# Bayesian models vs Bayesian network models

I'm new to statistical modeling and working on applications in spatial property prediction. Can you help me understand the difference between a hierarchical bayesian model and a bayesian network model? It seems that the dependencies of predictor variables can be well met within what I understand as "traditional" bayesian models, and I don't grasp what differences the bayesian network approach brings to the table.

• Though I don't quite understand your another question. About the difference of them is : Hierarchical Bayesian is a Bayesian Network in hierarchical structure. – WeiChing Lin Oct 2 '14 at 8:08
• @william, please stop spamming the site w/ tag edits. This shouldn't be done this way. You should raise the issue on meta.CV & we can make it a synonym. – gung - Reinstate Monica May 1 '16 at 19:31

Bayesian hierarchical models are rather dedicated to parameter estimation. For instance, you have a population of students, you assume their age is distributed normally with some parameters $\mu,\sigma^2$, i.e. the age of the $i$-th student is a density function $f(a_i|\mu,\sigma)$. In the frequentist approach, one would just calculate average $\frac{1}{n}\sum_{i=1}^n a_i$. In the Bayesian context, you have to consider some prior probability density function $f(\mu,\sigma^2)$ and to update it to posterior according to Bayes rule $$f(\mu,\sigma^2|a_i,a_{i-1}\dots,a_1)\propto f(a_i|\mu,\sigma^2)f(\mu,\sigma^2|a_{i-1}\dots,a_1)$$