Index: Concept Notes - Value of Information and Adaptive Decisions

Concept Notes - Value of Information and Adaptive Decisions

Routing Summary

Six concept notes (no raw source; each cites the literature) tying the ingested papers to the PyMC examples E87, E89, E92, E100 and E16: EVSI and the VoI hierarchy, pricing a model, EVSI-based monitor siting with known measurement error, when an exact GP earns its price, adaptive sampling on a noisy belief, and choosing an uncertainty display.

• Need EVPI, EVPPI, EVSI definitions or the normal closed form? → Value of Information Concept Note - EVPI, EVPPI and EVSI
• Need to decide whether a model or forecast is worth buying (E87)? → Value of Information Concept Note - Pricing a Model with EVPI
• Need EVSI of a monitor reading with known error (E89)? → Value of Information Concept Note - Kriging with Known Measurement Error and EVSI for Monitor Siting
• Need cost arithmetic and a decision test for exact versus approximate GPs (E92)? → Value of Information Concept Note - When an Exact Gaussian Process Earns Its Price
• Need UCB, Thompson sampling or replay evaluation for adaptive surveys (E100)? → Value of Information Concept Note - Adaptive Sampling and Acting on a Noisy Belief
• Need which uncertainty display fits which question (E16)? → Value of Information Concept Note - Showing Uncertainty and Choosing a Display

Concept Map

Concept	Note	Type	Depends On	Key Result
VoI hierarchy	Value of Information Concept Note - EVPI, EVPPI and EVSI	theorem	Heath 2015 - Net Benefit, EVPI and EVPPI Definitions	$0\le \text{EVSI}\le \text{EVPPI}\le \text{EVPI}$
EVSI normal closed form	Value of Information Concept Note - EVPI, EVPPI and EVSI	theorem	hierarchy	$\tau \phi (m/\tau )+m\Phi (m/\tau )-\max (m,0)$
Model purchase rule	Value of Information Concept Note - Pricing a Model with EVPI	definition	EVSI	buy iff EVSI exceeds price
Site EVSI	Value of Information Concept Note - Kriging with Known Measurement Error and EVSI for Monitor Siting	theorem	normal closed form, GP posterior	largest near threshold and large variance shrink
Exact-vs-approximate criterion	Value of Information Concept Note - When an Exact Gaussian Process Earns Its Price	theorem	GP cost	decision regret vs price gap
Adaptive policy	Value of Information Concept Note - Adaptive Sampling and Acting on a Noisy Belief	definition	acquisition functions	adaptivity free when variance-only and kernel known
Epistemic vs predictive band	Value of Information Concept Note - Showing Uncertainty and Choosing a Display	definition	posterior predictive	band is not a set of curves

Notes

• Value of Information Concept Note - EVPI, EVPPI and EVSI — CONTAINS: EVPI/EVPPI/EVSI definitions, hierarchy proof sketch, normal closed form with verified table, Python, ENBS.
• Value of Information Concept Note - Pricing a Model with EVPI — CONTAINS: model-purchase rule, price ceiling theorem, compute arithmetic, worked ENBS example.
• Value of Information Concept Note - Kriging with Known Measurement Error and EVSI for Monitor Siting — CONTAINS: kriging with noise, site EVSI formula, greedy and submodularity caveat, verified example.
• Value of Information Concept Note - When an Exact Gaussian Process Earns Its Price — CONTAINS: cost arithmetic for n=23,939, alternatives, decision-regret criterion.
• Value of Information Concept Note - Adaptive Sampling and Acting on a Noisy Belief — CONTAINS: UCB, Thompson, adaptivity result, replay evaluation.
• Value of Information Concept Note - Showing Uncertainty and Choosing a Display — CONTAINS: question-to-display table, epistemic vs predictive, band-vs-curve theorem.

Sources

• No raw PDFs. Literature cited inside each note (several citations from memory and marked “verify”). Example method strings from https://redam94.github.io/pymc-challenges/examples.html.

See Also

• Heath 2015 - Review of Expected Value of Information Methods - Overview, Vickers 2019 - Step-by-Step Guide to Decision Curve Analysis - Overview, Krause 2008 - Near-Optimal Sensor Placements in Gaussian Processes - Overview, Kay 2016 - When-ish is My Bus - Overview, Hullman 2015 - Hypothetical Outcome Plots - Overview.