Bayesian statistics: Bayesian generalized linear models (GLMs) · Introduction

Introduction

What this guide covers

A rigorous theoretical and computational approach to model non-Gaussian response variables under the Bayesian probabilistic uncertainty paradigm.

Overview

Topics covered

Introduction
Bayesian Generalized Linear Models
Introduction to Bayesian Inference
The Conjugability Limitation in MGL
Structure of Generalized Linear Models (GLM)
The Exponential Family of Distributions

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

p(\boldsymbol{\theta} | \mathbf{y}) = \frac{p(\mathbf{y} | \boldsymbol{\theta}) \, p(\boldsymbol{\theta})}{p(\mathbf{y})} = \frac{p(\mathbf{y} | \boldsymbol{\theta}) \, p(\boldsymbol{\theta})}{\int_{\boldsymbol{\Theta}} p(\mathbf{y} | \boldsymbol{\theta}) \, p(\boldsymbol{\theta}) \, d\boldsymbol{\theta}}

View LaTeX source

p(\boldsymbol{\theta} | \mathbf{y}) = \frac{p(\mathbf{y} | \boldsymbol{\theta}) \, p(\boldsymbol{\theta})}{p(\mathbf{y})} = \frac{p(\mathbf{y} | \boldsymbol{\theta}) \, p(\boldsymbol{\theta})}{\int_{\boldsymbol{\Theta}} p(\mathbf{y} | \boldsymbol{\theta}) \, p(\boldsymbol{\theta}) \, d\boldsymbol{\theta}}