Computational Biostatistics: Bayesian Inference in Biomedicine · Introduction

Introduction

What this guide covers

Theoretical foundations, conjugate exact models, Markov Chain Computing (MCMC), multivariate hierarchical models, survival analysis and adaptive designs.

Overview

Topics covered

Introduction
Bayesian Inference in Biomedicine
Paradigm and General Theory of Bayesian Modeling
Likelihood in Biomedicine
Taxonomy of Priori Distributions
Exact Analytic Conjugation in Exponential Families

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

p(\boldsymbol{\theta} \mid \boldsymbol{y}) = \frac{f(\boldsymbol{y} \mid \boldsymbol{\theta}) p(\boldsymbol{\theta})}{\int_{\Theta} f(\boldsymbol{y} \mid \boldsymbol{\theta}) p(\boldsymbol{\theta}) d\boldsymbol{\theta}} = \frac{L(\boldsymbol{\theta} \mid \boldsymbol{y}) p(\boldsymbol{\theta})}{p(\boldsymbol{y})}

View LaTeX source

p(\boldsymbol{\theta} \mid \boldsymbol{y}) = \frac{f(\boldsymbol{y} \mid \boldsymbol{\theta}) p(\boldsymbol{\theta})}{\int_{\Theta} f(\boldsymbol{y} \mid \boldsymbol{\theta}) p(\boldsymbol{\theta}) d\boldsymbol{\theta}} = \frac{L(\boldsymbol{\theta} \mid \boldsymbol{y}) p(\boldsymbol{\theta})}{p(\boldsymbol{y})}