  The optical and UV variability of the majority of AGN may be related to the
reprocessing of rapidly-changing X-ray emission from a more compact region near
the central black hole. Such a reprocessing model would be characterised by
lags between X-ray and optical/UV emission due to differences in light travel
time. Observationally however, such lag features have been difficult to detect
due to gaps in the lightcurves introduced through factors such as source
visibility or limited telescope time. In this work, Gaussian process regression
is employed to interpolate the gaps in the Swift X-ray and UV lightcurves of
the narrow-line Seyfert 1 galaxy Mrk 335. In a simulation study of five
commonly-employed analytic Gaussian process kernels, we conclude that the
Matern 1/2 and rational quadratic kernels yield the most well-specified models
for the X-ray and UVW2 bands of Mrk 335. In analysing the structure functions
of the Gaussian process lightcurves, we obtain a broken power law with a break
point at 125 days in the UVW2 band. In the X-ray band, the structure function
of the Gaussian process lightcurve is consistent with a power law in the case
of the rational quadratic kernel whilst a broken power law with a breakpoint at
66 days is obtained from the Matern 1/2 kernel. The subsequent
cross-correlation analysis is consistent with previous studies and furthermore,
shows tentative evidence for a broad X-ray-UV lag feature of up to 30 days in
the lag-frequency spectrum where the significance of the lag depends on the
choice of Gaussian process kernel.
