We consider inference and optimal design problems for finite clusters from bond percolation on the integer lattice Zd or, equivalently, for SIR epidemics evolving on a bounded or unbounded subset of Zd with constant life times. The bond percolation probability p is considered to be unknown, possibly depending, through the experimental design, on other parameters. We consider inference under each of the following two scenarios:
- The observations consist of the set of sites which are ever infected, so that the routes by which infections travel are not observed (in terms of the bond percolation process, this corresponds to a knowledge of the connected component containing the initially infected site--the location of this site within the component not being relevant to inference for p).
- All that is observed is the size of the set of sites which are ever infected.
This is a joint work with Professor Gavin Gibson and Dr Stan Zachary, both with Heriot-Watt University, Edinburgh.