Statistical Modeling & Regression · Bayesian Statistics

Bayesian statistics: Philosophical and theoretical foundations of the paradigm

Public introduction · full guide in Eikos

Introduction

What this guide covers

An analytical and rigorous exposition of the inductive probabilistic inference paradigm, from its axiomatic epistemology to its modern methods of simulation and variational inference.

Overview

Topics covered

  • Introduction
  • Bayesian Statistics: Theoretical and Philosophical Foundations
  • Epistemology and Philosophical Foundations
  • The Frequentist vs. Frequentist Dichotomy Bayesian
  • Cox's Theorem and the Coherence of Degrees of Belief
  • Interchangeability and Finetti's Representation Theorem

Related concepts

Main connections

  • Bayes' theorem & priors
  • Maximum likelihood estimation
  • Markov chain Monte Carlo (MCMC)
  • Calculus & differentiation
  • Mean & expected value
  • Variance & standard deviation

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

P(A)=limN→∞nAN
View LaTeX sourceP(A) = \lim_{N \to \infty} \frac{n_A}{N}