Time delays and stationarity in quasar light curves

We present a fully Bayesian framework for time delay inference and stationarity tests in quasar light curves using marginalized Gaussian processes. The model separates a deterministic, nonstationary drift (piecewise linear mean) from stationary stochastic variability (Matérn and Spectral Mixture kernels), and jointly models multiple images with per-image microlensing. Bayesian evidence and parameter posteriors are obtained via nested sampling and marginalized over model choices. Applied to the quasars WFI J2033–4723, B <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>1608</a:mn> <a:mo>+</a:mo> <a:mn>656</a:mn> </a:mrow> </a:math> , and HE 0435–1223, we find strong evidence for nonstationarity in B <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>1608</c:mn> <c:mo>+</c:mo> <c:mn>656</c:mn> </c:mrow> </c:math> and HE 0435–1223, while WFI J2033–4723 is consistent with stationarity. The stochastic component favors an Markovian exponential kernel for B <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mn>1608</e:mn> <e:mo>+</e:mo> <e:mn>656</e:mn> </e:mrow> </e:math> and a non-Markovian Matérn- <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mfrac> <g:mn>3</g:mn> <g:mn>2</g:mn> </g:mfrac> </g:math> kernel for WFI J2033–4723 and HE 0435–1223. Multilength-scale Spectral Mixture kernels are disfavored. Time delays are shown to be robust to model assumptions and consistent with prior work within the error. We further identify and mitigate a likelihood pathology which biases toward large delays, providing a practical nested sampling convergence protocol.