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Bayesian Filters via the Stochastic Category — arXiv:2611.03830

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03830
License (as archived): CC0-1.0
Archived: 2026-11-04T18:59:49.019Z
SHA-256 of the archived text: 50707ffbd552ad326e940a113cad18f42cbcfb421ebb8d1e289511ba9bcf84fc
Stable URL of this page: https://metraipolis.com/documento/dc_44d86ef578d7

How to cite

Bayesian Filters via the Stochastic Category — arXiv:2611.03830 — arXiv (en), https://arxiv.org/abs/2611.03830 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_44d86ef578d7 (Metraipolis archive dc_44d86ef578d7, sha256 50707ffbd552ad326e940a113cad18f42cbcfb421ebb8d1e289511ba9bcf84fc)

BibTeX

@misc{dc44d86ef578d7,
  title = {Bayesian Filters via the Stochastic Category — arXiv:2611.03830},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03830},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_44d86ef578d7; sha256 50707ffbd552ad326e940a113cad18f42cbcfb421ebb8d1e289511ba9bcf84fc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03830. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We extend the categorical treatment of Bayesian filters to models with feedback, whose transitions and observations may depend on the past observations. We work in the stochastic category, whose objects are measurable spaces and whose morphisms are Markov kernels, which we refer to as stochastic morphisms. We systematically parameterize stochastic morphisms by a measurable space, and develop the calculus of conditioning in a notation intuitively compatible with classical probability theory, requiring neither string diagrams nor densities. A stochastic morphism into a product space is regarded as a parameterized family of joint laws, and its conditional law is again a stochastic morphism, so that the rules of conditioning become equalities of stochastic morphisms. We define the Bayesian inverse with respect to a parameterized prior and prove Bayesian coherence. A model with feedback is then a model whose parameter space grows with the observations, and we derive the Bayesian filter, prediction and smoothing for such models, with standard Borel hidden states and countably generated observation spaces. The affine Gaussian stochastic morphisms parameterized by a measurable space form a family strictly larger than the Markov category $\mathbf{Gauss}$, closed under composition and Bayesian inversion, in which we obtain the Kalman filter and the Rauch-Tung-Striebel smoother with feedback.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.ST, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR) ; Category Theory (math.CT); Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2611.03830 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:37:37.516Z dalla pagina https://arxiv.org/list/math.ST/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).