This week we'll see the baptism of statistics by mathematicians, in the form a new field: "mathematical statistics". Intellectual decendents of Galton, Yule, and company feature prominently.

31 pages: sections 3.4 3.6 3.7 from "The Empire of Chance"

after this please do briefly read the primary sources:

Fisher defining science: approx 10 "real" pages: "The Design of Experiments", originally 1935, excerpt from a 1971 reprint ( see https://en.wikipedia.org/wiki/The_Design_of_Experiments ). According to the OED this introduced the term "null hypothesis."

Then, copious tea-spilling between Fisher and adversaries: ( https://en.wikipedia.org/wiki/Ronald_Fisher ) vs https://en.wikipedia.org/wiki/Jerzy_Neyman and https://en.wikipedia.org/wiki/Egon_Pearson (son of https://en.wikipedia.org/wiki/Karl_Pearson )

9 real pages: Fisher, R. A. (1955), "Statistical Methods and Scientific Induction". Journal of The Royal Statistical Society (B) 17: 69-78.

3 pages: Pearson, E. S. (1955), "Statistical Concepts in Their Relation to Reality," Journal of the Royal Statistical Society, B, 17: 204-207.

6 real pages: Neyman, J. (1956), "Note on an Article by Sir Ronald Fisher," Journal of the Royal Statistical Society. Series B (Methodological), 18: 288-294.

• Bayes
• art
• cookbook

• eugenics
• WWII, institutions (following GG)

• academic baptism
• ghost of Bayes past, present, future

• the scientist
  • "Eugenics was indeed Fisher's driving motivation"
  • Uncertainty as probability (as opposed to enumeration of cases)
• the hypothesis test
  • "cannot be reduced to a mechanical process"
  • "nuances...not picked up by Fisher's readers"
  • never looks at $p(D|M)$, "statistician's imagination"

• the mathematicians
  • N loved rigor
  • "errors of the second kind"
  • RAF fight with KP
• hybridization

Fisher’s theory of significance testing, which was historically first, was merged with concepts from the Neyman-Pearson theory and taught as ‘statistics’ per se. We call this compromise the “hybrid theory” of statistical inference, and it goes without saying that neither Fisher nor Neyman and Pearson would have looked with favor on this offspring of their forced marriage.

• Sci-Am piece
• Bayesian primer

• academics
• X-statistics
• consultants
• expert witnesses
• math envy from RAF
• science envy from KP "grammar of science"

Note: these 3 readings are doing a lot of work, summarizing in 3 letters 50 years of, as one student put it:

active challenging of ideas between mathematicians and statisticians.

Also:

The readings for this week were very dense.

All in all, the readings from this week felt a bit dense and hard to follow,

Oh man, very dense reading

• F vs PN (and all bayesians): who?
• rhetoric and posturing: why? why can't i just math it?
• Bayes rule, e.g., in Bayes field of application

• "Statistical Laboratories":
  • Galton, KP, ... Neyman
  • Iowa
• "Statistics goes to war"

how did this capability rearrange power? who can now do what, from what, to whom?

• contemporary debates:
  • NIH elaboration
  • ASA
  • Gigerenzer 2018
  • XKCD

role of rights, harms, justice?

---

sections 3.4 3.6 3.7 from "The Empire of Chance"

after this please do briefly read the primary sources:

Fisher, R. A. (1955), "Statistical Methods and Scientific Induction". Journal of The Royal Statistical Society (B) 17: 69-78.

Neyman, J. (1956), "Note on an Article by Sir Ronald Fisher," Journal of the Royal Statistical Society. Series B (Methodological), 18: 288-294.

Pearson, E. S. (1955), "Statistical Concepts in Their Relation to Reality," Journal of the Royal Statistical Society, B, 17: 204-207.

• Inference Experts: ONLY 3.4 3.6 3.7 are required

• Fisher, R. A. (1955), "Statistical Methods and Scientific Induction". Journal of The Royal Statistical Society (B) 17: 69-78.

• Neyman, J. (1956), "Note on an Article by Sir Ronald Fisher," Journal of the Royal Statistical Society. Series B (Methodological), 18: 288-294.

• Pearson, E. S. (1955), "Statistical Concepts in Their Relation to Reality," Journal of the Royal Statistical Society, B, 17: 204-207.

• bitter rivalry with Neyman and Pearson
• a scientist, not just a mathematician
  • claimed that Neyman and Pearson were mathematicians with insufficient real world experience
• did not view failure to reject null hypothesis (type II error) as an error
  • basically doesn't view failure to reject null hypothesis as a final decision
• agreed with Neyman and Pearson on one point: Bayesians were wrong

• more mathematically rigorous: formalized hypothesis testing, type I & II errors, power of tests
• notable result is Neyman-Pearson lemma, which identifies the most powerful test at a given significance level
• rejected probabilistic interpretation of power of hypothesis tests. Hence the use of the term power