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Computing Bayes factors from data with missing values.

Herbert Hoijtink1, Xin Gu2, Joris Mulder1

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This summary is machine-generated.

This study introduces a method for calculating Bayes factors with missing data using multiple imputation. This approach ensures the Bayes factor relies solely on observed data, unlike single imputation methods which are inaccurate.

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Area of Science:

  • Statistics
  • Hypothesis Testing
  • Computational Statistics

Background:

  • Bayes factors are crucial for hypothesis evaluation, accommodating both traditional and informative hypotheses.
  • Existing methods for Bayes factor computation do not address datasets with missing values.
  • A critical requirement for Bayes factors with missing data is that they must only use observed information.

Purpose of the Study:

  • To develop a method for computing Bayes factors from data containing missing values.
  • To ensure the computed Bayes factor is based exclusively on the observed data.
  • To demonstrate the utility of multiple imputation for this purpose.

Main Methods:

  • The study proposes using multiple imputation techniques to handle missing data in Bayes factor calculations.
  • A general framework is established, with specific elaborations for default, subjective, and training data-derived prior distributions.
  • The approach is implemented using R packages, combining multiple imputation tools with Bayes factor packages like Bain and BayesFactor.

Main Results:

  • Multiple imputation provides a valid method for computing Bayes factors when data are missing.
  • The proposed method ensures that the Bayes factor computation is based solely on the observed values.
  • Bayes factors calculated using single imputation are shown to be highly inaccurate approximations.

Conclusions:

  • Multiple imputation is a reliable technique for calculating Bayes factors in the presence of missing data.
  • This method allows for accurate hypothesis evaluation using all available observed information.
  • Researchers can leverage existing R packages to implement this approach effectively.