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.
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