How to estimate distance and velocity from parallax and proper motion

Abstract

If the observed parallax ϖ′ has a gaussian measurement error σ, there is a 68% probability that the actual parallax ϖ is in the range ϖ′ − σ < ϖ < ϖ′ + σ (the frequentist approach). The probability distribution within this range is not known from ϖ′ and σ alone, and in particular, we cannot state that the most probable distance D is given by D = 1/ϖ′. To obtain a probability distribution, we need to know or assume a distribution of pulsar distances. Similar assumptions are also required to estimate the v…