Limit theorems by simulation
Illustrate the law of large numbers and the central limit theorem by Monte Carlo, for several starting distributions.
All pathsDiscover Coursera PlusAfter step 4 After step 5 After step 6 After step 7
Data & AI · 04Intermediate
Mathematical Statistician
Scientifically minded learners who want to master the theory of inference.
Calculus and linear algebra, then probability, estimation, testing, generalised linear models and advanced statistical techniques.
598hours of coursework
60weeks at 10 h
7steps
23courses
3universities
Target skills
Data AnalysisApplied MathematicsStatistical AnalysisStatistical MethodsStatistical InferenceCalculusProbabilityStatisticsProbability & StatisticsData ScienceAlgebraLinear Algebra
Skill labels as listed on Coursera.
Target jobs
- Statistician
- Biostatistician
- Quantitative analyst
Progression
- 1Johns Hopkins UniversityBeginner
Stated prerequisites: Basic algebra (no calculus)
Show the 3 courses
Course Level Length Rating (reviews) Linear Algebra: Linear Systems and Matrix Equations Beginner 10 h 4.7 (183) Linear Algebra: Matrix Algebra, Determinants, & Eigenvectors — 15 h 4.8 (79) Linear Algebra: Orthogonality and Diagonalization Intermediate 9 h 4.8 (56) - 2Johns Hopkins UniversityIntermediateData Analysis Software
Stated prerequisites: Some familiarity with precalculus, specifically exponential and logarithm functions
Show the 4 courses
Course Level Length Rating (reviews) Calculus through Data & Modeling: Precalculus Review Beginner 8 h 4.8 (124) Calculus through Data & Modeling: Limits & Derivatives Beginner 10 h 4.7 (212) Calculus through Data & Modeling: Differentiation Rules Intermediate 8 h 4.8 (124) Calculus through Data & Modeling: Applying Differentiation Intermediate 7 h 4.7 (63) - 3Johns Hopkins UniversityIntermediate
Stated prerequisites: Working knowledge of differential calculus
Show the 4 courses
Course Level Length Rating (reviews) Calculus through Data & Modelling: Series and Integration Intermediate 9 h 4.9 (63) Calculus through Data & Modelling: Techniques of Integration Intermediate 5 h 4.7 (55) Calculus through Data & Modelling: Integration Applications Intermediate 6 h 4.6 (28) Calculus through Data & Modelling: Vector Calculus Intermediate 5 h 4.7 (53) - 4University of Colorado BoulderIntermediateR, Python, Jupyter Notebooksacademic credit
Stated prerequisites: Calculus through Calculus II (multivariate preferred) and some R or Python experience
Show the 3 courses
Course Level Length Rating (reviews) Probability Foundations for Data Science and AI Intermediate 43 h 4.5 (300) Discrete-Time Markov Chains and Monte Carlo Methods Intermediate 33 h 4.5 (22) Statistical Estimation for Data Science and AI Intermediate 29 h 4.0 (99) - 5University of Colorado BoulderIntermediateR, Jupyter Notebooksacademic credit
Stated prerequisites: Calculus through Calculus II (multivariate preferred) and some R programming experience
Show the 3 courses
Course Level Length Rating (reviews) Probability Foundations for Data Science and AIalready taken Intermediate 43 h 4.5 (300) Statistical Estimation for Data Science and AIalready taken Intermediate 29 h 4.0 (99) Statistical Inference and Hypothesis Testing in Data Science Applications Intermediate 37 h 4.6 (55) - 6University of Colorado BoulderIntermediateR, Jupyter Notebooksacademic credit
Stated prerequisites: Calculus, basic linear algebra and probability theory
Show the 3 courses
Course Level Length Rating (reviews) Modern Regression Analysis in R Intermediate 45 h 4.3 (40) ANOVA and Experimental Design Intermediate 40 h 4.0 (23) Generalized Linear Models and Nonparametric Regression Intermediate 42 h 4.2 (26) - 7Illinois TechIntermediateR, Python
Show the 5 courses
Course Level Length Rating (reviews) Linear Regression Intermediate 27 h 4.6 (31) Model Diagnostics and Remedial Measures Intermediate 20 h 4.9 (11) Variable Selection, Model Validation, Nonlinear Regression Intermediate 21 h — Bayesian Computational Statistics Intermediate 89 h — Data Preparation and Analysis Intermediate 80 h —
With Coursera Plus
This path takes 598 hours, about 14 months at 10 hours a week. A Coursera Plus subscription gives access to most of its courses during that time.
Projects to build
Interval coverage
Measure by simulation the actual coverage of confidence intervals when assumptions do not hold.
Factorial design
Design and analyse a two-factor experiment (ANOVA), for example cooking time and temperature.
Regularised regression
Compare least squares, ridge and lasso on data with many variables, using cross-validation.
Free textbooks
Calculus, Volumes 1 to 3OpenStaxFree, CC BY 4.0
Linear AlgebraJim HefferonFree
Introduction to Probability, 2nd ed.J. K. Blitzstein, J. HwangFree online version
OpenIntro StatisticsD. Diez, M. Çetinkaya-Rundel, C. BarrFree PDF