Bayesian Data Analysis¶
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis. Chapman and Hall.
Cited by¶
6 citations across 6 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Bayesian Updating
- The iterative update structure across observations
This sourceCanonical Bayesian reference: develops sequential/iterative updating (posterior becomes prior for the next datum), credible intervals, hierarchical models, and Bayesian adaptive designs (dose-finding, interim analysis, early stopping). SUPPORTS markers 005 (iterative update structure), 008 (adaptive Bayesian trial designs), and 012 (credible intervals + sequential evidence integration as operational decision support).
- The iterative update structure across observations
- Measurement Uncertainty and Observational Noise
- Interpreting results requires Bayesian reasoning: the measured value (e.g., a positive test) depends on both the true state (disease present or absent) and the test's noise characteristics (false positive and false negative rates), a posterior-update logic Gelman et al. (2013) develop systematically in their canonical Bayesian Data Analysis treatment.
This sourceCanonical Bayesian reference: develops posterior inference (including diagnostic-test interpretation) that combines prior probability of true state with likelihood under known measurement noise characteristics (sensitivity, specificity).
- Interpreting results requires Bayesian reasoning: the measured value (e.g., a positive test) depends on both the true state (disease present or absent) and the test's noise characteristics (false positive and false negative rates), a posterior-update logic Gelman et al. (2013) develop systematically in their canonical Bayesian Data Analysis treatment.
- Precision Weighting
- In Bayesian inference, Gaussian posterior beliefs combine prior and likelihood by precision.
This sourceDerives the Gaussian posterior mean as the precision-weighted average of prior and likelihood, with precisions adding.
- In Bayesian inference, Gaussian posterior beliefs combine prior and likelihood by precision.
Domain-specific¶
Mechanisms¶
- Bayesian Model Update
- Garbage priors or a misspecified likelihood yield confident nonsense — the tidy posterior lends false authority to assumptions no one checked.
This sourceEmphasizes that Bayesian inferences are conditional on the prior and likelihood and require model checking and sensitivity analysis because a precise posterior does not validate misspecified assumptions.
- Garbage priors or a misspecified likelihood yield confident nonsense — the tidy posterior lends false authority to assumptions no one checked.
Verification¶
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