Fundamentals of Statistics
A rapid introduction to the theoretical foundations of statistical methods that are useful in many applications. Covers a broad range of topics in a short amount of time with the goal of providing a rigorous and cohesive understanding of the modern statistical landscape. Mathematical language is used for intuition and basic derivations but not proofs. Main topics include: parametric estimation, confidence intervals, hypothesis testing, Bayesian inference, and linear and logistic regression. Additional topics may include: causal inference, nonparametric estimation, and classification.
Fall 2016 · Statistics for Applications
This course offers an in-depth the theoretical foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development of efficient statistical methods.
Spring 2015 · Statistics for Applications
Topics
- Distributions Derived from Normal Distribution
- Statistical Models: Classic One-sample Distribution Models
- Parameter Estimation: Method of Moments
- Parameter Estimation: Maximum Likelihood
- Maximum Likelihood: Large Sample Theory
- Bootstrap Confidence Intervals
- Sufficiency
- Parameter Estimation: Bayesian Approach
- Hypothesis Testing
- Hypothesis Testing II
- Assessing Goodness of Fit
- Summarizing Data
- Summarizing Data: Examples and Dynamic Graphics
- Regression Analysis
- Regression Analysis II
- Comparing Independent Samples and ANOVA
- Analysis of Categorical Data
Readings
- SES #: L1 · CHAPTER # AND TITLES: Chapter 6: Distributions Derived from the Normal Distribution · SECTIONS & PAGES: Sections 6.1–6.3.
- SES #: L2 · CHAPTER # AND TITLES: Chapter 8: Estimation of Parameters and Fitting of Probability Distributions · SECTIONS & PAGES: Sections 8.1–8.3.
- SES #: L3 · CHAPTER # AND TITLES: Section 8.4.
- SES #: L4 · CHAPTER # AND TITLES: Section 8.5.1.
- SES #: L5 · CHAPTER # AND TITLES: Section 8.5.2.
- SES #: L6 · CHAPTER # AND TITLES: Section 8.5.3.
- SES #: L7 · CHAPTER # AND TITLES: Section 8.8.
- SES #: R1 · CHAPTER # AND TITLES: No Readings: Exam 1 Review
- SES #: E1 · CHAPTER # AND TITLES: No Readings: Exam 1
- SES #: L8 · CHAPTER # AND TITLES: Chapter 8: Estimation of Parameters and Fitting of Probability Distribution · SECTIONS & PAGES: Section 8.6.
- SES #: L9 · CHAPTER # AND TITLES: Chapter 9: Testing Hypotheses and Assessing Goodness of Fit · SECTIONS & PAGES: Sections 9.1–9.2.
- SES #: L10 · CHAPTER # AND TITLES: Sections 9.3–9.4.
- SES #: L11 · CHAPTER # AND TITLES: Sections 9.5–9.9.
- SES #: R2 · CHAPTER # AND TITLES: No Readings: Exam 2 Review
- SES #: E2 · CHAPTER # AND TITLES: No Readings: Exam 2
- SES #: L12 · CHAPTER # AND TITLES: Chapter 10: Summarizing Data · SECTIONS & PAGES: Sections 10.1–10.4.
- SES #: L13 · CHAPTER # AND TITLES: Sections 10.5–10.7.
- SES #: L14 · CHAPTER # AND TITLES: Chapter 14: Linear Least Squares · SECTIONS & PAGES: Sections 14.1–14.3.
- SES #: L15 · CHAPTER # AND TITLES: Sections 14.4–14–7.
- SES #: R3 · CHAPTER # AND TITLES: No Readings: Exam 3 Review
- SES #: E3 · CHAPTER # AND TITLES: No Readings: Exam 3
- SES #: L16 · CHAPTER # AND TITLES: Chapter 12: The Analysis of Variance · SECTIONS & PAGES: Sections 12.1–12.2.
- SES #: L17 · CHAPTER # AND TITLES: Chapter 13: The Analysis of Categorical Data · SECTIONS & PAGES: Sections 13.1–13.4.
Fall 2006 · Statistics for Applications
This course offers a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. OCW offers an earlier version of this course, from Fall 2003. This newer version focuses less on estimation theory and more on multiple linear regression models. In addition, a number of Matlab examples are included here.
Readings
- DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics . 3rd ed. Boston, MA: Addison-Wesley, 2002.
- All readings refer to DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA: Addison-Wesley, 2002. ISBN: 0201524880.
- SES #: L2 · TOPICS: Maximum Likelihood Estimators · READINGS: Section 6.5
- SES #: L3 · TOPICS: Properties of Maximum Likelihood Estimators · READINGS: Sections 6.6 and 7.8
- SES #: L4 · TOPICS: Multivariate Normal Distribution and CLT · READINGS: Section 5.12 (for the 2-dimensional case)
- SES #: L5 · TOPICS: Confidence Intervals for Parameters of Normal Distribution · READINGS: Sections 7.3 and 7.5
- SES #: L6 · TOPICS: Gamma, Chi-squared, Student T and Fisher F Distributions · READINGS: Sections 5.9, 7.2, 7.4, and 8.7
- SES #: L7-L8 · TOPICS: Testing Hypotheses about Parameters of Normal Distribution, t-Tests and F-Tests · READINGS: Sections 8.5, 8.6, and 8.7
- SES #: L10 · TOPICS: Most Powerful Test for Two Simple Hypotheses · READINGS: Section 8.2
- SES #: L11 · TOPICS: Chi-squared Goodness-of-fit Test · READINGS: Section 9.1
- SES #: L12 · TOPICS: Chi-squared Goodness-of-fit Test for Composite Hypotheses · READINGS: Section 9.2
- SES #: L13 · TOPICS: Tests of Independence and Homogeneity · READINGS: Sections 9.3, 9.4, and 9.5
- SES #: L14 · TOPICS: Kolmogorov-Smirnov Test · READINGS: Section 9.6
- SES #: L15-L16 · TOPICS: Simple Linear Regression · READINGS: Sections 10.1, 10.2, and 10.3
- SES #: L17-L18 · TOPICS: Multiple Linear Regression · READINGS: Section 10.5
Prerequisites & course information
Same subject as IDS.014[J] Subject meets with 18.6501 Prereq: 6.3700 or 18.600 U (Fall, Spring) 4-0-8 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2016
- MIT OCW syllabus ↗
- MIT OpenCourseWare ↗Spring 2015
- MIT OCW readings ↗
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- MIT OpenCourseWare ↗Fall 2006
- MIT OCW syllabus ↗
- MIT OCW readings ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.