Vector Summary Pseudo Posteriors for Simulation-Based Inference with Applications to Cosmology

Vector Summary Pseudo Posteriors for Simulation-Based Inference with Applications to Cosmology. Patil, P., Rose, J., Garcia, A., Chen, M., Torrey, P., & Farahi, A. In Proceedings of the 2026 Statistics and Trustworthy AI for Cross (STAI-X), Cambridge, MA, August, 2026.

Paper abstract bibtex

Simulation-based inference often compares simulator output with low-dimensional summaries when likelihoods are unavailable. Such summaries can make inference fast and interpretable, but they also determine what is identified: a pseudo posterior may concentrate on a parameter set rather than a point. We introduce Vector Summary Pseudo Posteriors (VSPP), a generalized Bayes framework that weights simulator parameters by the mismatch between simulated residual summaries and a target vector defined relative to a reference relation. When exact matching is possible, adding informative summaries produces nested identified sets; under misspecification, VSPP targets the best matching parameter set. We show that local identification is governed by the rank of the population mismatch map, while recovery from a finite simulation bank improves when summaries better separate the held-out parameter from competing candidates. As a concrete example, we use residual mean and second raw moment summaries, which distinguish parameter values that match a mean relation but differ in residual dispersion. Synthetic examples show how added summaries shrink ridges and manifolds; in a nonlinear benchmark, adding the second raw moment moves the pseudo posterior closer to the exact posterior. In cosmological simulation studies, VSPP improves held-out parameter recovery in CAMELS IllustrisTNG and reduces residual moment mismatch in generated DREAMS samples for Milky Way–mass systems.

@inproceedings{patil_vector_2026,
	address = {Cambridge, MA},
	title = {Vector {Summary} {Pseudo} {Posteriors} for {Simulation}-{Based} {Inference} with {Applications} to {Cosmology}},
	url = {https://statsupai.org/STAIX2026/index.html},
	abstract = {Simulation-based inference often compares simulator output with low-dimensional summaries when likelihoods are unavailable. Such summaries can make inference fast and interpretable, but they also determine what is identified: a pseudo posterior may concentrate on a parameter set rather than a point. We introduce Vector Summary Pseudo Posteriors (VSPP), a generalized Bayes framework that weights simulator parameters by the mismatch between simulated residual summaries and a target vector defined relative to a reference relation. When exact matching is possible, adding informative summaries produces nested identified sets; under misspecification, VSPP targets the best matching parameter set. We show that local identification is governed by the rank of the population mismatch map, while recovery from a finite simulation bank improves when summaries better separate the held-out parameter from competing candidates. As a concrete example, we use residual mean and second raw moment summaries, which distinguish parameter values that match a mean relation but differ in residual dispersion. Synthetic examples show how added summaries shrink ridges and manifolds; in a nonlinear benchmark, adding the second raw moment moves the pseudo posterior closer to the exact posterior. In cosmological simulation studies, VSPP improves held-out parameter recovery in CAMELS IllustrisTNG and reduces residual moment mismatch in generated DREAMS samples for Milky Way–mass systems.},
	language = {en},
	booktitle = {Proceedings of the 2026 {Statistics} and {Trustworthy} {AI} for {Cross} ({STAI}-{X})},
	author = {Patil, Pratik and Rose, Jonah and Garcia, Alex and Chen, Min and Torrey, Paul and Farahi, Arya},
	month = aug,
	year = {2026},
}

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