# Meta-Posterior Consistency for the Bayesian Inference of Metastable System

arXiv: https://arxiv.org/abs/2408.01868 · HTML: https://mlsanity.com/paper/2408.01868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 92 references that are in the map.
- First posted on arXiv 3 Aug 2024.

## Builds on (most cited first, 6 of 6)

- [Parameterizations for Ensemble Kalman Inversion](https://mlsanity.com/paper/1709.01781/) (2017)
- [Kernel Density Estimation for Dynamical Systems](https://mlsanity.com/paper/1607.03792/) (2016)
- [Statistical Inference for Stochastic Differential Equations with Memory](https://mlsanity.com/paper/1307.1164/) (2013)
- [Bayesian Multinomial Logistic Normal Models through Marginally Latent Matrix-T Processes](https://mlsanity.com/paper/1903.11695/) (2019)
- [Understanding microbiome dynamics via interpretable graph representation learning](https://mlsanity.com/paper/2203.01830/) (2022)
- [Generalized Bayes Approach to Inverse Problems with Model Misspecification](https://mlsanity.com/paper/2210.06921/) (2022)

## Abstract (arXiv)

The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems are only metastable, that is, the dynamics appear to be stable on some time scale, but are in fact unstable over longer time scales. Consistency of inference for metastable systems may not be possible, but one can ask about metaconsistency: Do inference procedures converge when observations are taken over a large but finite time interval, but diverge on longer time scales? In this paper we introduce, discuss, and quantify metaconsistency in a Bayesian framework. We discuss how metaconsistency can be exploited to efficiently infer a model for a sub-system of a larger system, where inference on the global behavior may require much more data, or there is no theoretical guarantee as to the asymptotic success of inference procedures. We also discuss the relation between metaconsistency and the spectral properties of the model dynamical system in the case of uniformly ergodic and non-ergodic diffusions.