  We develop a likelihood methodology which can be used to search for evidence
of burst repetition in the BATSE catalog, and to study the properties of the
repetition signal. We use a simplified model of burst repetition in which a
number $N_{\rm r}$ of sources which repeat a fixed number of times $N_{\rm
rep}$ are superposed upon a number $N_{\rm nr}$ of non-repeating sources. The
instrument exposure is explicitly taken into account. By computing the
likelihood for the data, we construct a probability distribution in parameter
space that may be used to infer the probability that a repetition signal is
present, and to estimate the values of the repetition parameters. The
likelihood function contains contributions from all the bursts, irrespective of
the size of their positional errors --- the more uncertain a burst's position
is, the less constraining is its contribution. Thus this approach makes maximal
use of the data, and avoids the ambiguities of sample selection associated with
data cuts on error circle size. We present the results of tests of the
technique using synthetic data sets.
