• 1. Dakota Methods
• 2. Methods in SimCenterUQ Engine
  • 2.1. Nataf transformation
  • 2.2. Global sensitivity analysis
    • Video Resources
    • Variance-based global sensitivity indices
    • Estimation of Sobol indices using Probabilistic model-based global sensitivity analysis (PM-GSA)
    • Dealing with high-dimensional responses with PCA-PSA
    • Aggregated sensitivity index
  • 2.3. Global surrogate modeling
    • Introduction to Gaussian process regression (Kriging)
    • Dealing with noisy measurements
    • Construction of the surrogate model
    • Adaptive Design of Experiments (DoE)
    • Verification of surrogate model
  • 2.4. Multi-fidelity Monte Carlo (MFMC)
    • Models with different infidelities
    • Pre-execution checklist for MFMC
    • Algorithm details
    • Speed-up
• 3. Methods in UCSD UQ Engine
  • 3.1. Transitional Markov chain Monte Carlo
  • 3.2. Gaussian Process-Aided Bayesian Calibration (GP-AB)
    • Formulation of the Bayesian Calibration Problem
    • Likelihood Function
    • Surrogate Model Formulation
    • Adaptive Design of Experiments (DoE)
    • Convergence Assessment
    • Warm-Start TMCMC
    • Algorithm Summary
    • Remarks
  • 3.3. Bayesian Inference of Hierarchical Models
    • Special Case: Normal Population Distribution
    • Sampling the Posterior Probability Distribution of the Parameters of the Hierarchical Model