Fediverse #HiveMind request: Guidelines for causal DAGs in Bayesian modelling
One of my many personal peeves is sloppy conceptual diagramming. I have been exposed to far too many box and arrow diagrams where there is no clear and consistent interpretation of what types of things the boxes are supposed to represent (and ditto for the arrows).
I am starting to engage with a Bayesian modelling project (this I know from nothing - https://tomlehrersongs.com/wp-content/uploads/2018/12/lobachevsky.pdf) and am being exposed to causal DAGs. I presume these are reasonably consistent and interpretable. Nonetheless, they are typically presented as though the interpretation is self-evident and I keep coming up with multiple possible interpretations/constraints.
>>>>> Do people have recommendations for *detailed* interpretations of causal DAGs as used in Bayesian modelling? <<<<<
Issues covered should include things like:
* Constraints on node types: If nodes represent variables can they have multivariate values or are they constrained to be univariate?
* Interpretation with respect to "cases": Should the DAG be interpreted as referring to relationships that hold on a per-case basis?
* Interpretation with respect to "populations": If DAGs represent per-case relations, do they also represent populatiopns of those cases?
* Interpretation with respect to data matrices: How does a causal DAG map onto a matrix of data to be modelled?
* Interpretation with respect to multiple types of "case": Repeat all of the issues above but when there are multiple types of case not necessarily in one-to-one relationships (e.g. multi-level modelling).
* What is the relationship between the DAG and the equations/statements implementing that DAG in the probabilistic programming language of choice (e.g. STAN, PyMC)?
* What are the constraints on the temporal relationships of the variables at the nodes? Assuming the variables are measures at points in time you (presumably) don't want causes coming after their effects. Different variables may be measured at different points in time and a measurement at some point in time may be a measure of some cumulative process over prior times - so I would expect some nuanced consideration of temporal constraints.
#Bayesian #modelling #statistics #causal #DAG #DirectedAcylicGraph #diagram #interpretation