The real problem first, then the mathematics needed to describe it, with one running example carried to the end.
A methane inventory has to answer three questions about a basin: where are the sources, when are they emitting, and how much do they emit in total. Satellites answer none of them directly. They return thinned, noisy, scale-dependent snapshots, and the gap between those snapshots and an inventory is where the mathematics lives.
This section is the theory behind Tier V — Source population. It builds, one idea at a time, the random objects (point processes, completely random measures, Gaussian processes, Cox processes, thinning) that describe the problem, then maps them back onto the three phases of inventory work.
The task, in three phases¶
The three phases need different mathematical objects because a different thing is uncertain in each. Part II builds those objects; Part III maps them back onto the phases.
How this section is organised¶
Point versus area sources, what the instruments measure, the data products, and the Permian running example used throughout.
Measures, Poisson processes, completely random measures, fields, Cox processes, scale, thinning, and time, each introduced with the phase it serves.
Discovery, monitoring, and estimation of the basin total, with the running example worked to a number and the assumptions made explicit.
Point (atom) versus area (density), side by side: the prior, the instrument, the detection mechanism, and when each model fails. See §III.4.
Reading guide¶
Each object in Part II is tagged with the phase(s) it serves. If you care about one phase only, follow its thread: