Survival regression models with dependent Bayesian nonparametric priors.

with Fabrizio Leisen and Jim Griffin

We present a novel Bayesian nonparametric model for regression in survival analysis. Our model builds on the classical neutral to the right model of Doksum (1974) and on the Cox proportional hazards model of Kim and Lee (2003). The use of a vector of dependent Bayesian nonparametric priors allows us to efficiently model the hazard as a function of covariates whilst allowing nonproportionality. The model can be seen as having competing latent risks. We characterize the posterior of the underlying dependent vector of completely random measures and study the asymptotic behavior of the model. We show how an MCMC scheme can provide Bayesian inference for posterior means and credible intervals. The method is illustrated using simulated and real data. paper link

Compound vectors of subordinators and their associated positive Lévy copulas.

with Fabrizio Leisen

Lévy copulas are an important tool which can be used to build dependent Lévy processes. In a classical setting, they have been used to model financial applications. In a Bayesian framework they have been employed to introduce dependent nonparametric priors which allow to model heterogeneous data. This paper focuses on introducing anew class of Lévy copulas based on a class of subordinators called Compound Random Measures. The well-known Clayton Lévy copula is a special case of this new class. Furthermore, we provide some novel results about the underlying vector of subordinators such as a series representation and relevant moments. The article concludes with an application to a vector of stable processes simulation study and Danish fire real dataset study. paper link

On the estimation of partially observed continuous-time Markov chains.

with Ramsés Mena and Stephen Walker

Motivated by the increasing use of discrete-state Markov processes across applied disciplines, a Metropolis–Hastings sampling algorithm is proposed for a partially observed process. Current approaches, both classical and Bayesian, have relied on imputing the missing parts of the process and working with a complete likelihood. However, from a Bayesian perspective, the use of latent variables is not necessary and exploiting the observed likelihood function, combined with a suitable Markov chain Monte Carlo method, results in an accurate and efficient approach. A comprehensive comparison with simulated and real data sets demonstrate our approach when compared with alternatives available in the literature. paper link

Bayesian nonparametric estimation of survival functions with multiple-samples information.

with Fabrizio Leisen

In many real problems, dependence structures more general than exchangeability are required. For instance, in some settings partial exchangeability is a more reasonable assumption. For this reason, vectors of dependent Bayesian nonparametric priors have recently gained popularity. They provide flexible models which are tractable from a computational and theoretical point of view. In this paper, we focus on their use for estimating multivariate survival functions. Our model extends the work of Epifani and Lijoi (2010) to an arbitrary dimension and allows to model the dependence among survival times of different groups of observations. Theoretical results about the posterior behaviour of the underlying dependent vector of completely random measures are provided. The performance of the model is tested on a simulated dataset arising from a distributional Clayton copula. paper link

Integrability conditions for compound random measures.

with Fabrizio Leisen

Compound random measures (CoRM’s) are a flexible and tractable framework for vectors of completely random measure. In this paper, we provide conditions to guarantee the existence of a CoRM. Furthermore, we prove some interesting properties of CoRM’s when exponential scores and regularly varying Lévy intensities are considered. paper link