Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Finite-simulation synthetic likelihood is a random approximation
Remarks
Under AC for the Gaussian-density interface (The Axiom of Choice), the finite-simulation mean, covariance, and returned plug-in value depend on the simulated summaries. The approximation may be unavailable: the local lemma A two-simulation covariance in two dimensions is singular shows that with two two-dimensional summaries the covariance is never positive definite, so Finite-simulation plug-in synthetic-likelihood evaluation returns unavailable. A companion example gives two positive-probability simulation outcomes with different covariances (Two simulated square summaries give a random singular covariance ↗).
The ideal Gaussian summary density is not asserted to be the exact model likelihood. No unbiasedness or consistency claim is made for the finite plug-in quantity.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
17 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- David T. Frazier et al., Bayesian Inference Using Synthetic Likelihood: Asymptotics and Adjustments, Journal of the American Statistical Association 118(544), 2821–2832 (2023) (standard reference, not scraped)
- Victor M.-H. Ong et al., Variational Bayes with Synthetic Likelihood, Statistics and Computing 28(4), 971–988 (2018) (standard reference, not scraped)