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LIT-1525: Bayesian Experimental Design: A Review

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StatusActive — read 2026-10-25 (NOTE-1161) in full, from the authors' Technical Report #607 (University of Minnesota, July 1995) in the University of Minnesota Digital Conservancy; worth reading for Lindley's decision-theoretic formulation of design, for the derivation of Bayes D- and A-optimality from Shannon information and quadratic loss in the normal linear model (THEORY-956), and for the account of nonlinear design as prior-averaged local criteria, with local optimality as the point-mass case and its failure for the turning point (THEORY-954). Read it knowing that it is a 1995 survey, mostly of normal linear models, that its nonlinear criteria are approximations of unknown accuracy, that its treatment of model discrimination is brief, and that the copy read is the technical report, with equations lost to OCR, not the journal text.
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Tagsmathematical-statistics, probabilistic-modeling
Cited as “paper” byNOTE-1161 — Chaloner and Verdinelli — Bayesian experimental design: a review
Cited as “source” byTHEORY-954 — When the information a design yields depends on the unknown parameter, as in nonlinear models or nonlinear functions of linear ones, Bayesian design criteria are normal approximations to expected utility that average a local criterion over the prior, such as the expected log det of the Fisher information, and locally optimal design is the special case of a point-mass prior; a locally optimal design can leave the quantity of interest inestimable, as for the turning point of a quadratic regression on [−1, 1] with best guess ½, where the locally c-optimal design puts half its mass at 0 and half at 1 and identifies only θ₁ + θ₂, THEORY-956 — In the normal linear model with known error variance and a conjugate normal prior of precision R/σ², the design that maximizes the expected Shannon information of the posterior is the one maximizing det(nM(η) + R), Bayes D-optimality, and the design that minimizes expected quadratic loss with weight matrix A is the one minimizing tr A(nM(η) + R)^-1, Bayes A-optimality; both criteria depend on the design and not on the data, so in this model a sequential design gains nothing over the best fixed one

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Chaloner, K. & Verdinelli, I. (1995). Bayesian experimental design: A review. Statistical Science 10(3): 273–304. doi:10.1214/ss/1177009939.

Read 2026-10-25 in full (NOTE-1161), from the authors’ technical report of July 1995, not compared with the journal text. The summary was checked against it.

Why this is here

Cited at U29, in reply to the owner’s question whether the exchange had turned up content that would improve the record’s mathematical toolkit, as the theory for choosing which probes to put to an organization: given the Fisher information of each probe, choose the design that maximizes what the responses reveal about the allocation of authority. The record asks which probes distinguish organizations (CASE-124) but held no work on how to choose them. The construction CASE-159 computes the quantity a design would maximize, including the rare-context probe that A31 proposed.

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