• bayesian inference
• gravitational waves
• LISA
• LISA Global Fit

The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave (GW) interferometric detector planned to be launched around 2035. LISA is expected to observe a multitude of GW candidates, mainly: Massive Black Hole Binaries (MBHBs), Extreme Mass Ratio Inspirals (EMRIs), Galactic Binaries (GBs), and the inspiral of compact binary coalescences (CBCs) merging in the 10–100 Hz frequency band, currently probed by the LIGO, Virgo and Kagra ground-based detectors.
In the milli-Hz region of the LISA band, tens of thousands of GB signals plus eventual transient signals and EMRI signals are expected to overlap. The non-trivial task of extracting and characterising this multitude of signals is deemed in the literature as the ``LISA Global Fit”.
In this thesis, we propose a Bayesian inference scheme prototype organised as a simplified trans-dimensional sampler relying on grid evaluations to explore all the possible combinations of signals. Hence, we demonstrate its reliability using toy problems in which we inject, in synthetic white noise, some synthetic signals with similar features to the LISA GW candidates.
We also compare it with an original proposal for an iterative subtraction solution. To bypass some intrinsic problems of this procedure, we represent the residuals at each step as an autoregressive process of order p, and we implement a stopping criterion based on the signal-to-noise ratio.
We demonstrate that the proposed inference scheme can handle the LISA Global Fit problem, while the subtraction scheme could be better used to infer the properties of a transient signal overlapped with continuous signals.
We further investigate post-process diagnostics, relying on the overlap matrix between detected signals to assess whether an inferred source is significant or not. We also note that transient signals can significantly overlap with continuous signals, which indicates the possibility of such a situation happening even for different classes of LISA candidates.
We then study possible problems in the inference arising from some features of the overlap matrix between the signals inside the data stream. 
Finally, we apply our proposed Bayesian inference scheme by simulating 1 year of LISA data containing resolvable Double White Dwarf using the BALROG code, finding consistent results with the toy simulations.