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The Splendors and Miseries of MartingalesEncounters with Martingales in Statistics and Stochastic Optimization

The Splendors and Miseries of Martingales: Encounters with Martingales in Statistics and... [In this intellectual memoir, Professor Lai describes how martingales came into his world of mathematical statistics, first in sequential tests and confidence intervals, then in time series, stochastic approximation, sequential design of experiments, and stochastic optimization. He sketches the trajectories of many other statisticians that he met along the way. He emphasizes the roles of Harold Hotelling, Abraham Wald, and Herbert Robbins in their creation of the environment for the study of martingales at Columbia University and then his own subsequent work at Stanford University. At Stanford, he came to see stochastic optimization as a unifying theme for the use of martingales in statistical modeling. In conclusion, he describes the multifaceted applications of martingales to statistics and stochastic optimization in the BigData and MultiCloud era.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesEncounters with Martingales in Statistics and Stochastic Optimization

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn

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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05987-2
Pages
265 –293
DOI
10.1007/978-3-031-05988-9_12
Publisher site
See Chapter on Publisher Site

Abstract

[In this intellectual memoir, Professor Lai describes how martingales came into his world of mathematical statistics, first in sequential tests and confidence intervals, then in time series, stochastic approximation, sequential design of experiments, and stochastic optimization. He sketches the trajectories of many other statisticians that he met along the way. He emphasizes the roles of Harold Hotelling, Abraham Wald, and Herbert Robbins in their creation of the environment for the study of martingales at Columbia University and then his own subsequent work at Stanford University. At Stanford, he came to see stochastic optimization as a unifying theme for the use of martingales in statistical modeling. In conclusion, he describes the multifaceted applications of martingales to statistics and stochastic optimization in the BigData and MultiCloud era.]

Published: Oct 18, 2022

Keywords: Martingales; Harold Hotelling; Joseph Doob; Abraham Wald; Herbert Robbins; Sequential experimental design; Stochastic approximation; Multi-armed bandits; Hidden Markov models; Particle filters

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