I have an interest in a multi-dimensional forecasting the direction of a track navigating thru this region.
I would like to use the state space of previous values to forecast.
So, in two dimensions, this could look like:
The following would be known, and I would have multiple historical tracks of uniform time-step data
Xlatitude[ … ]
Xlongtude[ … ]
I would also have the “current track” which is the track I want to forecast form.
Then, I would like to get a prediction of future values a few time steps out.
Ylatitude[ … ]
Ylongtude[ … ]
The prediction would be based on two things:
The historical distribution of latitude/longitude points
The known track of the Latitude/Longitude values for the case of interest (what I want to forecast on).
Any direction would be appreciated.
There are a number of folks both in fishery and the mammal world that use tracking models in Stan for this kind of stuff. So like herehttps://arxiv.org/pdf/1806.10639.pdf
And I don’t remember where I saw the fishery one. If you hunt around for Stan Bayesian animal tracking model or fish tracking (not the right word) that might get ya started.
If you’re willing to discretize (i.e. rasterize) the geographic space, then two useful ecological terms to google might be “step selection function” and “resource selection function”. One popular and useful (albeit non-Bayesian) reference is Turchin’s Quantitative Analysis of Movement Quantitative Analysis of Movement – Peter Turchin
In a simple case, the relative probabilities of different next steps might be based on the inherent suitability (historical use), step length, and the cosine of the turning angle, and then each step can be modeled via a categorical logit regression.
The model I describe above is simple in the sense that the process in this case is assumed to have no memory beyond the previous two locations visited (which together define the turning angle to the any possible next location). But the sky is the limit as you can think about whether/how to incorporate information from earlier steps.
This is just one flavor of approach to this problem, but perhaps you’ll find it useful. The link that @Ara_Winter provides is based on this framework, but builds out additional structure by modeling multiple hidden markov states that correspond to unobserved discrete underlying behavioral modalities for the moving agent.
Thank you for the two nice replies. I had downloaded the paper from Ara’s post it was in my read queue (https://arxiv.org/pdf/1806.10639.pdf). Also, on the discretization, I may get some traction with that approach coupled with the paper. I do have a LSTM RNN that provides reasonable forecast, but I want to develop more of a probability assessment as to the direction.
Thank you for your time and consideration.