Upon my return [to academia, after years of private statistical consulting], I started reading the *Annals of Statistics* … and was bemused. Every article started with:

Assume that the data are generated by the following model…

followed by mathematics exploring inference, hypothesis testing, and asymptotics…. I [have a] very low … opinion … of the theory published in the *Annals of Statistics*. [S]tatistics [is] a science that deals with data.

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The linear regression model led to many erroneous conclusions that appeared in journal articles waving the 5% significance level without knowing whether the model fit the data. Nowadays, I think most statisticians will agree that **this is a suspect way to arrive at conclusions.**

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In the mid-1980s … A new research community … sprang up. Their goal was predictive accuracy….. They began working on complex prediction problems where it was obvious that data models were not applicable: speech recognition, image recognition, nonlinear time series prediction, handwriting recognition, prediction in financial markets.

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The advances in methodology and increases in predictive accuracy since the mid-1980s that have occurred in the research of machine learning has been phenomenal…. What has been learned? The three lessons that seem most important:

**• Rashomon:**the multiplicity of good models;-
**• Occam:**the conflict between simplicity and accuracy; -
**• Bellman:**dimensionality — blessing or curse