# Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models

arXiv: https://arxiv.org/abs/1604.07949 · HTML: https://mlsanity.com/paper/1604.07949/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2016.

## Built on by (most cited first, 5 of 5)

- [Recurrent Neural Networks and Universal Approximation of Bayesian Filters](https://mlsanity.com/paper/2211.00335/) (2022)
- [Sequential Importance Sampling for Hybrid Model Bayesian Inference to Support Bioprocess Mechanism Learning and Robust Control](https://mlsanity.com/paper/2205.02410/) (2022)
- [Dynamic Exploration-Exploitation Trade-Off in Active Learning Regression with Bayesian Hierarchical Modeling](https://mlsanity.com/paper/2304.07665/) (2023)
- [Likelihood-Free Inference in State-Space Models with Unknown Dynamics](https://mlsanity.com/paper/2111.01555/) (2021)
- [Sample-efficient neural likelihood-free Bayesian inference of implicit HMMs](https://mlsanity.com/paper/2405.01737/) (2024)

## Abstract (arXiv)

A computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a 'match' between observed and simulated summaries are retained, and used to estimate the inaccessible posterior. With no reduction to a low-dimensional set of sufficient statistics being possible in the state space setting, we define the summaries as the maximum of an auxiliary likelihood function, and thereby exploit the asymptotic sufficiency of this estimator for the auxiliary parameter vector. We derive conditions under which this approach - including a computationally efficient version based on the auxiliary score - achieves Bayesian consistency. To reduce the well-documented inaccuracy of ABC in multi-parameter settings, we propose the separate treatment of each parameter dimension using an integrated likelihood technique. Three stochastic volatility models for which exact Bayesian inference is either computationally challenging, or infeasible, are used for illustration. We demonstrate that our approach compares favorably against an extensive set of approximate and exact comparators. An empirical illustration completes the paper.