Prior distributions · Advanced Bayesian statistics · Introduction

Introduction

What this guide covers

Introduction Advanced Statistical Theory Module

Overview

Topics covered

Introduction
Priori distributions: mathematical formulation of the initial information
The Bayesian Paradigm and the Role of Priori Knowledge
Taxonomy of Priori Distributions
2.1 Informative vs. Non-informative
2.2 Objectives vs. Subjective

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

\pi(\boldsymbol{\theta} \mid \mathbf{X}) = \frac{f(\mathbf{X} \mid \boldsymbol{\theta})\pi(\boldsymbol{\theta})}{\int_{\Theta} f(\mathbf{X} \mid \boldsymbol{\theta}')\pi(\boldsymbol{\theta}')d\boldsymbol{\theta}'} = \frac{L(\boldsymbol{\theta} \mid \mathbf{X})\pi(\boldsymbol{\theta})}{m(\mathbf{X})}

View LaTeX source

\pi(\boldsymbol{\theta} \mid \mathbf{X}) = \frac{f(\mathbf{X} \mid \boldsymbol{\theta})\pi(\boldsymbol{\theta})}{\int_{\Theta} f(\mathbf{X} \mid \boldsymbol{\theta}')\pi(\boldsymbol{\theta}')d\boldsymbol{\theta}'} = \frac{L(\boldsymbol{\theta} \mid \mathbf{X})\pi(\boldsymbol{\theta})}{m(\mathbf{X})}