A Subordinated Stochastic Process Model

Abstract

We introduce a new stochastic model for non-decreasing processes which can be used to include stochastic variability into any deterministic growth function via subordination. This model is useful in many applications such as growth curves (children's height, fish length, diameter of trees, etc) and degradation processes (crack size, wheel degradation, laser light, etc). One advantage of our approach is to be able to easily deal with data that are irregularly spaced in time or different curves that are observed at different moments of time. With the use of simulations and applications, we examine two approaches to Bayesian inference for our model: the first based on a Gibbs sampler and the second based on approximate Bayesian computation.