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Uncertainty

Uncertainty

Apr 23, 20231 min read

Probability Theory

  • Sample Space vs Event
  • Random Variable
  • Expected Value
  • Normal Distribution and Log-normal Distribution
  • Probability Density Function (PDF)
  • Cumulative Distribution Function (CDF)
  • Relationship between CDF and PDF
  • Moment of a Random Variable
  • Moment Generation Function
  • Covariance
  • Correlation
  • Variance of a Uniform Distribution
  • Quick way to find Eigenvalues
  • Quick way to find Eigenvectors
  • Shortcuts for finding Eigenvalues & Eigenvectors
  • Orthogonality

Karhunen-Loève Expansion

  • Multivariate Gaussian PDF
  • Karhunen-Loève Expansion
    • Discrete KLE Example - a
    • Discrete KLE Example - b
    • Continuous KLE Example

First Order Second Moment Method

  • FOSM
  • FOSM Example

Quadrature

  • Quadrature to Approximate Expected Value
  • Quadrature Example

Surrogate Modeling

  • Definition of Surrogate Modeling
  • Polynomial Chaos Expansion (GPC)
  • Expected Value and Variance Calculations using PCE
  • Multi-Dimensional Polynomial Chaos Expansion
  • 250731 GPC Example
  • non-Intrusive Surrogate Modeling

Sensitivity Analysis

  • Sobol Indices
  • Calculating Sobol Indices

Monte Carlo Methods

  • Monte Carlo Methods
  • Monte Carlo Method to Approximate Expectation

Misc

  • Formulary
  • Practice Problems

Graph View

  • Probability Theory
  • Karhunen-Loève Expansion
  • First Order Second Moment Method
  • Quadrature
  • Surrogate Modeling
  • Sensitivity Analysis
  • Monte Carlo Methods
  • Misc

Backlinks

  • Ahoy!

  • Website
  • Substack