Gaussian processes for survival analysis

Thesis

Survival analysis is an old area of statistics dedicated to the study of time-to-event random variables. Typically, survival data have three important characteristics. First, the response is a waiting time until the occurrence of a predetermined event. Second, the response can be "censored", meaning that we do not observe its actual value but a bound for it. Last, the presence of covariates. While there exists some feasible parametric methods for modelling this type of data, they usually impose very strong assumptions on the real complexity of the response and how it interacts with the covariates. While these assumptions allow us to have tractable inference schemes, we lose inference power and overlook important relationships in the data. Due to the inherent limitations of parametric models, it is natural to consider non-parametric approaches.

In this thesis, we introduce a novel Bayesian non-parametric model for survival data. The model is based on using a positive map of a Gaussian process with stationary covariance function as prior over the so-called hazard function. This model is thoughtfully studied in terms of prior behaviour and posterior consistency. Alternatives to incorporate covariates are discussed as well as an exact and tractable inference scheme.

Authors: Aguilar, T

• Alternative title: A BNP model for hazard functions
• DOI: 10.5287/ora-o054bygep
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford