Analytic upper bounds for Zig-Zag thinning rates in polyhazard models

Determine an analytical dominating rate function M(t) that tightly upper bounds the Zig-Zag sampler’s inhomogeneous flip rate Λ^F(t) used to simulate event times via Poisson thinning when sampling the parameter vector θ in polyhazard survival models, so that efficient generation of inhomogeneous Poisson process events is possible without resorting to numerically constructed bounds.

Background

The Zig-Zag sampler requires simulating event times from an inhomogeneous Poisson process with rate Λ^F(t). A standard approach uses Poisson thinning, which in turn needs a dominating rate M(t) ≥ Λ^F(t). In many models, tight analytic bounds for M(t) exist and facilitate efficient sampling.

In the context of polyhazard survival models, the authors report that they are unaware of an analytic choice of M(t) that is suitable, and consequently propose a numerical bounding strategy extending the Automatic Zig-Zag method. Establishing an analytic bound would simplify implementation and may improve efficiency and reliability of PDMP-based sampling in this class of models.