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Lecture notes. Written from the material of Berkeley Stat 210A, licensed CC BY 4.0. Notes, not a transcript — reorganised and rewritten, carrying the same licence.

Berkeley Stat 210A

83 chapters, written from the course's material.

Contents

  1. Introduction to Asymptotic Theory
  2. Why Bayesian Computation Needs MCMC
  3. Bayes Risk and Bayes Estimator
  4. Where Does the Prior Come From?
  5. Completeness
  6. Convergence and the Delta Method (part 1)
  7. Gaussian sequence model
  8. Statistical Models and Estimation
  9. Exponential Family Structure
  10. The Factorization Theorem
  11. Fall 2018 Final Examination
  12. 2019 Practice Final Exam
  13. Final Exam Review Problems
  14. Fall 2024 Final Examination
  15. Hierarchical Bayes
  16. Standing Homework Conventions
  17. Hypothesis Testing and Neyman-Pearson
  18. Course Overview and Schedule
  19. Statistics as Inductive Reasoning
  20. The James-Stein Estimator
  21. Reader Notation Conventions
  22. Measures, Integration, and Densities
  23. Measures, Integrals, and Densities
  24. Induction and the Coin-Flip Example
  25. Statistical Models and Decision Theory
  26. Probability as a Measure
  27. Statistical models and decisions
  28. Canonical Form
  29. Sufficient Statistics and Factorization
  30. Sufficiency and Minimal Sufficiency (part 1)
  31. Exponential Families
  32. Completeness of Sufficient Statistics
  33. Completeness and Basu's Theorem
  34. Rao–Blackwell and UMVU Estimators
  35. Score, Fisher Information, and CRLB (part 1)
  36. Unbiased Estimation and the UMVUE
  37. Fisher Information and Cramér–Rao Bound
  38. Bayes Estimation for Frequentists
  39. Where does \(\Lambda\) come from?
  40. Hierarchical Bayes Models
  41. Empirical Bayes and James-Stein
  42. Minimax Estimation (part 1)
  43. Empirical Bayes, James-Stein
  44. Minimax Estimation (part 2)
  45. Hypothesis Testing and Power Functions
  46. One-Sided Tests in General
  47. Testing with one real parameter
  48. \(p\)-Values and Confidence Sets
  49. P-Values and Confidence Sets
  50. Nuisance Parameters and Conditioning
  51. Multiparameter Exp. Families
  52. The Canonical Linear Model
  53. One-Sample T-Test and the Linear Model
  54. Convergence and the Delta Method (part 2)
  55. Convergence and the Delta Method (part 3)
  56. MLE in Exponential Families
  57. MLE: Consistency and Efficiency
  58. Asymptotic Distribution of the MLE
  59. Wald, Score, and Likelihood-Ratio Tests (part 1)
  60. Wald, Score, and Likelihood-Ratio Tests (part 2)
  61. The Nonparametric Bootstrap
  62. Multiple Testing and FWER
  63. Wald and Score Tests
  64. Maximum Likelihood Estimation
  65. Measure Theory for Probability
  66. Least Favorable Priors
  67. Multiple Testing
  68. Old Exams Archive
  69. Measure-Theoretic Foundations of Probability
  70. Recitation Materials Index
  71. Score, Fisher Information, and CRLB (part 2)
  72. A Curved Gaussian Family
  73. Sufficiency, Minimax, and Asymptotic Theory
  74. UMVU, Shrinkage, and Exact Testing
  75. Regression with Correlated Errors
  76. Sufficiency, Testing, and Bayes: A Final Exam
  77. Sufficiency and Minimal Sufficiency (part 2)
  78. Stat 210A: Course Information
  79. p-Values
  80. t, F, and Linear Models
  81. Nuisance Parameters
  82. Testing With One Real Parameter
  83. Unbiased Estimation

Sources

3 course offerings were merged. The book carries CC BY 4.0.

Offering Original Commit Licence
Fall 2024 github.com/berkeley-stat210a/fall-2024 812543b CC BY 4.0
Fall 2025 github.com/berkeley-stat210a/fall-2025 5eb849a CC BY 4.0
Fall 2026 github.com/berkeley-stat210a/fall-2026 7dc8f80 CC BY 4.0