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bayesics: Core Statistical Methods via Bayesian Inference in R

Daniel K. Sewell, Alan T. Arakkal

Abstract

Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample inference to general mediation analysis. bayesics leans hard away from the requirement that users be familiar with sampling algorithms by using closed-form solutions whenever possible, and automatically selecting the number of posterior samples required for accurate inference when such solutions are not possible. bayesics} focuses on providing key inferential quantities: point estimates, credible intervals, probability of direction, region of practical equivalance (ROPE), and, when applicable, Bayes factors. While algorithmic assessment is not required in bayesics, model assessment is still critical; towards that, bayesics provides diagnostic plots for parametric inference, including Bayesian p-values. Finally, bayesics provides extensions to models implemented in alternative R packages and, in the case of mediation analysis, correction to existing implementations.

bayesics: Core Statistical Methods via Bayesian Inference in R

Abstract

Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample inference to general mediation analysis. bayesics leans hard away from the requirement that users be familiar with sampling algorithms by using closed-form solutions whenever possible, and automatically selecting the number of posterior samples required for accurate inference when such solutions are not possible. bayesics} focuses on providing key inferential quantities: point estimates, credible intervals, probability of direction, region of practical equivalance (ROPE), and, when applicable, Bayes factors. While algorithmic assessment is not required in bayesics, model assessment is still critical; towards that, bayesics provides diagnostic plots for parametric inference, including Bayesian p-values. Finally, bayesics provides extensions to models implemented in alternative R packages and, in the case of mediation analysis, correction to existing implementations.
Paper Structure (14 sections, 8 equations, 11 figures)

This paper contains 14 sections, 8 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Inference, not Algorithms
  3. What can Bayesians do for you?
  4. Monte Carlo accuracy
  5. bayesics automated approach
  6. Diagnostics and Remediations
  7. Diagnostic plots
  8. Non-parametric methods
  9. Method Extensions and Corrections
  10. Information criteria
  11. Bayesian model averaging
  12. Mediation analysis
  13. Demonstration
  14. Discussion

Figures (11)

  • Figure 1: Proportion of peer-reviewed articles catalogued by Europe PMC that contain either "credible interval" or "confidence interval" from 1981 - 2025.
  • Figure 2: Illustration of the ratio of posterior samples required for the lower credible interval bound vs. the posterior mean to be within the same margin of error. CI levels range from 90% to 99%.
  • Figure 3: Bayesian p-values for regression data generated according to the negative binomial
  • Figure 4: Semi-parametric estimated survival curves for advanced lung cancer, disaggregated by sex.
  • Figure 5: A mis-specified linear regression model fit using a parametric approach and the non-parametric loss-likelihood bootstrap.
  • ...and 6 more figures