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Average Power01:13

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In practical electrical applications, the concept of time-varying instantaneous power is not frequently utilized. Instead, focus shifts to the more practical quantity known as average power. Average power is determined by integrating the instantaneous power over a specified time period and subsequently dividing it by that duration.
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On the normalized power prior.

Luiz Max Carvalho1, Joseph G Ibrahim2

  • 1School of Applied Mathematics, Getúlio Vargas Foundation (FGV), Rio de Janeiro, Brazil.

Statistics in Medicine
|October 12, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel bisection-type algorithm for accurately approximating normalizing constants in power prior models. This method enhances Bayesian inference by properly including these constants, crucial for accurate parameter estimation and uncertainty quantification.

Keywords:
doubly intractableelicitationhistorical datanormalizationpower priorsensitivity analysis

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Computational Statistics

Background:

  • The power prior is a widely used method for incorporating historical data into Bayesian analyses.
  • Estimating the discounting factor within a Bayesian framework requires computing a normalizing constant, which is often intractable.
  • Accurate computation of normalizing constants is essential for valid statistical inference.

Purpose of the Study:

  • To develop an efficient algorithm for approximating the normalizing constant in power prior models.
  • To enable joint posterior sampling of model parameters and the discounting factor.
  • To improve the accuracy and reliability of Bayesian inference when using power priors.

Main Methods:

  • Derivation and analysis of properties of the normalizing constant.
  • Development of a bisection-type algorithm for approximating the normalizing constant.
  • Application to various models, including those with intractable normalizing constants.

Main Results:

  • The proposed algorithm accurately approximates the normalizing constant, yielding approximate posteriors close to exact distributions.
  • In intractable cases, the method produces posteriors that better cover data-generating parameters.
  • The algorithm is accurate, easy to implement, and applicable to a broad range of models.

Conclusions:

  • The developed method provides an accurate and accessible approach for handling normalizing constants in power prior models.
  • Properly accounting for the normalizing constant is critical for correct inference and uncertainty quantification.
  • This technique facilitates more robust Bayesian analyses using historical data.