No makeup midterm or quizzes will be given. (If you miss the midterm, the final will count towards 70% of your grade.)

Homework will be assigned in class as we go along and will be due in class on the Thursday of the week after the assignment. No late homework will be accepted; to compensate for this, we will drop the lowest score. We'll also drop the lowest quiz score (out of about three quizzes).

Date | Topic | Notes |
---|---|---|

Tu, Sept 6 | Introduction | |

Th, Sept 8 | Sample spaces, probability functions; conditional probability, Bayes' rule, independence; discrete vs. continuous random variables; transformation formulas | Due for Thursday Sept. 15: Exercises 1 and 2 from the lecture notes. |

Tu, Sept 13 | means, variances; joint, conditional, marginal distributions | |

Th, Sept 15 | correlation, covariance; moment-generating functions, convolution | Due for Thursday Sept. 22: Exercises 4, 5, 6, 8, 9, 11, 14, 15 from the lecture notes. |

Tu, Sept 20 | special distributions: binomial, Gaussian (normal), Poisson, uniform, exponential, etc. | |

Th, Sept 22 | probability inequalities: Markov, Chebysheff, Chernoff, Jensen, Cauchy-Schwarz. Convergence in probability and distribution. Law of large numbers. | Due for Thursday Sept. 29: Exercises 17, 18, 21, 23, 24, 25, 26, 27 from the lecture notes. |

Tu, Sept 27 | Central limit theorem, delta method |

Date | Topic | Notes |
---|---|---|

Th, Sept 29 | loss functions, expected loss, worst-case vs. average risk; domination + admissibility of decision rules | Due for Thursday Oct 6: Exercises 31, 32, 33, 36, 37, 39 from the lecture notes. |

Date | Topic | Notes |
---|---|---|

Tu, Oct 4 | Bayes estimators, bias and variance, bias-variance decomposition, unbiased, minimum-variance estimators | |

Th, Oct 6 | Maximum likelihood estimation | Quiz today: on material covered in HW sets 1-3. Due for Thursday Oct 13: Exercises 40, 42, 43, 44, 45, 50 from the lecture notes. |

Tu, Oct 11 | More on MLE | |

Th, Oct 13 | Sufficient statistics | Due for Thursday Oct 20: Exercises 51-54, 57, 58, 60, 61 from the lecture notes. |

Tu, Oct 18 | Minimal sufficiency; Rao-Blackwell theorem | |

Th, Oct 20 | Exponential families | Due for Thursday Oct 27: Exercises TBA from the lecture notes. (Just kidding, take a break.) |

Tu, Oct 25 | Midterm review | Come with questions! |

Th, Oct 27 | Midterm | On material covered in HW sets 1-6 (HW 6 was the one that was due on Oct. 20). Due for Thursday Nov 3: Exercises 62, 64-71 from the lecture notes. |

Tu, Nov 1 | Midterm post mortem | |

Th, Nov 3 | More on exponential families | Due for Thursday Nov 10: Exercises 73, 75-79 from the lecture notes. |

Tu, Nov 8 | No class (holiday) | Vote. |

Th, Nov 10 | Asymptotics of estimation: consistency, method of moments, confidence intervals | Due for Thursday Nov 17: Exercises 83-87 from the lecture notes. |

Tu, Nov 15 | Consistency of the MLE | Quiz today: on sufficiency and exponential families |

Th, Nov 17 | More MLE asymptotics: Fisher information | Due for Thursday Dec 1: Exercises 88-95 from the lecture notes. |

Tu, Nov 22 | Cramer-Rao bound, asymptotic efficiency | Happy Thanksgiving |

Date | Topic | Notes |
---|---|---|

Tu, Nov 29 | Simple hypotheses: ML tests; power, size; Neyman-Pearson lemma | |

Th, Dec 1 | Compound alternate hypotheses; uniformly most powerful tests | Due for Thursday Dec 8 (last homework!): Exercises 99-101, 107, 108, and 110-113 from the lecture notes. |

Tu, Dec 6 | Compound null and alternate; t-tests; likelihood ratio test in compound case | |

Th, Dec 8 | Exam review (optional) | Bring questions! |

Tu, Dec 13 | Exam review (optional) | Bring questions! |

Th, Dec 15 | Exam (not optional) | At the usual time and place. |