BART EWMV Model

[Emma Herms]

Hello,

I have attempted to modify the bart_ewmv stan file to include a reward value that increases with pump number. In this version of the BART, there is a maximum of 12 pumps, where the reward and probability of the balloon exploding increases with each pump (see table 1 of this paper).

However, after modifying the stan file (see changes to stan file here) to include increasing reward values, the chains are not well mixed or converging, despite multiple attempts. I am wondering if by adding a non 1 value for reward to the calculation of u_pump (the utility of pumping) the model integrity is broken? For example, the chains seem to be sampling tau values around 80 and lambda values around 400, but never converging (I have included some image attachements). 

To rule out data issues, I ran the original EWMV model on my data. The chains were well mixed, and the model converged.

If you are able to provide any insight, it would be greatly appreciated. Thank you in advance for your time!

Best,

Emma Herms

[Emma Herms]

I may have found a solution? 

In the version of the BART that I am using, reward is highly correlated with the explosion probability, such that the amount of reward you can gain increases as the explosion probability increases (see table 1 of this paper). 

When adding reward to the bart_ewmv model, I originally used the "total value" of a balloon at a given pump number (i.e., [0.05, 0.15, 0.25, 0.55, 0.95, 1.45, 2.05, 2.75, 3.45, 4.25, 5.15]). I have now changed that to the "reward gained" with each pump (i.e., [0.05, 0.10, 0.10, 0.30, 0.40, .50, .60, .70, .70, .80, .90]). However, it might also be the case that using decimal numbers for reward would make it difficult for the model to calculate u_pump. So, a colleague suggested multiplying by 10 to get whole numbers for reward (i.e., [5, 10, 10, 30, 40, 50, 60, 70, 70, 80, 90]. 

These two changes seem to have solved my problems, as the models are now converging. 

Happy to hear any thoughts on these changes!

[wooyou...@gmail.com]

Hi Emma,

Sorry for the long delay! Yes, I believe this is a rather scaling issue and I think your approach makes a lot of sense. Thanks for sharing it with us!

Best,

Young