Philosophy of mathematical statistics

Philosophy of mathematical statistics
Advanced course in data analysis

Author Ksenia N. Kyzyurova


This course focuses on philosophy of statistical inference from data. The aim is to bring the synergy among three perspectives on implementation of statistical inference: subjective, objective and frequentist. Assessment of the advantages and disadvantages of each of the three mathematical constructions highlights realms of their applicability as well as their limitations. The teaching method is to construct and discuss simple mathematical examples which illustrate the above. The course does not aim at sharpening one's calculus or programming skills.


Excellent calculus is expected but not required.
The knowledge of the material from the course ``Bayesian metaphysics" is expected but not required.


Outline syllabus

Teaching methods



Full syllabus

  1. Subjective inference: elicitation of the prior distribution of unknowns.
  2. Conjugate analysis.
  3. Frequentist statistics: central limit theorem, normal distribution.
  4. Hypothesis testing and its limitations.
  5. Objective inference: principles of insufficient reasoning, Jeffrey's developments, Berger's reference analysis.
  6. Closed-form inference from a statistical model.
  7. Standard models based on binomial and normal distribution which are to be implemented within the objective framework.
  8. Mathematical challenges of objective inference for an arbitrary statistical model.

Reading materials