PULSAR TIMING AND THE UPPER LIMITS ON A GRAVITATIONAL-WAVE BACKGROUND- A BAYESIAN-APPROACH

Stringent limits on Omega, the energy density in a gravitational wave background per logarithmic frequency interval in units of the closure density, have recently been suggested by Thorsett and Dewey using obse rvational data of PSR B1855+09. We show that their use of the Neyman-P earson test of hypotheses cannot, in the general case, provide reliabl e upper limits on an unknown parameter. The alternative presented here is the calculation of the probability distribution and repartition fu nction for Omega using a Bayesian formalism. A prior distribution must be specified and the choice of ''Jeffreys' prior'' is justified on th e grounds that it best represents a total lack of prior knowledge abou t the parameter. The Bayesian approach yields an upper limit at 95% co nfidence of 9.3 x 10(-8) for Omega h2(.) This limit is less stringent by a factor of 10 than that placed by Thorsett and Dewey.