High energy astrophysical transients at cosmological distances allow us to test the fundamental assumptions of the standard models of cosmology and particles physics, such as Lorentz invariance, the massless nature of the photon or the weak equivalence principle. If any of these assumptions are incorrect, photons of different energies propagate differently through spacetime, which could be observable in the spectral lags of Gamma Ray Bursts. Constraining such violations can challenging in the presence of uncertainties in the redshifts of sources, uncertain systematics in the model for other contributions to the spectral lag, and the long range of the gravitational potential. In this talk I will discuss how one can overcome these hurdles by constructing probabilistic source-by-source forward models and by combining constrained realisations of the local density field with unconstrained large-scale modes to obtain some of the tightest constraints on these models to date.
