Detection and characterisation of weak periodic signals from noisy time series is a common problem in many different fields of astrophysics. Here I detail one approach for testing whether a signal with roughly known characteristics exists in the data, using a search of secondary eclipses from Kepler-observed photometric time series as an example. The method is based on Bayesian model selection and uses Gaussian processes to model the stochastic variability in the data in non-parametric fashion.