Greetings,
Before I begin, I have to say that if you think that anything I'm saying below is incorrect, your corrections would be much appreciated!
I've been working on modelling various clinical use cases (mostly diseases) with Bayesian networks, and I am a little bit confused about the use of deterministic functions during modelling.
In some situations, there is already an established approach to expressing the relationship between a set of explanatory variables and a response variable. For example a Bayesian network is build to model parameters of a deterministic function, like a linear regression function, and inference provides outcomes driven by both the deterministic function and the distribution of parameters of the function.
In this case, we end up with a more flexible relationship description compared to a point estimator for the regression function parameters, so I can see a benefit here.
However, in many Bayesian network examples, random variables are just domain concepts, like the famous Asia example or many other disease/symptom examples. In this case the network is just a collection of random variables, and there is no deterministic function involved.
As a general modelling approach, is it better to try to include a deterministic function and perform Bayesian inference, or is it enough to simply express random variables from the domain and perform inference.
Most, (if not all) resources begin with the example where random variables are dropped into the model, and without clearly underlining the difference between the two cases start talking about generalized linear models etc.
This makes it hard for self thought people like myself to develop a modelling approach.
Are there generic yet robust approaches that I may attempt to use like generalized linear models or radial basis function based polynomial regression etc..? Would I generally get better outcomes if I try to use an underlying modelling approach like these, which are then inferred via Bayesian networks? This seems to introduce a limitation to the overall approach, since I'd have to define response variable(s) and explanatory variables, whereas in the domain variables only case, belief update in every direction does not have such semantics when propagation walks over the nodes.
I'm trying to develop a generic approach to modelling clinical conditions, but I'm not sure if I'm going to loose opportunity to have better performing models by not considering an underlying deterministic relationship between variables of my model.
I hope I could express my problem clear enough. Your guidance, corrections and pointers would be much appreciated.
Best Regards
Seref Arikan
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