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Advances in sampling schemes for Markov jump processes have recently enabledmultiple inferential tasks. However, in statistical and machine learningapplications, we often require that these continuous-time models find supporton structured and infinite state spaces. In these cases, exact sampling mayonly be achieved by often inefficient particle filtering procedures, andrapidly augmenting observed datasets remains a significant challenge. Here, webuild on the principles of uniformization and present a tractable framework toaddress this problem, which greatly improves the efficiency of existingstate-of-the-art methods commonly used in small finite-state systems, andfurther scales their use to infinite-state scenarios. We capitalize on themarginal role of variable subsets in a model hierarchy during the processjumps, and describe an algorithm that relies on measurable mappings betweenpairs of states and carefully designed sets of synthetic jump observations. Theproposed method enables the efficient integration of slice sampling techniquesand it can overcome the existing computational bottleneck. We offer evidence bymeans of experiments addressing inference and clustering tasks on bothsimulated and real data sets.

On Bayesian inferential tasks with infinite-state jump processes: efficient data augmentation