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Stochastic approximation cut algorithm for inference in modularized Bayesian models.

Yang Liu1, Robert J B Goudie1

  • 1MRC Biostatistics Unit, University of Cambridge, Cambridge, UK.

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Summary
This summary is machine-generated.

We introduce the stochastic approximation cut (SACut) algorithm for Bayesian modeling. SACut addresses concerns with model misspecification by providing a convergent and computationally efficient method for sampling from complex distributions.

Keywords:
Cutting feedbackDiscretizationIntractable normalizing functionsStochastic approximation Monte Carlo

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Area of Science:

  • Statistics
  • Computational Statistics
  • Bayesian Inference

Background:

  • Bayesian modeling is powerful for complex data but vulnerable to model misspecification.
  • Modularizing models with cut models helps isolate suspect components.
  • Existing sampling algorithms for cut distributions lack clear convergence guarantees.

Purpose of the Study:

  • To propose a novel algorithm for sampling from cut distributions in Bayesian models.
  • To provide theoretical convergence guarantees for the sampling process.
  • To offer a computationally efficient and parallelizable alternative to existing methods.

Main Methods:

  • Developed the stochastic approximation cut (SACut) algorithm with two parallel chains.
  • The main chain approximates the cut distribution; the auxiliary chain adapts proposals.
  • Proved theoretical convergence properties and the exact limit of the algorithm's samples.

Main Results:

  • Demonstrated convergence of samples generated by the SACut algorithm.
  • Showed that bias in SACut can be geometrically reduced by adjusting a tuning parameter.
  • Highlighted the suitability of SACut for parallel computing, reducing overall computation time.

Conclusions:

  • The SACut algorithm offers a theoretically sound and practically efficient method for Bayesian inference with partially misspecified models.
  • SACut provides a robust approach to handling complex distributions arising from model modularization.
  • The algorithm's parallelizability and tunable bias reduction make it a valuable tool for complex statistical modeling.