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We use a Bayesian approach to derive the distance probability distributionfor one object from its parallax with measurement uncertainty for two spatialdistribution priors, viz. a homogeneous spherical distribution and agalactocentric distribution - applicable for radio pulsars - observed fromEarth. We investigate the dependence on measurement uncertainty, and show thata parallax measurement can underestimate or overestimate the actual distance,depending on the spatial distribution prior. We derive the probabilitydistributions for distance and luminosity combined, and for each separately,when a flux with measurement error for the object is also available, anddemonstrate the necessity of and dependence on the luminosity function prior.We apply this to estimate the distance and the radio and gamma-ray luminositiesof PSR J0218+4232. The use of realistic priors improves the quality of theestimates for distance and luminosity, compared to those based on measurementonly. Use of a wrong prior, for example a homogeneous spatial distributionwithout upper bound, may lead to very wrong results.

astronomy and astrophysics

The distance and luminosity probability distributions derived from  parallax and flux with their measurement errors with application to the  millisecond pulsar PSR J0218+4232