Statistical Inference I

2018

Professor: |
Caroline J. Klivans |

office:
182 George Street, Office 316 e-mail: Caroline_Klivans@brown.edu office hours: Mondays 2-3pm and by appointment. |

TAs: |
Erin Bugbee office hours: Friday 10-11, Room 217, 170 Hope St. Tuesday 3-4, Location Sayles 200. Elliot Youth office hours: Tuesdays 4-6. Location Sayles Hall 012. Soryan Kumar office hours: Monday 6-8. Location 101 Thayer St, Room 116D. Jenna Washington (GTA) office hours: Monday and Thursday 10-11, Sayles 002. |

Lecture: |
MWF 11:00 - 11:50, SmithB 106 |

Mathematical Statistics with Applications, Wackery, Mendenhall, Scheaffer. 7th Edition.

There will be weekly homework assignments. You are encouraged to work together but all students

If you

Below is an approximate schedule for the course.

Week 1: Introduction to central ideas of statistics and probability.

Week 2: Definition of a Probability Space, sample space, probability distribution. Examples. Uniform distribution. Tools for counting. Products, orderings, binomial coefficients, multinomial coefficients. (Approx. textbook sections: 2.1-2.6)

Week 3: Conditional probability, Bayes Law, Theorem of Complete Probability. Independence. Additive Law, Multiplicative Law, Tree diagrams. (Approx. textbook sections: 2.7-2.10)

Week 4: Random variables, Binomial, Geometric pdfs. Expectation. Linearity of expectation. Indicator R.V.s (Approx. textbook sections: 2.11, 3.1-3.5)

Week 5: Deviations from the mean: Variance. (3.3) Markov's inequality, Chebyshev's inequality (~3.11). Weak Law of Large Numbers.

Midterm one covers the topics above.

Week 6: Poisson distribution (3.8). Moment generating functions. (3.9)

Markov Chains

Continuous probabilities. CDFs, densities. (4.1-4.3)

Week 7: More CDFs, densities. Uniform distribution, Normal distribution, Gamma, exponential distributions (4.4-4.6)

Week 8: Gamma, exponential distributions, Multivariate, marginal and conditional distributions, independence (5.1-5.6)

Week 9: conditional expectation (5.1-5.6) Covariance and correlation. (5.7) Sampling, point estimators, Bias, MSE. (8.1-8.4)

Week 10: Central Limit Theorem. Error of estimation, confidence intervals. (7.1-7.3, 8.5-8.10)

Week 11: Method of Moments, MLE. (9.1-9.7)

Week 12: Hypothesis Testing (10.1-10.6)

Week 13: Hypothesis Testing (10.7-10.10)

Week 14: Likelihood Ratio tests (10.11)

There will be two midterms(~33%) and a final(~33%) in addition to weekly assignments(~33%).

Midterm 1 Wed. Oct. 10th. Midterm 2 Nov. 14th. Final - to be announced by the registrar.