum
entropy" (or "maxent") priors. His discussion of the
similarities and differences between various Objective Bayesian approaches is
illuminating, and his treatment of simplicity and "sample coverage"
merits close study. Of particular interest is Rosenkrantz's careful treatment
of Popper's philosophy of science; he maintains that many of Popper's
methodological insights can be recaptured within a Bayesian framework.

__________,
"Why Glymour *Is* a Bayesian," in Earman (1983), pp. 69-98.

Just what it sounds like.
Rosenkrantz argues that notwithstanding his criticisms of Bayesians, Glymour is
actually more Bayesian than many who march under that banner.

*W. Salmon, *The
Foundations of Scientific Inference* (Pittsburgh: University of Pittsburgh
Press, 1966).

An early and trenchant argument for
the applicability of Bayesian probability to problems of scientific inference.
The initial survey of approaches to the problem of induction is very useful,
and the Bayesian sections of the book are worth reading even though they are
not the latest or deepest work on the subject.

__________,
"Bayes's Theorem and the History of Science," in R. Stuewer, ed.,*
Historical and Philosophical Perspectives of Science*, vol. 5, *Minnesota
Studies in the Philosophy of Science* (Minneapolis: University of Minesota
Press, 1970), pp. 68-86.

A classic essay in which Salmon
treats with good sense and sophistication the traditional problem of separating
the context of discovery from the context of justification. In the end he
argues for the applicability of Bayesian analyses to episodes in the history of
science and suggests that the difficult problem of prior probabilities is best
approached through "plausibility constraints."

__________,
"Rationality and Objectivity in Science, *or* Tom Kuhn Meets Tom
Bayes," in C. W. Savage, ed., *Scientific Theories*, vol. 14, *Minnesota
Studies in the Philosophy of Science*
(Minneapolis: University of Minnesota Press, 1990), pp. 175-204.

An attempt to clean up the
subjectivity rampant in Kuhn's philosophy of science by imposing some Bayesian
constraints on scientific inference. Kuhn, in his reply, disavowed even the
constraints Salmon wanted to place on such reasoning, though it's not entirely
clear whether he was caricaturing Salmon's position in so doing.

G. Schlesinger, *The
Sweep of Probability* (Notre Dame: Notre Dame University Press, 1991).

A wide-ranging survey of the
applications of probability theory in general and Bayesian methods in
particular to various conundrums in epistemology and the philosophy of science.

A. Shimony, *Search
for a Naturalistic World View*, vol. 1, *Scientific Method and
Epistemology* (Cambridge: Cambridge University Press, 1993).

For the past several decades
Shimony has made important contributions to Bayesian epistemology and
philosophy of science. This collection of his papers contains much important
material, including the initial essay endorsing "tempered"
Bayesianism, the "Adamic derivation" of the probability calculus, and
too many other goodies to list. Required reading for Bayesians (and non-Bayesians!)
of any flavor.