  We introduce a semi-parametric Bayesian model for survival analysis. The
model is centred on a parametric baseline hazard, and uses a Gaussian process
to model variations away from it nonparametrically, as well as dependence on
covariates. As opposed to many other methods in survival analysis, our
framework does not impose unnecessary constraints in the hazard rate or in the
survival function. Furthermore, our model handles left, right and interval
censoring mechanisms common in survival analysis. We propose a MCMC algorithm
to perform inference and an approximation scheme based on random Fourier
features to make computations faster. We report experimental results on
synthetic and real data, showing that our model performs better than competing
models such as Cox proportional hazards, ANOVA-DDP and random survival forests.
