BDA3 arrived!

It’s mine… my own… my precious.

My wife says that a glance at the spine gives the impression that it reads “Badass”.

Error Statistics and the Severity Principle, part one: The Way that Denies by Denying

Error Statistics

Error statistics aims to provide a philosophical foundation for the application of frequentist statistics in science. As in any frequency-based approach, error statistics adheres to what I consider to be the fundamental tenet of frequentist learning: any particular data-based inference is deemed well-warranted only to the extent that it is the result of a procedure with good sampling characteristics.

What kind of procedures are we talking about, and what characteristics of those procedures ought we to care about? The error statistical approach distinguishes itself from other frequentist frameworks (e.g., frequentist statistical decision theory) by the answer it gives to that question.

A foundation for Bayesian statistics, part two: Cox’s postulates

Why these postulates?

Recall Cox’s five postulates:

1. Cox-plausibilities are real numbers.
2. Consistency with Boolean algebra: if two claims are equal in Boolean algebra, then they have equal Cox-plausibility.
3. There exists a conjunction function f such that  for any two claims A, B, and any prior information X, 

. 

4. There exists a negation relation (actually a function too). In slightly different notation that in the previous post, it is:

.

5. The negation relation and conjunction function (and their domains) satisfy technical regularity conditions.