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  2. Simulation-based Calibration Checking For Bayesian Computation: The Choice Of Test Quantities Shapes Sensitivity.
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Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity.

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View abstract on PubMed

Summary
This summary is machine-generated.

We introduce a new simulation-based calibration checking (SBC) method to validate posterior distributions. This enhanced approach detects more issues than previous methods, including when the posterior equals the prior, by using new data-dependent test quantities.

Keywords:
62C10calibrationprobabilistic programmingsoftware testing

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Area of Science:

  • Computational Statistics
  • Bayesian Inference

Background:

  • Simulation-based calibration checking (SBC) is crucial for validating posterior distributions from computational models.
  • Existing SBC methods have limitations in detecting certain classes of posterior distribution errors, such as when the posterior is indistinguishable from the prior.

Purpose of the Study:

  • To introduce a novel variant of simulation-based calibration checking (SBC) that enhances the detection of errors in posterior distributions.
  • To address limitations of previous SBC implementations, enabling the identification of a broader range of potential issues.

Main Methods:

  • Development of a new SBC variant incorporating additional data-dependent test quantities.
  • Theoretical analysis of the enhanced SBC method to understand its statistical underpinnings.
  • Investigation of the joint likelihood of the data as a key test quantity.
  • Numerical case studies using a multivariate normal distribution and an ordered simplex data type with Hamiltonian Monte Carlo.
  • Main Results:

    • The proposed SBC variant can detect a wider range of posterior distribution problems compared to existing methods.
    • The joint likelihood of the data is demonstrated as a powerful test quantity for SBC.
    • Theoretical analysis provides a deeper understanding of SBC mechanisms.
    • Case studies validate the practical utility and effectiveness of the new SBC approach.

    Conclusions:

    • The enhanced SBC variant offers a more comprehensive validation of posterior distributions in computational statistics.
    • The inclusion of specific data-dependent test quantities significantly improves the diagnostic power of SBC.
    • This work clarifies common misconceptions and provides a robust tool for Bayesian inference validation.