Probabilistic Modelling for Delay Estimation in Gravitationally Lensed Photon Streams

We test whether a more principled treatment of delay estimation in lensed photon streams, compared with the standard kernel estimation method, can have benefits of more accurate (less biased) and/or more stable (less variance) estimation. To that end, we propose a delay estimation method in which a single latent inhomogeneous Poisson process underlying the lensed photon streams is imposed. The rate function model is formulated as a linear combination of nonlinear basis functions. Such unifying rate function is then used in delay estimation based on the corresponding Innovation Process. This method is compared with a more straightforward and less principled baseline method based on kernel estimation of the rate function. Somewhat surprisingly, the overall emerging picture is that the theoretically more principled method does not bring much practical benefit in terms of the bias/variance of the delay estimation. This is in contrast to our previous findings on daily flux data.