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Information-Computation Inversion in Pseudo-Marginal MCMC

  • Zihan Xu
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Abstract

Observation refinement changes posterior uncertainty and the likelihood calculation in pseudo-marginal MCMC. We compare their combined effect through finite-run squared-error risk. A sufficient inversion condition relates information gain to accepted event flow and coarse-kernel contraction. A bootstrap construction realizes inversion at every fixed particle count. We then couple cross-event proposals and refresh same-event proposals independently. A swap identity establishes invariance; continuation identities describe subsequent risk. In the same finite model, a rational certificate proves inversion against optimized constant mixtures and repair by selective allocation over an initialization class at a common action-price budget. Reaction-network experiments measure CPU costs. Under finite-pool initialization, selective allocation reduces event mean-squared error by 40.5% against a tuned mixture at 25 post-initialization CPU seconds. Paired transcription observations show how increased particle effort can raise finite-budget error.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026informationcomputation,
  title = {{Information-Computation Inversion in Pseudo-Marginal MCMC}},
  author = {Zihan Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.19718},
  eprint = {2608.19718},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.19718},
}
RIS
TY  - UNPB
TI  - Information-Computation Inversion in Pseudo-Marginal MCMC
AU  - Zihan Xu
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2608.19718
UR  - https://arxiv.org/abs/2608.19718
AB  - Observation refinement changes posterior uncertainty and the likelihood calculation in pseudo-marginal MCMC. We compare their combined effect through finite-run squared-error risk. A sufficient inversion condition relates information gain to accepted event flow and coarse-kernel contraction. A bootstrap construction realizes inversion at every fixed particle count. We then couple cross-event proposals and refresh same-event proposals independently. A swap identity establishes invariance; continuation identities describe subsequent risk. In the same finite model, a rational certificate proves inversion against optimized constant mixtures and repair by selective allocation over an initialization class at a common action-price budget. Reaction-network experiments measure CPU costs. Under finite-pool initialization, selective allocation reduces event mean-squared error by 40.5% against a tuned mixture at 25 post-initialization CPU seconds. Paired transcription observations show how increased particle effort can raise finite-budget error.
ER  -