1.017
Computing and Data Analysis for Environmental Applications
Fall 2003
Topics
- Course Introduction Course Logistics Repeated Trials, Virtual Experiments, Probability, Statistics
- Programming in MATLAB® Downloading Data, Accessing MATLAB®, MATLAB® Environment, Variables, Arrays, Scripts Plotting Data
- Descriptive Statistics Histograms, Percentiles, Mean, Median, Variance, etc. Characterizing Streamflow Data
- Probability Experiments, Outcomes, Sample Spaces, Events, Probability, Axioms of Probability Methods for Assigning Probabilities
- MATLAB® Operations Internal MATLAB® Functions. Common MATLAB® Operations, Element-wise Computations, Loops Translating Equations to Programs
- Joint Probability, Independence, Repeated Trials Joint Probability, Independent Events, Repeated Trials
- Combinatorial Methods Counting Rules, Combinatorial Techniques for Evaluating Probabilities. Examples
- MATLAB® Tests and Loops Relational and Logical Operations, User-defined Functions, if Tests. Virtual Experiments
- Conditional Probability and Bayes Theorem Joint Probability, Conditional Probability, Prior & Posterior Probabilities, Bayes Theorem Engineering Applications
- Random Variables and Probability Distributions Definition of a Random Variable Cumulative Distribution Functions, Mass and Density Functions Using Distributions to Assign Probabilities
- Virtual Experiments
- Expectation, Functions of a Random Variable Expectation, Population Mean and Variance Defining and Functions of a Single Random Variable Solving Derived Distribution Problems with Stochastic Simulation
- Risk Defining and Evaluating Risk Engineering Applications
- Some Common Probability Distributions Uniform, Exponential, Normal, and Lognormal Distributions Special Properties of Normal Random Variables Fitting Distributions to Data
- Multivariate Probability Multiple Random Variables, Joint and Conditional Distributions, Independence, Covariance and Correlation Computing Conditional Probabilities in MATLAB®
- Functions of Many Random Variables Derived distributions for multivariate problems, moments of linear functions of several random variables. Central Limit Theorem
- Time Series and Central Limit Theorem
- Populations and Samples Populations, random samples. Sample statistics, moments of the sample mean and variance.
- Estimation Estimating Distributional Properties, Assessing Estimation Error Comparing Alternative Estimators
- Confidence Intervals Basic Concepts, Large Sample Confidence Intervals for the Population Mean Computing Large Sample Confidence Intervals
- Testing Hypotheses about a Single Population Formulating Hypothesis Testing Problems, Definitions Large Sample Tests of Hypotheses about a Single Population Applications Using MATLAB®
- Testing Hypotheses about Two Populations Large Sample Tests of Hypotheses about Two Populations Controlled Experiments Applications Using MATLAB®
- Small Samples t, chi-squared and F statistics. Small sample confidence intervals and hypothesis tests. Applications using MATLAB®.
- Analysis of Variance (ANOVA) Testing the Significance of a Single Factor, the F Test
- Multifactor Analysis of Variance Extension of the Single-Factor Model, Significance Testing Applications on MATLAB®
- Examples
- Linear Regression Objectives and Assumptions of Linear Regression, Estimating Regression Coefficients, Normal Equations Some Typical Environmental Applications
- Analyzing Regression Results Accuracy of Regression Estimates and Predictions, Prediction Confidence Intervals, Testing Significance Continuation of Environmental Examples
- Some Practical Applications
Readings
- D: Devore, Jay L. Probability and Statistics for Scientists and Engineers . Duxbury Press, 2000. ISBN: 0495557447.
- E: Etter, D. Introduction to MATLAB® for Engineers and Scientists . Prentice-Hall, 1996. ISBN: 0135197031.
- LEC/REC #: L1 · TOPICS: Course Introduction Course Logistics Repeated Trials, Virtual Experiments, Probability, Statistics · READINGS: D1.1
- LEC/REC #: R1 · TOPICS: Programming in MATLAB® Downloading Data, Accessing MATLAB®, MATLAB® Environment, Variables, Arrays, Scripts Plotting Data · READINGS: E2.1-2.6
- LEC/REC #: L3 · TOPICS: Probability Experiments, Outcomes, Sample Spaces, Events, Probability, Axioms of Probability Methods for Assigning Probabilities · READINGS: D1.2-1.4
- LEC/REC #: R2 · TOPICS: MATLAB® Operations Internal MATLAB® Functions. Common MATLAB® Operations, Element-wise Computations, Loops Translating Equations to Programs · READINGS: E3.1-3.4
- LEC/REC #: L4 · TOPICS: Joint Probability, Independence, Repeated Trials Joint Probability, Independent Events, Repeated Trials · READINGS: D2.1-2.2
- LEC/REC #: L5 · TOPICS: Combinatorial Methods Counting Rules, Combinatorial Techniques for Evaluating Probabilities. Examples · READINGS: D2.3
- LEC/REC #: R3 · TOPICS: MATLAB® Tests and Loops Relational and Logical Operations, User-defined Functions, if Tests. Virtual Experiments · READINGS: E3.5-3.6
- LEC/REC #: L6 · TOPICS: Conditional Probability and Bayes Theorem Joint Probability, Conditional Probability, Prior & Posterior Probabilities, Bayes Theorem Engineering Applications · READINGS: D2.4-2.5
- LEC/REC #: L8 · TOPICS: Expectation, Functions of a Random Variable Expectation, Population Mean and Variance Defining and Functions of a Single Random Variable Solving Derived Distribution Problems with Stochastic Simulation · READINGS: D3.1-3.2, E4.1-4.2
- LEC/REC #: L9 · TOPICS: Risk Defining and Evaluating Risk Engineering Applications · READINGS: D3.3
- LEC/REC #: L10 · TOPICS: Some Common Probability Distributions Uniform, Exponential, Normal, and Lognormal Distributions Special Properties of Normal Random Variables Fitting Distributions to Data · READINGS: D3.4-3.6, D4.3-4.6
- LEC/REC #: L11 · TOPICS: Multivariate Probability Multiple Random Variables, Joint and Conditional Distributions, Independence, Covariance and Correlation Computing Conditional Probabilities in MATLAB® · READINGS: D5.1-5.2
- LEC/REC #: L13 · TOPICS: Populations and Samples Populations, random samples. Sample statistics, moments of the sample mean and variance. · READINGS: D5.3-5.5
- LEC/REC #: L14 · TOPICS: Estimation Estimating Distributional Properties, Assessing Estimation Error Comparing Alternative Estimators · READINGS: D6.1-6.2
- LEC/REC #: L15 · TOPICS: Confidence Intervals Basic Concepts, Large Sample Confidence Intervals for the Population Mean Computing Large Sample Confidence Intervals · READINGS: D7.1-7.3
- LEC/REC #: L16 · TOPICS: Testing Hypotheses about a Single Population Formulating Hypothesis Testing Problems, Definitions Large Sample Tests of Hypotheses about a Single Population Applications Using MATLAB® · READINGS: D8.1-8.5
- LEC/REC #: L17 · TOPICS: Testing Hypotheses about Two Populations Large Sample Tests of Hypotheses about Two Populations Controlled Experiments Applications Using MATLAB® · READINGS: D9.1-9.3
- LEC/REC #: L21 · TOPICS: Multifactor Analysis of Variance Extension of the Single-Factor Model, Significance Testing Applications on MATLAB® · READINGS: D11.1-11.4
- LEC/REC #: L22 · TOPICS: Linear Regression Objectives and Assumptions of Linear Regression, Estimating Regression Coefficients, Normal Equations Some Typical Environmental Applications · READINGS: D12.1-12.2
- LEC/REC #: L23 · TOPICS: Analyzing Regression Results Accuracy of Regression Estimates and Predictions, Prediction Confidence Intervals, Testing Significance Continuation of Environmental Examples · READINGS: D12.3-12.4
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW readings ↗
- MIT OCW syllabus ↗
- MIT OCW calendar ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.