Model Expansion Under Surprise¶

Why It Matters¶

Standard Bayesian updating assumes your hypothesis space is complete - the truth is somewhere in your partition. But this is often false. When genuinely surprising evidence arrives (not just unlikely, but "I didn't think this was possible"), updating within your model entrenches error. Model expansion is the escape valve: sometimes "none of my hypotheses is right" and you need new ones. Recognizing when to expand versus when to update is crucial for avoiding dogmatism.

The Key Move¶

After seeing evidence, ask: "How surprised am I, really?" If evidence was unlikely but within the range you'd imagined, do standard Bayesian updating. If evidence seems to violate assumptions underlying your entire model, pause before updating. Ask: "What hypothesis would make this evidence unsurprising?" Generate new possibilities you'd previously discarded as implausible or hadn't imagined. Add them to your partition with non-zero prior probability. Then update. This converts surprise into model improvement.

Classic Application¶

Scientific anomalies. Michelson-Morley experiment found no evidence of luminiferous ether. This wasn't just "ether has different properties than we thought" (update within model) - it was "ether doesn't exist, and light propagation works differently than we imagined" (model expansion). The evidence was so surprising under all existing hypotheses that it demanded expanding the hypothesis space to include special relativity. Kuhnian paradigm shifts are model expansions.

Surprising Application¶

Debugging beliefs about people. Someone you trusted betrays you (high surprise). Standard updating: "I was wrong about their trustworthiness" (update probability within "trustworthy/untrustworthy" model). Model expansion: maybe your model of trustworthiness is incomplete. Perhaps "trustworthy in domain X but not Y" or "trustworthy unless under specific pressures" are hypotheses you hadn't considered. The surprise signals that your binary model is inadequate - expand it to capture context-dependent reliability. This is more accurate than just lowering trust generally.

Failure Modes¶

Excessive model expansion - every small surprise doesn't require new hypotheses; you need judgment about when surprise is genuine. Confirmation of prior beliefs - using "surprise" to discard evidence that contradicts you rather than expanding honestly. Unfalsifiable expansion - adding "magic happens" hypotheses that explain everything. Computational explosion - richer models are harder to reason about; there's a complexity-accuracy tradeoff.

Go Deeper¶

Jaynes, Probability Theory: The Logic of Science, Chapter 18 on model comparison; Kuhn, Structure of Scientific Revolutions on paradigm shifts as model expansions.

Bayesian Updating - Information Economics: Reasoning Under Asymmetry and Uncertainty
Surprise - Military Strategy & Strategic Thinking: A Map of the Territory