I am new to the Bayesian “world” and I have a few fundamental questions regarding hierarchical models. But before going any further, I thought it would be useful to introduce myself. I am a materials engineer working for an aeronautical company. One of my responbilities is to ensure that the raw materials we receive from our supplier is compliant to our requirements. On a monthly basis, I receive mechanical test data performed on the products manufactured from our suppliers. In my department, I am the lucky guy that performs the statistical analysis and I admit that before I bumped into the Bayesian methods, I was mainly using frequentist methods. Among the frequentist methods, I was using hypothesis testing such as 2 sample t-test, parameters estimation and also the calculation of tolerance intervals (99 quantile with 0.95 confidence intervals). In my field… Bayesian methods is inexistant and I would like to start introduce it to answer statistical questions in a more rigorous and elegant way.
I was seduced by Bayesian Hierarchical models because I could use the prior knowledge on legacy data to answer questions when there is not much data available. In fact, the mechanical testing our suppliers perform is destructive and has a cost!
So here are the questions:
1) Is there a limit of levels in modelling hierarchical models with Stan?
Typically, the parts we receive from our suppliers can be grouped in batches. But If we consider the whole process, the batches can also be grouped in further batches. Additionally, a part can be manufactured by different suppliers - so it would be interesting to take this into account.
Is there any consensus on how many levels can have a hierarchical model?
2) Can I use hierarchical models to monitor deviation in the products I receive from my supplier?
Sometimes, there can be shift (average shifted significantly ) or trends in the mechanical properties from the products we receive from our suppliers.
However, If I assume the exchangeability assumption at every level of my hierarchical model, will I be able to spot any shift or trend? If not, how do I capture it?
3) Can I use Stan to model the 99th quantile?
The question says it all - but in aeronautics we are very interesting in estimating the 99th quantile of mechanical property to set our safety margins. After I built my hierachical model, and assuming that at every level I have a gaussian distribution, can I generate the distribution of 99th quantile using Stan?
Many thanks !