104 Metastatistics for the Non-Bayesian Regression Runner
In what follows, when I describe something as “Bayesian” I do not mean to
suggest any writer in particular holds all the views so attributed here. There is
considerable heterogeneity: some view concepts like “the weight of evidence” as
important, others do not. Some view expected utility as important, others do not.
This is not intended to be a “primer” on Bayesian statistics. Neither is it intended
to be a “critique” of Bayesian views. There are several very good ones, some dating
as far back as Venn (1888) (although some of these arguments will appear in what
follows). Indeed, I will admit that, given the types of questionsItypically find
interesting, I don’t find Bayesian ideas particularly helpful (and sometimes harm-
ful). On the other hand, I can imagine situations where others might find formal
Bayesian reasoning helpful. Indeed, given the prominent role that “models” play
in economics, I am frankly a bit surprised that Bayesian techniques are not more
popular than they are.
My purpose is not to do Bayesian ideas justice (or injustice!) but, rather, to try to
selectively choose some implications of various strands of Bayesianism and non-
Bayesianism for actual statistical practice that highlight their differences so as to
be clear to a non-Bayesian perspective.
After having surveyed the metastatistics literature, one feels it is almost impos-
sible to use the English language to label or describe the practically minded
non-Bayesian regression runner.^13 When not being dismissed as belaboring
under fallacious reasoning (Howson, 1997), she has been variously described as a
“frequentist” – someone who is congenial to the notion of probability being about
“relative frequency,” or an NP (Neyman–Pearson) statistician – even though, as
Mayo and Spanos (2006) observe, there is a great deal of confusion about what
this means. Indeed, in my experience, most regression runners are not entirely
sure what it means to be a user of “NP theory” (which is not surprising given
that it is not clear that either Neyman or Pearson practiced or believed NP statis-
tical theory!) Most congenial is Mayo’s (1996) term “error statistician” – someone
engaged in “severe testing.” On the other hand, as a firm adherent of LeCam’s
Basic Principle Zero – “Do not trust any principle” – I will settle on the term
“non-Bayesian.”^14
My hope is that consideration of some of the underlying metastatistics will make
it easier to detect some sources of methodological disagreement. Put differently,
one focus of what follows is to consider a claim, from Mayo and Kruse (2002), that
“principles of inference have consequences” for actual practice.
More on this subsequently, but to ground the discussion, let me list the types of
research questions I would like to consider as the aims of the practically minded
regression runner:
- What is the “causal effect” of some new medical treatment?
- What are the the iatrogenic effects of morphine use? Does the use of pain
medicine cause more pain? - Does (US) unionization lead to business failures?
- Do “unions raise wages?”,
as well as the types of questions I amnotgoing to consider: