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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!

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Regarding Question 1/2: Working with the Bayesian framework allows to incorporate expert information into your model. This can be helpful is limited data is available (like in the case of credit default events), but only if this expert information is based on strong facts. Prior allow only to express expert information in a limited way. Try to match the first moments of the beta distribution to your expert information. If you feel, your prior information lacks foundation, you should use a non-informative prior (e.g. uniform distribution).

Note, that the Bayesian approach is not intended to be used exclusively for analysis with few data available. Comparing it to the e.g. Likelihood approach, Bayesian Inference allows not only to obtain a point estimate (MAP), but also to model a posterior density which gives the distribution of the true parameter. Thus, in comparison to the point estimates of the Frequentist school, the Bayesian analysis allows to address uncertainty. If more data become available, the posterior can be updated. There is no such philosophy at what number of observations one switches between these philosophies, because this is not intended.

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  • $\begingroup$ Hi Stephen, thanks a ton for your comment! Can you please give me a little background on informative/ non informative priors for starters, and maybe some links where I may get adequate information. In any case, I would look up text books/ articles to know more. $\endgroup$ – Bik Mar 19 '13 at 14:10
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    $\begingroup$ Sure @Bik, Laplace (1820) formulated the "principle of insufficient reason" which states that you would use uniform prior. In this case, all possible realizations of the unknown parameter are equally likely and thus, the MAP-estimate will coincide with the ML-estimate. There are other concepts like Jeffrey's prior, which is invariant in case of a reparametraization. $\endgroup$ – Stephen Mar 19 '13 at 14:30
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    $\begingroup$ @Bik, I find the best book to start with is Box/Tiao (1973). I've found Geweke (2005) very helpful, although it accesses Bayesian Inference from an Econometric point-of-view. See Kass/Wasserman (1996) "The selection of prior distributions by formal rules" for more information on prior selection. $\endgroup$ – Stephen Mar 19 '13 at 14:37

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