1
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ Though I don't quite understand your another question. About the difference of them is : Hierarchical Bayesian is a Bayesian Network in hierarchical structure. $\endgroup$ – WeiChing Lin Oct 2 '14 at 8:08
  • $\begingroup$ @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. $\endgroup$ – gung May 1 '16 at 19:31
1
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Thanks, Karel. I've been chasing this and not getting the differences. Your clarification seems key. If I'm interested in modeling the interactions of the covariates specifically, then the network model would be the right choice. If I'm more interested in a multivariate predictive model, where I am not so much interested in modeling the covariate dependencies, as including some metric of their influence on the output, then I use a more traditional Bayesian inferential model. Is that a fair summary? $\endgroup$ – Don29826 Oct 5 '14 at 17:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.