1. Introduction

Where does Sequential Analysis fit

  • It grows out of hypothesis testing, estimation, and decision theory in mathematical statistics.

  • It draws on stochastic processes like Markov chain, martingales, and renewal theory.

  • It expands to modern data science fields in economics, industrial quality control, and clinical trials.

WWII and Sequential Analysis

Read this article Lessons from World War II Statisticians ， and answer the following questions:

  1. In your own words, why would reinforcing the areas with the most holes be a mistake? How does this connect to the general idea of survivorship bias in modern examples (finance, education, or health care)?

  2. A general observed that an experienced officer could often tell early in testing whether new ordnance was much better or worse than expected. How did this observation inspire the idea of sequential testing? Why was it such a breakthrough compared to fixed-sample tests?

History of Sequential Analysis

  • Before the WWII, most testing assumed a fixed sample size.
  • 1940s: Abraham Wald developed the Sequential Probability Ratio Test (SPRT).
  • 1950s - 1980s: Sequential monitoring became a standard practice in clinical trials by the 1980s to save lives and resources.
  • 1980s - 2000s: Sequential methods blended naturally with Bayesian thinking.
  • 2000s - today: A/B testing and online monitoring fit into the big data age.

Summary

Sequential analysis was born in wartime urgency, grew up in industrial efficiency, matured in medical ethics, and now thrives in data science and online experimentation.