Computing and Data Analysis for Environmental Applications

Calendar

LEC/REC #	TOPICS	KEY DATES
L1	Course Introduction  Course Logistics  Repeated Trials, Virtual Experiments, Probability, Statistics
R1	Programming in MATLAB®  Downloading Data, Accessing MATLAB®, MATLAB® Environment, Variables, Arrays, Scripts  Plotting Data
L2	Descriptive Statistics  Histograms, Percentiles, Mean, Median, Variance, etc.  Characterizing Streamflow Data
L3	Probability  Experiments, Outcomes, Sample Spaces, Events, Probability, Axioms of Probability  Methods for Assigning Probabilities	PS1 Issued
R2	MATLAB® Operations Internal MATLAB® Functions. Common MATLAB® Operations, Element-wise Computations, Loops  Translating Equations to Programs
L4	Joint Probability, Independence, Repeated Trials  Joint Probability, Independent Events, Repeated Trials
L5	Combinatorial Methods  Counting Rules, Combinatorial Techniques for Evaluating Probabilities. Examples	PS1 Due  PS2 Issued
R3	MATLAB® Tests and Loops  Relational and Logical Operations, User-defined Functions, if Tests. Virtual Experiments
L6	Conditional Probability and Bayes Theorem Joint Probability, Conditional Probability, Prior & Posterior Probabilities, Bayes Theorem  Engineering Applications
L7	Random Variables and Probability Distributions  Definition of a Random Variable  Cumulative Distribution Functions, Mass and Density Functions  Using Distributions to Assign Probabilities	PS2 Due  PS3 Issued
R4	Virtual Experiments
L8	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
L9	Risk  Defining and Evaluating Risk  Engineering Applications	PS3 Due
R5	Recitation 5 — Quiz Review
	Quiz 1
L10	Some Common Probability Distributions  Uniform, Exponential, Normal, and Lognormal Distributions  Special Properties of Normal Random Variables  Fitting Distributions to Data	PS4 Issued
L11	Multivariate Probability  Multiple Random Variables, Joint and Conditional Distributions, Independence, Covariance and Correlation  Computing Conditional Probabilities in MATLAB®
L12	Functions of Many Random Variables   Derived distributions for multivariate problems, moments of linear  functions of several random variables. Central Limit Theorem
R6	Time Series and Central Limit Theorem
L13	Populations and Samples   Populations, random samples. Sample statistics, moments of the sample mean and variance.	PS4 Due  PS5 Issued
L14	Estimation  Estimating Distributional Properties, Assessing Estimation Error  Comparing Alternative Estimators
L15	Confidence Intervals  Basic Concepts, Large Sample Confidence Intervals for the Population Mean  Computing Large Sample Confidence Intervals	PS5 Due  PS6 Issued
R7	Review
L16	Testing Hypotheses about a Single Population  Formulating Hypothesis Testing Problems, Definitions  Large Sample Tests of Hypotheses about a Single Population  Applications Using MATLAB®
L17	Testing Hypotheses about Two Populations Large Sample Tests of Hypotheses about Two Populations  Controlled Experiments  Applications Using MATLAB®	PS6 Due
R8	Quiz Review
	Quiz 2
L18	Small Samples t, chi-squared and F statistics. Small sample confidence intervals and hypothesis tests. Applications using MATLAB®.	PS7 Issued
L19-L20	Analysis of Variance (ANOVA)  Testing the Significance of a Single Factor, the F Test	PS7 Due  PS8 Issued
	Review of Quiz 2, ANOVA examples
L21	Multifactor Analysis of Variance  Extension of the Single-Factor Model, Significance Testing  Applications on MATLAB®	PS8 Due  PS9 Issued
	Examples
L22	Linear Regression  Objectives and Assumptions of Linear Regression, Estimating Regression Coefficients, Normal Equations  Some Typical Environmental Applications
R11	Quiz Review
L23	Analyzing Regression Results  Accuracy of Regression Estimates and Predictions, Prediction Confidence Intervals, Testing Significance  Continuation of Environmental Examples	PS9 Due
	Quiz 3
	Some Practical Applications