Tim Vieira Explains Conditional Poisson Sampling with Verified Identities and Interactive Visuals
xtimv · x · 2026-10-29
Researcher Tim Vieira published a deep dive on Conditional Poisson Sampling (CPS): a distribution over fixed-size subsets where each size-n subset's probability is proportional to the product of its items' weights.
- The normalizing constant is a weighted generalization of the binomial coefficient, recovering C(N,n) for uniform weights.
- Inclusion probabilities relate nonlinearly to weights — the size constraint means doubling wi doesn't double pipi; an interactive widget explores this.
- CPS is an exponential family (natural parameters log wi) and the unique maximum-entropy distribution over size-n subsets with prescribed inclusion probabilities.
- Every identity is numerically verified with linked test cases, plus interactive tree-based sampling visualizations.
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