A framework for LISA population inference

The Laser Interferometer Space Antenna (LISA) is expected to have a source rich data stream containing signals from large numbers of many different types of source. This will include both individually resolvable signals and overlapping stochastic backgrounds, a regime intermediate between current ground-based detectors and pulsar timing arrays. The resolved sources and backgrounds will be fitted together in a high dimensional Global Fit. To extract information about the astrophysical populations to which the sources belong, we need to decode the information in the Global Fit, which requires new methodology that has not been required for the analysis of current gravitational wave detectors. Here, we %start that development, presenting present a hierarchical Bayesian framework to infer the properties of astrophysical populations directly from the output of a LISA Global Fit, consistently accounting for information encoded in both the resolved sources and the unresolved background. Using a simplified model of the Global Fit, we illustrate how the interplay between resolved and unresolved components affects population inference and highlight the impact of data analysis choices, such as the signal-to-noise threshold for resolved sources, on the results. Our approach provides a practical foundation for population inference using LISA data.