Essentials of Probability Theory for Statisticians

ISBN-13: 9780367871635 / Angielski / Miękka / 2019 / 328 str.

Michael A. Proschan; Pamela A. Shaw

Opis

This text provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes b

Spis treści

Introduction. Size Matters. The Elements of Probability Theory. Random Variables and Vectors. Integration and Expectation. Modes of Convergence. Laws of Large Numbers. Central Limit Theorems. More on Convergence in Distribution. Conditional Probability and Expectation. Applications. Appendices. Index.

O autorze

Michael A. Proschan is a mathematical statistician in the Biostatistics Research Branch at the U.S. National Institute of Allergy and Infectious Diseases (NIAID). A fellow of the American Statistical Association, Dr. Proschan has published more than 100 articles in numerous peer-reviewed journals. His research interests include monitoring clinical trials, adaptive methods, permutation tests, and probability. He earned a PhD in statistics from Florida State University.

Pamela A. Shaw is an assistant professor of biostatistics in the Department of Biostatistics and Epidemiology at the University of Pennsylvania Perelman School of Medicine. Dr. Shaw has published several articles in numerous peer-reviewed journals. Her research interests include methodology to address covariate and outcome measurement error, the evaluation of diagnostic tests, and the design of medical studies. She earned a PhD in biostatistics from the University of Washington.