Yesterday’s slight detour [i] presents an opportunity to (re)read Lindley’s “Philosophy of Statistics” (2000) (see also an earlier post). I recommend the full article and discussion. There is actually much here on which we agree.
The Philosophy of Statistics
Dennis V. Lindley
The Statistician (2000) 49:293-319
Summary. This paper puts forward an overall view of statistics. It is argued that statistics is the study of uncertainty. The many demonstrations that uncertainties can only combine according to the rules of the probability calculus are summarized. The conclusion is that statistical inference is firmly based on probability alone. Progress is therefore dependent on the construction of a probability model; methods for doing this are considered. It is argued that the probabilities are personal. The roles of likelihood and exchangeability are explained. Inference is only of value if it can be used, so the extension to decision analysis, incorporating utility, is related to risk and to the use of statistics in science and law. The paper has been written in the hope that it will be intelligible to all who are interested in statistics.
Around eight pages in we get another useful summary:
Let us summarize the position reached.
(a) Statistics is the study of uncertainty.
(b) Uncertainty should be measured by probability.
(c) Data uncertainty is so measured, conditional on the parameters.
(d) Parameter uncertainty is similarly measured by probability.
(e) Inference is performed within the probability calculus, mainly by equations (1) and (2) (301).