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Statistical Modeling & Regression · Bayesian Statistics

Bayesian statistics: Single-parameter models and conjugate families

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Advanced Scientific Inference · Decision Theory

Overview

Topics covered

  • Introduction
  • Bayesian Statistics: Monoparametric Models
  • Fundamentals of the Bayesian paradigm and epistemological differences
  • The anatomy of Bayes' Theorem
  • The Likelihood Principle and the Role of Stop Sampling
  • General theory of conjugate families

Related concepts

Main connections

  • Bayes' theorem & priors
  • Maximum likelihood estimation
  • Calculus & differentiation
  • Mean & expected value
  • Binomial distribution
  • Poisson distribution

Compatible notation

Mathematical sample in LaTeX

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

p(X1=x1,X2=x2,…,Xn=xn)=p(Xπ(1)=x1,Xπ(2)=x2,…,Xπ(n)=xn).
View LaTeX sourcep(X_1 = x_1, X_2 = x_2, \dots, X_n = x_n) = p(X_{\pi(1)} = x_1, X_{\pi(2)} = x_2, \dots, X_{\pi(n)} = x_n).