Stateful processes in probabilistic programming
summary
Shows how Polya urn, Gaussian process and Indian Buffet Process implementations rely on explicit local state, stochastic memoization and countable duplication to preserve exchangeability; formalizes programs as event structures with randomized partial variables and defines uniformity/symmetry conditions so fixed random seeds yield deterministic strategies. Covers measurable kernels, sequential-environment race conditions for memoization, and when sample spaces must be uncountable. Useful if wanting a concrete semantics (game/event-structure) for stateful probabilistic primitives and their inference implications.
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