Update no-U-turn criteria and added some unit tests

[xukai92]

• Update no-U-turn criteria
• Implement generalised no-U-turn criteria
• Create a synthetic multivariate Gaussian test for pre-conditioning adaption Create a synthetic multivariate Gaussian test for pre-conditioning adaption #25
• Remove symbol iniitalisation of NUTS
• Seperate termination from tree
• Seperate TrajectorySampler from tree
• More unit tests for HMC building blocks More unit tests for HMC building blocks #84
• Add test for U-turn

[yebai]

Great work - looks correct to me! I have left some minor comments above.

[xukai92]

Thanks for your review. I resolved most of the comments and left some replies to those I have questions. Please take a look.

[yebai]

Thanks for your review. I resolved most of the comments and left some replies to those I have questions. Please take a look.

Perhaps rename FullBinaryTree ==> BinaryTree for brevity? Also, it can be a bit confusing to include Full in the type name here, since it indicates that we store the full tree including internal nodes, which we don't in fact.

[xukai92]

Perhaps rename FullBinaryTree ==> BinaryTree for brevity? Also, it can be a bit confusing to include Full in the type nam

Sure. Let me do this.

[yebai]

Actually, after seeing the new commits, I think TrajectoryMultinomialSampler and TrajectorySliceSampler are more accurate names than XTrajectorySampler. What do you think?

Also, seems that some tests are not updated to the new type names: https://travis-ci.org/TuringLang/AdvancedHMC.jl/jobs/573887417#L754

[xukai92]

I just fixed the tests.

The thing I like ?TrajectorySampler over Trajectory?Sampler is because it's a subtype of AbstractTrajectorySampler. But I'm OK with both. In fact I think only Slice or Multonomial would be fine. They are a subtype of AbstractTrajectorySampler anyway.

[yebai]

In fact I think only Slice or Multonomial would be fine. They are a subtype of AbstractTrajectorySampler anyway.

I'm happy with Slice and Multonomial too. But if we want to be a bit explicit, I think Trajectory?Sampler is a bit more self-explanatory.

[xukai92]

Let's go for the Slice and Multonomial for now. They are use for constructing NUTS (or other trajectories) ATM so I guess it's fine and looks clean.

[xukai92]

I'm happy to merge it if no rejections.