Hurricane Path Forecasts using HSGP and Vector Auto Regression

[Dekermanjian]

Notebook proposal

Title: Hurricane Path Forecasts

Why should this notebook be added to pymc-examples?

I think this would be an interesting example to have because of the following:

• This model is a multi-output estimation (distance + direction) problem
• It is a relevant topic with real world implications that are currently newsworthy
• It shows how one can apply/extend the very cool work depicted in example_1 by @NathanielF and in example_2 by @ricardoV94

Suggested categories:

• Level: Beginner/Intermediate

Related notebooks

Links to related notebooks mentioned above.

References

references in notebooks above + any other if relevant at completion of example.

Preliminary work

I have a good chunk of the work complete but it is still a work in progress. I am trying to gauge if this will be of interest to the PYMC community. here is a link to what I have so far.

[NathanielF]

Sounds super! Would love to see it.

One thing to note perhaps is that @jessegrabowski has improved on the PyMC implementation of VAR models with a nice api and wrapper in pymc-experimental.

Just flagging in case you hadn't seen it, but it would be interesting if you can leverage any of his work there: https://discourse.pymc.io/t/webinar-time-series-analysis-with-bayesian-state-space-models-in-pymc-aug-26-4-00-pm-utc/14937

That said, it looks like you're aiming at a complex hierarchical structure which might not fall neatly into to the pymc-experimental API. @jessegrabowski can you comment on that?

In any case @Dekermanjian, it would be great to see this use-case developed!

[jessegrabowski]

Arbitrary prior specifications are allowed in statespace, as long as the final system of equations that describes the kinematics of the system is linear, and the prediction errors are Guassian. I only glanced at the notebook, but I didn't see anything that wouldn't fit.

[Dekermanjian]

Thank you, @NathanielF! I am glad that this is something that others are interested in!

@jessegrabowski The statespace work you've done is really cool! I am going to watch through the webinar recording and go through the notebooks to adapt what I currently have to utilize the api you've built.

[Dekermanjian]

Hey @jessegrabowski I am so sorry to bother you but I ran into a bit of a road block while trying to adapt the VARMAX model using the State Space API.

At this point I am trying to integrate the 2-dimensional GP that is meant to capture spatial information into the Kalman Filter process. I am stuck with trying to go from defining $S(x)$ to defining $S(X_{t-1})$ so that I can add the spatial information as a covariate in the estimation of the current state_matrix:
$$x_{t} = A_{t-1}x_{t-1} + S(x_{t-1}) + c_{t} + R_{t}\epsilon_{t}$$

Is there a way I can get a new variable to be apart of the (I am assuming) pytensor.scan function that computes the Kalman Filter steps?

PS: If I am completely off base here I wholeheartedly apologize. I only learned of Kalman Filters when I started looking into the State Space API.

I also updated the notebook here, at the very bottom you can see my attempt at using the State Space API.

Edit:
Okay, I added the GPs to the state matrix in the initialization of the ssm and then passed in the GP variables into the Kalman Filter by concatenating it to the data. I don't know if this will pose any issues, obviously it is not a clean way to do it. I updated the notebook in the link above to reflect this change.