Adding fault slip rate constraints in MCMC

[brendanjmeade]

Following up on the discussion with @aseyboldt

This is important for constraining rates and for setting the sense of fault slip (e.g., [0-999] mm/yr for left-lateral, [-999-0] mm/yr for right-lateral).

Bounds like this are implemented in the SQP problem. PYMC seems to support beta distributions for smooth boxcar-like distributions.

[aseyboldt]

Do you mean the constrains encoded in segment.ss/ds/ts_rate_flag? I didn't consider those, because they are all disabled in all examples in the repo, and blindly adding features didn't sound like a great idea.

A beta likelihood to keep some values positive or negative doesn't sound like the right thing to do, that will for sure kill the sampler. But if we have data about what's happening at some segments (ie we know the ss rate is 10+-3mm/year or so), that will be easy to add as an additional observation, just like the station velocities. But I'd rather do that with an actual example where we need it in a follow-up project.

[brendanjmeade]

Do you mean the constraints encoded in segment.ss/ds/ts_rate_flag? I didn't consider those, because they are all disabled in all examples in the repo, and blindly adding features didn't sound like a great idea.

We have two types of fault slip rate constraints:

1. Soft constraints like the one you mentioned above. These are typically included in the big linear operator.
2. Hard constraints. These are implemented in the SQP algorithm. The bounding values are set with:

ss_rate_bound_flag,ss_rate_bound_min,ss_rate_bound_max...etc.

In a segment file. We use these a lot in the classic SQP models and I can add some example versions to the demo files in the /data folder.

A beta likelihood to keep some values positive or negative doesn't sound like the right thing to do, that will for sure kill the sampler. But if we have data about what's happening at some segments (ie we know the ss rate is 10+-3mm/year or so), that will be easy to add as an additional observation, just like the station velocities. But I'd rather do that with an actual example where we need it in a follow-up project.

Would pm.Uniform do the trick for these relatively sharply bounded constraints? Relatively sharply bounded constraints are a common form of geologic data.