106 Metastatistics for the Non-Bayesian Regression Runner
sort that is sure to be satisfied sooner or later [such as the requirement that a
“t-statistic” exceed some critical value], then the import of the sequence of
n data actually observed will be exactly the same as it would be had you
planned to take exactly n observations in the first place. (Edwardset al.,
1963, pp. 238–9).- The problem of “how to reason” has been solved:
Determining which underlying truth is most likely on the basis of the data
is a problem in inverse probability, or inductive inference, that was solved
quantitatively more than 200 years ago by the Reverend Thomas Bayes.
(Goodman, 1999)
[They are mistaken,] those who have insinuated that the Doctrine of Chances
...cannot have a place in any serious inquiry...[it can] shew what reason we
have for believing that there in the constitution of things fixt laws according
to which things happen, and that, therefore the frame of the world must be
to the effect of the wisdom and power of an intelligent cause; and thus to
confirm the argument taken from final causes for the existence of the Deity.
It will be easy to show that the problem solved in this essay [by the Reverend
Bayes] is more directly applicable to this purpose. (Bayes, 1958)- Usual (non-Bayesian) practice is very badly wrong:
...almost every frequentist [non-Bayesian] technique has been shown to be
flawed, the flaws arising because of the lack of a coherent underpinning that
can only come through probability, not as frequency, but as belief. (Lindley,
2000)
Why it is taking the statistics community so long to recognize the essentially
fallacious nature of NP [Neyman–Pearson, or non-Bayesian] logic is difficult
to say, but I am reasonably confident in predicting that it will not last much
longer. Indeed, the tide already seems strongly on the turn. (Howson, 1997)
I explore the historical and logical foundations of the dominant school of
medical statistics, sometimes referred to as frequentist statistics, which might
be described as error-based. I explicate the logical fallacy at the heart of this
system. (Goodman, 1999)- Randomization rarely makes sense in those contexts where it is most often
employed:
Physicists do not conduct experiments as Fisher would have them do. For
instance, a simple experiment to determine the acceleration due to gravity
might, say, require a heavy object to be dropped close to the earth. The
conditions would be controlled by ensuring that the air is still, that the space
between the object and the ground is free of impediments, and so on for
other factors that are thought to interfere with the rate at which the object