108 Metastatistics for the Non-Bayesian Regression Runner
the two experiments:
- Are the two “experiments” different?
- Does the “evidential import” of the two experiments for your beliefs about the
true valueμdiffer when presented with either experiment A or B? - Does your evaluation of the experiment depend on the “mental state” of the
investigator?
If your instinct is that “the evidential import” of both “experiments” is the same,
you may be Bayesian. To many Bayesians such an example is a demonstration of
a logical flaw in non-Bayesian statistics: in both cases someone has drawn 9 black
balls and 3 red balls. Why should I bother to consider which experiment was being
performed? If the “mental state” of the experimenter is “locked up” in his/her
head and, say, inaccessible by someone else analyzing the data, doesn’t such a
case represent a fundamental problem for the non-Bayesian? I will return to this
problem below, but before I do it will be helpful to sketch out some generalizations
about the differences between Bayesians and non-Bayesians regarding theroleof
statistics.
3.3 What is statistics good for?
First, the Bayesian is typically more ambitious about the goals of statistics: “Accord-
ing to the Bayesian view, scientific and indeed much of everydayreasoningis
conducted in probabilistic terms” (Howson and Urbach, 1993, p. 17).
John Maynard Keynes, for example, an exponent of “logical probability,”
deployed statistics to a very diverse range of subjects, including teleological ques-
tions – whether perceived order could be used to provide evidence of the existence
of God. He concluded that, although such questions were well suited to study
by Bayes’ law, the problem was that such evidence could only make the exis-
tence of God more credible if it were supported by otherevidence for God’s
existence (Keynes, 1921, p. 267).
To understand this point of view it is helpful to think of probability and statistics,
for the Bayesian, as tools to bridge the gap between deductive and inductive logic.^15
Deductive logic is about the validity of “risk-free” arguments.
All men are mortal.
John is a man.
Conclusion: John is mortal. (*)Such an argument is deductively valid sinceifthe premises are true, then so is the
conclusion. A sound argument is a valid argument that has true premises. There
are many types of risky arguments. Consider the following example. Imagine you
are given the option of randomly selecting an orange from a box known to contain
mostly good oranges and a few bad oranges.