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I'm a bit new in the spatial statistics (althought I'm not new in statistical analysis, particular in Bayesian inference). When we have point measurements in space - geostatistics/spatial statistics has an answer. But what if we measure not at points but maybe along lines, that streches over some area? For example a power grid line - it crossess some area, and number of failures of that line is associated not with a point in space but with that particular line. More generally - take a network, for which measurements are taken not at points but instead sample point is associated with the entire edge. Whats then? Is there any reasearch done in that direction? I know some papers dealing with river networks but still the sampling is done at particular points.

My though would be to impose a grid on that network. Then identify cells that are crossed by a particular edge and then, proportionally divide the measurement of that edge to those crossed cells. This way would provide with equally spaced "virtual" measurements on which then I could do spatial analysis. However, there is a question of robustness because the results will likely depend on the grid.

Maybe someone knows a better way to deal with this kind of spatial data? A reference to some paper would be great.

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  • $\begingroup$ Pretty much anywhere in spatial statistics you can substitute geographic distance with distance along a network. What analyses are you actually conducting? $\endgroup$ – Andy W May 17 '16 at 12:09
  • $\begingroup$ @AndyW More specifically I have outage data of power grid. Outages are collected for each line separatele. The network is over a large area. Large part of the outages are related to weather conditions, therefore there is a dependence. In my case distance along the edges would not work, because if I have two long parallel lines, then the distance along these lines would be large while in space it is small. $\endgroup$ – Tomas May 18 '16 at 12:00
  • $\begingroup$ Dependence in the weather does not that matter - dependence between lines does. If one of the parallel lines goes out, does it automatically cause other parallel line to go out? You can consider a model of outages as Prob(Outage) = f(Weather,Outages in Nearby Lines). The effect of outages in nearby lines can be formalized with a spatial weights matrix. Say we had a simple network on one line, A<->B<->C. If A going out can cause C to go out, you would want the weights to incorporate higher order connections. If only B affects C, then you only need first order neighbors. $\endgroup$ – Andy W May 18 '16 at 12:19
  • $\begingroup$ @AndyW The problem of dependence between lines is more complicated than that, as outage of one line can cause outage of a line that is very far in the network - that is the result of electricity flow governed by Kirchhov law. Dependence on the weather does matter as it is the major cause of the outages (discarding outages in the subsequent stages of the cascade). Since weather manifest ifself through spatial dependencies (closer to the cost - stronger the winds, etc.), the question remains - how to model network data by spatial statistics. $\endgroup$ – Tomas May 18 '16 at 18:49
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as you noted it would not be wise to consider such data as a planar point pattern where the general metric between points would be Euclidean distance. Consider for example the dataset which is presented in the following paper, where the author of the thesis discusses distribution of crime along streets of Chicago or distribution of spider webs between bricks. Here's the link : https://www.google.cz/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwj89qrh2tbWAhXiCpoKHW6RCo4QFggwMAA&url=http%3A%2F%2Fescholarship.org%2Fuc%2Fitem%2F1t01p61g&usg=AOvVaw21vMqoh9q0-oS8eGaTfWXR

Therefore in such cases you would define something which they use in spatial statistics called Manhattan distance. So for example you were during an analysis of taxi trip duration in NYC, you would use Manhattan distance because that is how the streets are organized.I hope the paper helps you.

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