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Likelihood-free Bayesian inference (LFBI) algorithms can be computationally expensive. This study introduces a multifidelity approach to reduce simulation costs in LFBI, achieving near-optimal efficiency for parameter inference.

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Area of Science:

  • Computational Statistics
  • Bayesian Inference
  • Stochastic Modeling

Background:

  • Likelihood-free Bayesian inference (LFBI) algorithms are crucial for complex stochastic models but demand extensive simulations.
  • High computational costs limit the feasibility of traditional LFBI in many practical scenarios.
  • Multifidelity methods offer a potential solution by incorporating cheaper, approximate models.

Purpose of the Study:

  • To demonstrate the applicability of multifidelity techniques within the general LFBI framework.
  • To derive analytical results for optimal resource allocation across different simulation fidelities.
  • To develop an adaptive multifidelity LFBI algorithm for efficient parameter inference.

Main Methods:

  • Derivation of analytical results for optimal computational resource allocation in multifidelity simulations.
  • Practical implementation of these analytical findings.
  • Development of an adaptive algorithm that learns inter-fidelity model relationships and adjusts resource allocation.

Main Results:

  • Successful application of multifidelity techniques to general LFBI.
  • Demonstration of near-optimal efficiency in posterior estimation using the proposed adaptive algorithm.
  • Validation of the derived analytical results on optimal resource allocation.

Conclusions:

  • Multifidelity approaches significantly reduce the computational burden of LFBI.
  • The adaptive multifidelity LFBI algorithm provides efficient and accurate parameter inference.
  • This work enables the application of LFBI to a wider range of computationally intensive problems.