Published online by Cambridge University Press: 05 July 2016
The subjective theory of statistical inference descends from Bayes; its immediate progenitors are Ramsey and de Finetti; Savage is its most recent distinguished patron. It aims at analysing rational, or at least consistent, procedures for choosing among statistical hypotheses. In some ways reaching further than our theory of support, it is in a correspondingly less stable state. But the two theories are compatible. Some tenets of subjectivists conflict with the theory of support, but do not seem essential to subjectivism. Both theories combine elements of caution and ambition, but where one is bold, the other is wary. The present chapter will not contribute to the subjective theory, but will try to distinguish its province from the theory of statistical support.
The two theories
As presented in this book the theory of support analyses only inferences between joint propositions; essentially, inferences from statistical data either to statistical hypotheses, or else to predictions about the outcomes of particular trials. It attempts a rather precise analysis of these inferences, and in so doing is perhaps too audacious, but at least it proffers postulates rich enough in consequences that they can be tested and, one hopes, revised in the light of counterexamples. But in another respect the theory is timid, for it gives no account of how to establish statistical data. Thus although it may claim to encompass all that is precisely analysable in statistical inference, it cannot pretend to cover all the intellectual moves made by statisticians. It would defend itself against criticism on this score by maintaining that the way in which statistical data are agreed on—partly by experiment, partly by half-arbitrary, half-judicious simplification—is not peculiar to statistics and so should not seek an especially statistical foundation.
But the subjective theory embraces all work done in statistics, and perhaps all inductive reasoning in any field. At the same time it hesitates to appraise inferences made on the basis of particular statistical data. It is concerned only that inferences be consistent with each other. The theory's key concept has been variously called ‘subjective probability’, ‘personal probability’, ‘intuitive probability’, ‘probability’ and ‘personal betting rate’.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.