Week | Date | Topic | Course Notes | Practice | Assignment |
---|---|---|---|---|---|

1 | Tue 1/17 | Probability: axioms, rules, approximation |
Ch 1: Fundamentals Ch 2: Calculating Chances |
Guide | HW 1 |

Th 1/19 | Random variables: distributions, conditioning, equality |
Ch 3: Random Variables Ch 4: Relations Between Variables |
Lab 1: Matches in Random Sampling | ||

2 | Tue 1/24 | Induction, counting, and bounds |
Ch 5: Collections of Events |
Guide | HW 2 |

Th 1/26 | Binomial and Multinomial Distributions; The Poisson Limit |
Ch 6: Random Counts |
Lab 2: Poisson Approximations in Random Permutations | ||

3 | Tue 1/31 | Independence and Poissonization; dependence and symmetry |
Ch 7: Poissonization Ch 8: Dependence |
Guide | HW 3 |

Wed 2/1 | Quiz 1 | ||||

Th 2/2 | Prior and posterior distributions; random sampling | Lab 3: Riffle Shuffles and Randomness | |||

4 | Tue 2/7 | Expectation: properties and tail bounds |
Ch 9: Expectation |
Guide | HW 4 |

Th 2/9 | SD: properties, tail bounds, least squares |
Ch 10: Standard Deviation |
Lab 4: Minimum, Median, and Maximum | ||

5 | Tue 2/14 | Probabilities and expectation by conditioning |
Ch 11: Conditioning Revisited |
Guide | HW 5 |

Wed 2/15 | Quiz 2 | ||||

Th 2/16 | Long run behavior of Markov Chains |
Ch 12: Markov Chains |
Lab 5: Tsetlin Library and PageRank | ||

6 | Tue 2/21 | Hitting and occupation times |
Ch 13: Hitting and Occupation Times |
Midterm Guide | HW 6 |

Th 2/23 | Reversibility and MCMC |
Ch 14: Reversing Markov Chains |
Problems | Lab 6: Codebreaking by MCMC | |

7 | Tue 2/28 | Review | No HW 7 | ||

Th 3/2 | Midterm | No Lab 7 | |||

8 | Tue 3/7 | Covariance and its uses |
Ch 15: Variance Via Covariance |
Guide | HW 8 |

Th 3/9 | Central Limit Theorem |
Ch 16: The Central Limit Theorem |
Lab 8: Binomial, Poisson, and Normal | ||

9 | Tue 3/14 | Probability densities |
Ch 17: Continuous Distributions |
Guide | HW 9 |

Th 3/16 | Transformations |
Ch 18: Transformations |
Lab 9: Simulation and the CDF | ||

10 | Tue 3/21 | Joint densities |
Ch 19: Joint Density |
Guide | HW 10 |

Wed 3/22 | Quiz 3 | ||||

Th 3/23 | The Beta Family | No Lab 10 (Spring Break) | |||

11 | Tue 4/4 | Independent normals; maximum likelihood |
Ch 20: Applications of the Normal |
Guide | HW 11 |

Th 4/6 | Sums and the gamma family | Lab 11: MLE, Chi-Squared, and Goodness of Fit | |||

12 | Tue 4/11 | Moment generating functions; Chernoff bound |
Ch 21: Distributions of Sums |
Guide | HW 12 |

Wed 4/12 | Quiz 4 | ||||

Th 4/13 | Prior and posterior densities; beta-binomial |
Ch 22: Prior and Posterior Distributions |
Lab 12: Chinese Restaurant Process I | ||

13 | Tue 4/17 | Best predictor | Guide | HW 13 | |

Th 4/21 | Best linear predictor: correlation and regression |
Ch 23: Prediction |
Lab 13: Chinese Restaurant Process II | ||

14 | Tue 4/25 | The multivariate normal |
Ch 24: The Bivariate Normal Distribution |
Final Exam Resources | No HW due in RRR week |

Th 4/27 | Conclusion | ||||

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