Principles of Uncertainty

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kadane, Joseph B.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Milton : CRC Press LLC, 2020.
Edición:2nd ed.
Colección:Chapman and Hall/CRC Texts in Statistical Science Ser.
Temas:
Bayesian statistical decision theory.
Mathematical statistics.
Théorie de la décision bayésienne.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Dedication
  • Table of Contents
  • List of Figures
  • List of Tables
  • Foreword
  • Preface
  • 1 Probability
  • 1.1 Avoiding being a sure loser
  • 1.1.1 Interpretation
  • 1.1.2 Notes and other views
  • 1.1.3 Summary
  • 1.1.4 Exercises
  • 1.2 Disjoint events
  • 1.2.1 Summary
  • 1.2.2 A supplement on induction
  • 1.2.3 A supplement on indexed mathematical expressions
  • 1.2.4 Intersections of events
  • 1.2.5 Summary
  • 1.2.6 Exercises
  • 1.3 Events not necessarily disjoint
  • 1.3.1 A supplement on proofs of set inclusion
  • 1.3.2 Boole's Inequality
  • 1.3.3 Summary
  • 1.3.4 Exercises
  • 1.4 Random variables, also known as uncertain quantities
  • 1.4.1 Summary
  • 1.4.2 Exercises
  • 1.5 Finite number of values
  • 1.5.1 Summary
  • 1.5.2 Exercises
  • 1.6 Other properties of expectation
  • 1.6.1 Summary
  • 1.6.2 Exercises
  • 1.7 Coherence implies not a sure loser
  • 1.7.1 Summary
  • 1.7.2 Exercises
  • 1.8 Expectations and limits
  • 1.8.1 A supplement on limits
  • 1.8.2 Resuming the discussion of expectations and limits
  • 1.8.3 Reference
  • 1.8.4 Exercises
  • 2 Conditional Probability and Bayes Theorem
  • 2.1 Conditional probability
  • 2.1.1 Summary
  • 2.1.2 Exercises
  • 2.2 The birthday problem
  • 2.2.1 Exercises
  • 2.2.2 A supplement on computing
  • 2.2.3 References
  • 2.2.4 Exercises
  • 2.3 Simpson's Paradox
  • 2.3.1 Notes
  • 2.3.2 Exercises
  • 2.4 Bayes Theorem
  • 2.4.1 Notes and other views
  • 2.4.2 Exercises
  • 2.5 Independence of events
  • 2.5.1 Summary
  • 2.5.2 Exercises
  • 2.6 The Monty Hall problem
  • 2.6.1 Exercises
  • 2.7 Gambler's Ruin problem
  • 2.7.1 Changing stakes
  • 2.7.2 Summary
  • 2.7.3 References
  • 2.7.4 Exercises
  • 2.8 Iterated expectations and independence
  • 2.8.1 Summary
  • 2.8.2 Exercises
  • 2.9 The binomial and multinomial distributions
  • 2.9.1 Refining and coarsening
  • 2.9.2 Why these distributions have these names
  • 2.9.3 Summary
  • 2.9.4 Exercises
  • 2.10 Sampling without replacement
  • 2.10.1 Polya's Urn Scheme
  • 2.10.2 Summary
  • 2.10.3 References
  • 2.10.4 Exercises
  • 2.11 Variance and covariance
  • 2.11.1 An application of the Cauchy-Schwarz Inequality
  • 2.11.2 Remark
  • 2.11.3 Summary
  • 2.11.4 Exercises
  • 2.12 A short introduction to multivariate thinking
  • 2.12.1 A supplement on vectors and matrices
  • 2.12.2 Least squares
  • 2.12.3 A limitation of correlation in expressing negative association between non-independent random variables
  • 2.12.4 Covariance matrices
  • 2.12.5 Conditional variances and covariances
  • 2.12.6 Summary
  • 2.12.7 Exercises
  • 2.13 Tchebychev's Inequality
  • 2.13.1 Interpretations
  • 2.13.2 Summary
  • 2.13.3 Exercises
  • 3 Discrete Random Variables
  • 3.1 Countably many possible values
  • 3.1.1 A supplement on in nity
  • 3.1.2 Notes
  • 3.1.3 Summary
  • 3.1.4 Exercises
  • 3.2 Finite additivity
  • 3.2.1 Summary
  • 3.2.2 References
  • 3.2.3 Exercises
  • 3.3 Countable additivity
  • 3.3.1 Summary

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