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.

Prerequisites

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

Aims

To highlight elements of historical development and philosophy of mathematical statistics.

To make an emphasis on objective attempt towards inference from a statistical model.

To prepare students to perform a PhD within one of the STEM subjects.

To find students interested in performing a philosophy doctor (PhD) thesis with me.

Outline syllabus

Subjective inference.

Objective inference.

Computational implementation of the inference.

Frequentist developments.

Teaching methods

Lectures, tutorials, including problem-solving and computer simulations.

Assessment

Assignments

Full syllabus

Subjective inference: elicitation of the prior distribution of unknowns.

Conjugate analysis.

Frequentist statistics: central limit theorem, normal distribution.