I have a situation where I am monitoring events at 50 or so geographical sites in a town and at each of these sites, I am making measurements regarding the count of certain particles (so the measurements are discrete). The measurements are done every 5 minutes and we have been monitoring these sites for many months now.

Now, what I am interested in is spatiotemporal interpolation and extrapolation i.e. be able to forecast these counts at the sites say 15 minutes in the future at these sites (and perhaps also in their vicinity).

As far as I understand it, this is equivalent to fitting some sort of a function where the output depends on the spatial and temporal coordinates. I am at a complete loss on how I can do something like this in the sense of how to model this discrete output and the spatiotemporal aspect.

I have played a bit with time series analysis but that has always been predicting a continuous output which is only a function of time.

Does anyone know of any toolkits I can use for just trying some pre-made models on my data? I do not want something latest and greatest, even a "simple" model would do! I just want to see what it would generate on our data as a first step.

  • $\begingroup$ Have you tried machine learning ? Let is figure out the necessary spatiotemporal dependence on the nodes. $\endgroup$ – onurcanbektas May 18 '19 at 6:48
  • $\begingroup$ @onurcanbektas I have not thought about that yet. Can you recommend some ML frameworks/paradigms for learning such models? $\endgroup$ – Luca May 20 '19 at 14:25

The typical approach to this problem is land-use regression (LUR).

LUR hybridize methods for correlated data analysis and spatiotemporal dependence structures. Typically, at each site, there are one or more covariates which can be predicted at each geographic location, like proximity to highway, season, time of day, elevation, or other features. It's desirable to condition on these factors to increase predictive accuracy and consequently decrease spatiotemporal dependence. To handle the residual dependence structure, variograms are used to assess the extent of residual correlation over time and space, and these can estimate the variance-components of complex autoregressive covariance structures.

There are quite a number of good review articles on LUR, one for instance is here: https://www.sciencedirect.com/science/article/pii/S1352231008005748 but pubmed will be your guide.

  • $\begingroup$ This is a very interesting method. I, of course, need to look into more detail but I am guessing that it can be extended to work with counts or Poisson statistics. $\endgroup$ – Luca May 10 '19 at 14:55
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    $\begingroup$ @Luca easy peasy. $\endgroup$ – AdamO May 10 '19 at 14:57
  • $\begingroup$ hahaha....for you, perhaps :) $\endgroup$ – Luca May 10 '19 at 14:59

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