  Transmission spectroscopy, which consists of measuring the
wavelength-dependent absorption of starlight by a planet's atmosphere during a
transit, is a powerful probe of atmospheric composition. However, the expected
signal is typically orders of magnitude smaller than instrumental systematics,
and the results are crucially dependent on the treatment of the latter. In this
paper, we propose a new method to infer transit parameters in the presence of
systematic noise using Gaussian processes, a technique widely used in the
machine learning community for Bayesian regression and classification problems.
Our method makes use of auxiliary information about the state of the
instrument, but does so in a non-parametric manner, without imposing a specific
dependence of the systematics on the instrumental parameters, and naturally
allows for the correlated nature of the noise. We give an example application
of the method to archival NICMOS transmission spectroscopy of the hot Jupiter
HD 189733, which goes some way towards reconciling the controversy surrounding
this dataset in the literature. Finally, we provide an appendix giving a
general introduction to Gaussian processes for regression, in order to
encourage their application to a wider range of problems.
