Long-term precise timing of Galactic millisecond pulsars holds great promise for measuring long-period (months-to-years) astrophysical gravitational waves. In this work we develop a Bayesian data analysis method for projects called pulsar timing arrays; projects aimed to detect these gravitational waves by using millisecond pulsars as very precise extraterrestrial clocks. We also introduce the gravitational-wave memory effect, and we describe how to detect this effect with pulsar timing arrays with the Bayesian method. The Bayesian data analysis method is developed, extensively tested, and applied to real data. This has resulted in the most accurate upper-limit on the stochastic gravitational-wave background.UBL - phd migration 201
