Courses:

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DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Pearson Addison Wesley. ISBN: 0201524880.

Prerequisites

Probability and Random Variables (18.440) or Probabilistic Systems Analysis (6.041).

We will cover parts of Chapters 6-10 (estimation, sampling distributions of estimators, testing hypotheses, categorical data and non-parametric methods, and linear statistical models). Necessary facts from probability will be recalled throughout the course. Some lectures will not be limited to the textbook, so attendance is important.

Course Description

This course provides a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry.

Topics

Estimation Theory

• Estimates by method of moments, their properties;
• Maximum likelihood estimates, their properties, Fisher information, Rao-Cramer inequality, efficient estimates;
• Bayes estimates, prior and posterior distributions, conjugate priors;
• Sufficient and jointly sufficient statistics, Neyman-Fisher factorization criterion, Rao-Blackwell theorem;
• Estimates for parameters of normal distribution, their properties;
• Chi-square, Fisher and Student distributions, confidence intervals for parameters of normal distribution.
  

Hypotheses Testing

• Testing simple hypotheses, Bayes decision rules, types of error, most powerful tests, likelihood ratio tests, randomized tests;
• Composite hypotheses, power function, monotone likelihood ratio and uniformly most powerful tests;
• t-tests and F-tests;
• Goodness-of-fit tests, chi-square tests, tests of independence and homogeneity, Kolmogorov-Smirnov test.
  

Regression and Classification

• Simple linear regression, least-squares fit, statistical inference in simple linear regression, confidence intervals, prediction intervals;
• Classification problem, boosting algorithm.

Grades