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.