Optimal state space partitioning

The partitioning problem of a parameter state space Ω into observation subsets is addressed. The initial knowledge about this parameter is a prior probability distribution over Ω. This distribution is recursively updated through parallel observation results, that are actually binary informations about the presence or the absence of the parameter inside subsets ω_i of Ω. Each subset is scanned with some errors, corresponding to misdetections and false alarms. It is shown how the partitioning of Ω into the {ω_i} may be optimized under different optimality criteria related to various measures of the “information” contained in the posterior probability density function. Simulations results are presented and computability issues are discussed