2023-02-14 18:00:57
Перечитывал свой архив по статистике и наткнулся на настоящую жемчужину: APTS: Statistical Inference
Сложно охарактеризовать жанр, что-то среднее между манускриптом по философии и учебником по статистике.
Вот выдержка оттуда. Интересующимся - рекомендую
For example, if asked for a set estimate of θ, a Bayesian statistician might produce a 95% High Density Region, and a classical statistician a 95% confidence set, but they might be effectively the same set. But it is not the inference that is the primary concern of the auditor: it is the justification for the inference, among the uncountable other inferences that might have been made but weren’t. The auditor checks the ‘why’, before passing the ‘what’ on to the client.
So the auditor will ask: why do you choose algorithm Ev? The classical statisticianwill reply, “Because it is a 95% confidence procedure for θ, and, among the uncountable number of such procedures, this is a good choice [for some reasons that are then given].”
The Bayesian statistician will reply “Because it is a 95% High Posterior Density region for θ for prior distribution π(θ), and among the uncountable number of prior distributions, π(θ) is a good choice [for some reasons that are then given].” Let’s assume that the reasons are compelling, in both cases. The auditor has a follow-up question for the classicist but not for the Bayesian: “Why are you not concerned about violating the Likelihood Principle?” A well-informed auditor will know the theory of the previous sections, and the consequences of violating the SLP that are given in Section 2.8. For example, violating the SLP is either illogical or obtuse - neither of these properties are desirable in an applied statistician.
This is not an easy question to answer.
The classicist may reply “Because it is important to me that I control my error rate over the course of my career”, which is incompatible with the SLP. In other words, the statistician ensures that, by always using a 95% confidence procedure, the true value of θ will be inside at least 95% of her confidence sets, over her career. Of course, this answer means that the statistician puts her career error rate before the needs of her current client.
I can just about imagine a client demanding “I want a statistician who is right at least 95% of the time.” Personally, though, I would advise a client against this, and favour instead a statistician who is concerned not with her career error rate, but rather with the client’s particular problem.
5.9K views15:00
В
