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
Figure 1

The small but crucial insight is that inference is relative to 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 me catching a rhinovirus is no biggie, but a 1% chance of a global nuclear war is a biggie. We don’t want to guess what is true; we want to guess what is useful, and that depends on the consequences of being wrong.

This sounds obvious, but failures to take this into account are ubiquitous even amongst 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.