PoGO+ is a Compton-scattering polarimeter, which measured the linear polarization of hard X-rays (~20-170 keV) emitted by the Crab nebula/pulsar and the black-hole binary Cygnus X-1. Measurements were conducted from a stabilized balloon-borne platform in the stratosphere in July 2016. Polarization properties were determined by measuring the distribution of azimuthal Compton-scattering angles in an array of collimated plastic scintillators, housed in a thick Bi4Ge3O12 anticoincidence shield. Observations are complicated by the significant flux of background particles present in the stratosphere due to the interaction of primary cosmic rays with the upper layers of the atmosphere. The resulting modest signal-to-background ratio of ~1/7, combined with the positive-definite nature of the measurements, motivates a data analysis using Bayesian statistics. The Bayesian method is not limited to PoGO+ data but is universal and can thus be used for any instruments and detection techniques in high-energy polarimetry. After an overview of the instrument measurement principles and design, the data-analysis procedure is described in detail. This chapter concludes with an overview of results from observations and a discussion on the future development of balloon-borne hard X-ray polarimetry, including missions that are currently being prepared for flight.