Bayesian models vs Bayesian network models

Question

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.

Answer 1

Bayesian networks model dependencies of categorical variables (e.g. how the gender, level of education, religion, social class etc. interact each other).

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 $$ f(\mu,\sigma^2|a_i,a_{i-1}\dots,a_1)\propto f(a_i|\mu,\sigma^2)f(\mu,\sigma^2|a_{i-1}\dots,a_1) $$