The Prior Can Often Only Be Understood in the Context of the Likelihood
By Andrew Gelman, Daniel P. Simpson, Michael Betancourt. Entropy, 2017
481 citations recorded by the source corpus.
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys’ priors, reference priors, maximum entropy priors, and weakly informative priors. These methods, however, often manifest a key conceptual tension in prior modeling: a model encoding true prior information should be chosen without reference to the model of the measurement process, but almost all common prior modeling techniques are implicitly motivated by a reference likelihood. In this paper we resolve this apparent paradox by placing the choice of prior into the context of the entire Bayesian analysis, from inference to prediction to model evaluation.
Subfields: Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/d6aec3a33b61987c5b18973e9cc46d6b9ae66767
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Management Science and Operations Research
- Paul-Christian Burkner
- Charles C. Margossian
- Andrew Gelman
- Jonah Gabry
- Daniel P. Simpson
- Aki Vehtari
- Yuling Yao
In Statistics and Probability
- Paul-Christian Burkner
- Aki Vehtari
- Andrew Gelman
- Yuling Yao
- Daniel P. Simpson
- Charles C. Margossian
- Jonah Gabry
- Bob Carpenter
Citations in the corpus
- Bayesian Workflow (2020, background): “…of the joint prior over all the parameters in a model, to be assessed in the context of the generative model for the data, lest unfortunate cancellations or resonances lead to less stabilizing or more informative priors than the modeler actually wants (Gelman et al., 2017, Kennedy et al., 2019).”
- Bayesian Item Response Modeling in R with brms and Stan (2019, background): “Rather, the prior can only be understood in the context of the model it is a part of (Gelman et al. 2017).”
- Visualization in Bayesian workflow (2017, background): “This is a vital component of understanding how prior distributions actually work for a given problem (Gelman et al., 2017).”