Decision theory

August 23, 2014 — October 4, 2024

algebra
Bayes
decision theory
functional analysis
Hilbert space
how do science
linear algebra
machine learning
model selection
nonparametric
statistics
uncertainty
utility

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Figure 1

The small but crucial insight is that inference depends on what you do with it; a 1% chance of rain is a big deal if you’re a farmer, but not if you’re a city slicker. A 1% chance of catching a rhinovirus is no biggie, but a 1% chance of a global nuclear war is a big deal. We don’t want to guess what is true; we want to guess what is useful, which depends on the consequences of being wrong.

This sounds obvious, but ignoring this is common, even among scientists. I’ve seen things.

1 In classification

This simple but crucial case is the most important one for most people.

(Ferrer 2023; Provost and Fawcett 2001; Dyrland, Lundervold, and Mana 2023b; Suzuki 2022).

TBC

2 Incoming

3 References

Binmore. 2009. Rational Decisions. The Gorman Lectures in Economics.
Dyrland, Lundervold, and Mana. 2023a. “Does the Evaluation Stand up to Evaluation? A First-Principle Approach to the Evaluation of Classifiers.”
———. 2023b. “Don’t Guess What’s True: Choose What’s Optimal. A Probability Transducer for Machine-Learning Classifiers.”
Feldman, and Choi. 2022. “Meaning and Reference from a Probabilistic Point of View.” Cognition.
Fernández-Loría, and Provost. 2021. “Causal Decision Making and Causal Effect Estimation Are Not the Same… and Why It Matters.” arXiv:2104.04103 [Cs, Stat].
Ferrer. 2023. “Analysis and Comparison of Classification Metrics.”
Provost, and Fawcett. 2001. “Robust Classification for Imprecise Environments.” Machine Learning.
Raiffa. 2002. “Decision Analysis: A Personal Account of How It Got Started and Evolved.” Oper. Res.
Raiffa, and Schlaifer. 2000. Applied Statistical Decision Theory. Wiley Classics Library.
Robert. 2007. The Bayesian choice: from decision-theoretic foundations to computational implementation. Springer texts in statistics.
Rothblum, and Yona. 2022. “Decision-Making Under Miscalibration.” arXiv:2203.09852 [Cs].
Suzuki. 2022. “Policy Implications of Statistical Estimates: A General Bayesian Decision-Theoretic Model for Binary Outcomes.” Statistics and Public Policy.