Saddle Point
Back to the cover

Part I · Foundations

  1. 0 Mathematical Foundations
  2. 1 Observation, Beliefs, and Decision

Part II · Engines

  1. 2 Competing for Allocation: The Blotto Game
  2. 3 Bargaining, Commitment, and Repeated Cooperation
  3. 4 Signals, Disclosure, and Persuasion
  4. 5 Different Models of One Game
  5. 6 Leadership and Rules: Inspection
  6. 7 Decisions in Time
  7. 8 Many Agents
  8. 9 Networks, Dependence, and Resilience
  9. 10 Aggregating Information

Part III · Systems

  1. 11 Architecture of Decision Support
  2. 12 Simulation and Wargaming with AI Agents

Part IV · Limits

  1. 13 Where the Mathematics Stops

Chapter 10 · Aggregating Information

Glenn W. Brier

1913 – 1998

The problem on the desk

Weather forecasts expressed as probabilities needed a score that rewarded accuracy without encouraging a forecaster to misstate uncertainty. Brier’s 1950 proposal supplied a quadratic score.1

A life in moments

  1. 1940

    George Washington University · Washington, D.C.

    Completed a master’s degree in statistics with a dissertation on the discriminant function.2

  2. 1950

    United States Weather Bureau · Washington, D.C.

    Published his probability-forecast verification note.3

  3. 1952

    Worked with Isadore Enger on statistical questions in cloud seeding.4

  4. 1955

    Published on the cost/loss ratio with Jack Thompson.4

  5. 1958

    United States Weather Bureau · Washington, D.C.

    Was chief of the Statistics Section when Glahn first worked with him.4

  6. 1990

    Published with Hansen on periodicities associated with El Niño.4

Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.

In their own words

should influence the forecaster in no undesirable way.

The First International Statistical Climatology Achievement Award: Glenn W. Brier (Harry R. Glahn)5

A story

He called it the P-score

Glahn recalls that Brier used the name P-score, even when colleagues were discussing what became widely known by his surname.4

Two desks

Brier and Savage Evaluating reported probabilities. The same problem from two desks →

The card in the book

Statistician at the United States Weather Bureau in Washington, where for many years he headed meteorological statistics (in 1958 he was chief of the Statistics Section in its Office of Meteorological Research); later he was associated with Colorado State University. He worked on the verification and evaluation of forecasts. His 1950 note introduced the quadratic score for probability forecasts that now carries his name; it is summed over all forecast categories, so that the binary score in this chapter is half of his.

Main works “Verification of forecasts expressed in terms of probability” (Monthly Weather Review 78, 1950).

To read further

Sources (5)
  1. The First International Statistical Climatology Achievement Award: Glenn W. Brier, Harry R. Glahn; Discussion of the 1950 paper
  2. The First International Statistical Climatology Achievement Award: Glenn W. Brier, Harry R. Glahn; Education paragraph
  3. Verification of Forecasts Expressed in Terms of Probability, Glenn W. Brier, 1950; Monthly Weather Review 78(1), pp. 1–3; bibliographic record
  4. The First International Statistical Climatology Achievement Award: Glenn W. Brier, Harry R. Glahn; Award remarks; 1958 recollection, 1950 scoring paper and 1955 cost/loss paper
  5. The First International Statistical Climatology Achievement Award: Glenn W. Brier, Harry R. Glahn; Glahn’s quotation attributed to Brier’s forecast-verification writings; exact originating paper not identified

The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.