期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 115, 期 8, 页码 1760-1765出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1715306115
关键词
effective theory; model selection; renormalization group; Bayesian prior choice; information theory
资金
- NIH [R01GM107103]
- National Science Foundation (NSF)-Energy, Power, and Control Networks [1710727]
- Lewis-Sigler Fellowship
- NSF Division of Physics [0957573]
- Narodowe Centrum Nauki Grant [2012/06/A/ST2/00396]
- Direct For Mathematical & Physical Scien
- Division Of Physics [0957573] Funding Source: National Science Foundation
- Div Of Electrical, Commun & Cyber Sys
- Directorate For Engineering [1710727] Funding Source: National Science Foundation
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter space. Thus, it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there are sufficient data to tightly constrain any number of parameters, this reduces to the Jeffreys prior. However, we argue that this limit is pathological when applied to the hyperribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.
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