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Modeling, Statistical Analysis, and Uncertainty


Course Description

Modeling and analysis of engineering problems under uncertainty with applications of probability and statistical concepts and methods. Data collection, measurements, simulation, model development, misinformation, validation, and analysis with environmental applications.


Athena Title

Modeling, Statistical Analysis


Prerequisite

MATH 2260


Semester Course Offered

Offered every year.


Grading System

A - F (Traditional)


Student Learning Outcomes

  • Students will understand the uncertainty inherent to collection of environmental data.
  • Students will understand simulation and analysis within uncertain environmental problem spaces.
  • Students will understand the principles and concepts of probability and statistics in analyzing and designing environmental engineering systems.
  • Students will understand systematic technique for describing uncertainty and realizing risk in environmental applications.
  • Students will understand quantitative methods for describing direct and indirect relationships among environmental variables.

Topical Outline

  • Descriptive statistics: Mean
  • Descriptive statistic: Medians
  • Descriptive statistic: Variance
  • Descriptive statistic: Co-variance
  • Descriptive statistic: Percentiles
  • Programming in MATLAB: MATLAB Language
  • Programming in MATLAB: Vectors and Matrices in MATLAB
  • Programming in MATLAB: Variables, Arrays, and Scripts
  • Programming in MATLAB: Loops
  • Probability: Sample spaces
  • Probability: Assigning probabilities
  • Probabilities: Outcome
  • Probabilities: Distribution
  • Probabilities: Random variable in environmental applications
  • Probabilities: Independent events
  • Probabilities: Joint and conditional probabilities
  • Probabilities: Repeated trials
  • Combinatorics: Combinatorial methods
  • Combinatorics: Combinatorial techniques for evaluating probability
  • Simulation: Stochastic
  • Simulation: Monte Carlo
  • Simulation: Deterministic
  • Simulation: Probability distribution
  • Simulation: Expectation
  • Simulation: Population mean and variance
  • Evaluating risk within uncertain domains
  • Data fitting
  • Error associated with measurements
  • Error propagation
  • Time series
  • Central limit theorem
  • Sampling: Population, samples, random sampling
  • Sampling: Error associated with sampling
  • Sampling: Confidence intervals
  • Hypothesis formulation
  • Analysis of Variance: T-test
  • Analysis of Variance: Chi-squared
  • Analysis of Variance: F statistics
  • Analysis of Variance: ANOVA
  • Analysis of Variance: Linear regression
  • Analysis of Variance: Significance testing

Syllabus