Choosing priors for an important class of signal processing problems

Proper choice of prior distributions is a very important issue in Bayesian methodology. It is particularly important when the number of available data for processing is rather small. When little is known a priori, noninformative priors are usually employed. A well known approach for determining noninformative priors is Jeffreys' rule, which practically provides meaningful and locally uniform priors of the unknowns. In this paper, we carefully follow Jeffreys' rule to determine noninformative priors for an important class of signal processing problems that involve frequency estimation and DOA estimation. Cases of one and two signals are discussed in detail. Their analysis is also extended to include more general scenarios.