Bayesian statistics: Bayesian hierarchical models · Introduction

Introduction

What this guide covers

An analytical and rigorous exposition on the hierarchical paradigm, conditional interchangeability, the parametric contraction effect and contemporary simulation algorithms in continuous vector spaces.

Overview

Topics covered

Introduction
Bayesian Hierarchical Models
Foundational Theory of Bayesian Inference
Epistemic Interpretation of Probability
Mathematical Structure and Likelihood Principle
The Challenge of Marginal Integration

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

p(\mathbf{y}, \boldsymbol{\theta}) = p(\mathbf{y} \mid \boldsymbol{\theta}) p(\boldsymbol{\theta}) = p(\boldsymbol{\theta} \mid \mathbf{y}) p(\mathbf{y})

View LaTeX source

p(\mathbf{y}, \boldsymbol{\theta}) = p(\mathbf{y} \mid \boldsymbol{\theta}) p(\boldsymbol{\theta}) = p(\boldsymbol{\theta} \mid \mathbf{y}) p(\mathbf{y})