Likelihood-free inference in state-space models with unknown dynamics

Alexander Aushev*, Thong Tran, Henri Pesonen, Andrew Howes, Samuel Kaski

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
25 Downloads (Pure)


Likelihood-free inference (LFI) has been successfully applied to state-space models, where the likelihood of observations is not available but synthetic observations generated by a black-box simulator can be used for inference instead. However, much of the research up to now has been restricted to cases in which a model of state transition dynamics can be formulated in advance and the simulation budget is unrestricted. These methods fail to address the problem of state inference when simulations are computationally expensive and the Markovian state transition dynamics are undefined. The approach proposed in this manuscript enables LFI of states with a limited number of simulations by estimating the transition dynamics and using state predictions as proposals for simulations. In the experiments with non-stationary user models, the proposed method demonstrates significant improvement in accuracy for both state inference and prediction, where a multi-output Gaussian process is used for LFI of states and a Bayesian neural network as a surrogate model of transition dynamics.

Original languageEnglish
Article number27
Issue number1
Early online date3 Nov 2023
Publication statusPublished - Feb 2024
MoE publication typeA1 Journal article-refereed


  • Bayesian optimisation
  • Likelihood-free inference
  • Multi-objective optimisation
  • Non-linear dynamics
  • Simulator-based inference
  • State-space models


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