Paradoxes of probabilistic programming

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Probabilistic programs that multiply weights by pdfs produce unit errors and paradoxes: a simple height example gives 1.75 normally but a coin-conditional version yields 1.72 in one encoding and 170 after converting meters to centimeters. The paper replaces point observations with interval conditioning, models measure-zero events as limits using infinitesimal probabilities (infinite-decimal arithmetic), and shows importance sampling/rejection sampling converge and become invariant under parameter transformations; it ships as a DSL in Julia and the implementation matches the theoretical claims.

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" chapters (10)

1. 0:00Start
2. 1:36Paradox 1
3. 4:32Overview
4. 5:24Probabilistic programming 101: manual rejection sampling
5. 9:09Probabilistic programming 101: importance sampling
6. 9:22Probabilistic programming 101: continuous distributions
7. 10:29What went wrong conditionals
8. 11:08What went wrong: nonlinear parameter transformations
9. 15:42Infinitesimal numbers
10. 22:21Recap