Foundations of Agnostic Statistics

Front Cover
Cambridge University Press, Jan 31, 2019 - Mathematics - 314 pages
Reflecting a sea change in how empirical research has been conducted over the past three decades, Foundations of Agnostic Statistics presents an innovative treatment of modern statistical theory for the social and health sciences. This book develops the fundamentals of what the authors call agnostic statistics, which considers what can be learned about the world without assuming that there exists a simple generative model that can be known to be true. Aronow and Miller provide the foundations for statistical inference for researchers unwilling to make assumptions beyond what they or their audience would find credible. Building from first principles, the book covers topics including estimation theory, regression, maximum likelihood, missing data, and causal inference. Using these principles, readers will be able to formally articulate their targets of inquiry, distinguish substantive assumptions from statistical assumptions, and ultimately engage in cutting-edge quantitative empirical research that contributes to human knowledge.
 

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Contents

1
5
Summarizing Distributions
44
1
66
Learning from Random Samples
91
4
107
9
126
Regression
143
14
145
Parametric Models
178
Missing Data
207
21
232
Causal Inference
235
Glossary of Mathematical Notation
282
References
288
30
289
36
295

18
173

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About the author (2019)

Peter M. Aronow is an Associate Professor of Political Science, Public Health (Biostatistics), and Statistics and Data Science at Yale University, Connecticut and is affiliated with the University's Institution for Social and Policy Studies, Center for the Study of American Politics, Institute for Network Science, and Operations Research Doctoral Program.

Benjamin T. Miller is a doctoral candidate in Political Science at Yale University, Connecticut. In 2012, Mr Miller received a B.A. in Economics and Mathematics from Amherst College.

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