Currently I am working on a bayesian model framework and have questions related to the philosophy of using such techniques of modeling. 1. How do I know that the prior which I have captured from the experts is valid. There are parameters of the model which has captured a very wide range - say, 10% to 90%. It does not give me comfort, rather, it may show that the expert panel inputs missed out on the clear range. Is there any method out there which may allow me to check this?
2. We do not have enough data to work on, thus, the Bayesian framework. When can we say that Bayesian analysis is not required and the whole analysis/ model can be done using data. Is there any threshold on data availability/ philosophy where it indicates the transition from Bayesian to classical? (I understand that they are techniques from two different school of thought, so Bayesian is used in our case for lack of data)
3. The conjugate prior method for a beta-beta-beta model gives alpha estimate for posterior = a1+a2-1 beta estimate for posterior = b1+b2-1. the question which haunts me is, how will the effect of a larger data set be captured in the posterior parameters, if this model is being used post the required amount of data is available?
It would be great if someone can answer my questions. If further clarification is required on my thoughts/ questions... please do let me know. Thanks!