# Uncertainty Quantification Methods¶

- Thread: Analysis of the core model using Gaussian Process methods
- Thread: Bayes linear emulation for the core model
- Thread: Generic methods to emulate derivatives
- Thread: History Matching
- Thread: Generic methods for combining two or more emulators
- Thread: Experimental design
- Thread: Screening
- Thread: Sensitivity analysis
- Thread: Dynamic Emulation
- Thread Variant: Linking Models to Reality using Model Discrepancy
- Thread: Analysis of a simulator with multiple outputs using Gaussian Process methods
- Thread Variant: Two-level emulation of the core model using a fast approximation
- Thread: Emulators with derivative information

- Procedure: Adaptive Sampler for Complex Models (ASCM)
- Procedure: Multivariate lognormal approximation for correlation hyperparameters
- Procedure: Iterate the single step emulator using an approximation approach
- Procedure: Use simulation to recursively update the dynamic emulator mean and variance in the approximation method
- Procedure: Automatic Relevance Determination (ARD)
- Procedure: Calculation of adjusted expectation and variance
- Procedure: Predict simulator outputs using a BL emulator
- Procedure: Bayes linear method for learning about the emulator residual variance
- Procedure: Branch and bound algorithm
- Procedure: Building a Bayes linear emulator for the core problem (variance parameters known)
- Procedure: Empirical construction of a Bayes linear emulator for the core problem using only simulator runs
- Procedure: Build Gaussian process emulator for the core problem
- Procedure: Build Gaussian process emulator of derivatives
- Procedure: Build multivariate Gaussian process emulator for the core problem
- Procedure: Complete the multivariate Gaussian process emulator with a separable covariance function
- Procedure: Build Gaussian process emulator with derivative information
- Procedure: Data Pre-Processing and Standardisation
- Procedure: Iterate the single step emulator using an exact simulation approach
- Procedure: Exchange Algorithm
- Procedure: Explore the full simulator design region to identify a suitable single step function design region
- Procedure: Fourier Expansion
- Procedure: Haar wavelet expansion
- Procedure: Generate a Halton design
- Procedure: Generate a Latin hypercube
- Procedure: Generate a lattice design
- Procedure: Sampling the posterior distribution of the correlation lengths
- Procedure: Morris screening method
- Procedure: Generate an optimised Latin hypercube design
- Procedure: Generate random outputs from an emulator at specified inputs
- Procedure: Transformed outputs
- Procedure: Principal components and related transformations of simulator outputs
- Procedure: Pivoted Cholesky decomposition
- Procedure: Predict simulator outputs using a GP emulator
- Procedure: Predicting a function of multiple outputs
- Procedure: Predict functions of simulator outputs using multiple independent emulators
- Procedure: Simulating realisations of an emulator
- Procedure: Generating a Sobol’s Sequence
- Procedure: Uncertainty Analysis for a Bayes linear emulator
- Procedure: Uncertainty analysis for dynamic emulators
- Procedure: Uncertainty Analysis using a GP emulator
- Procedure: Uncertainty analysis for a function of simulator outputs using multiple independent emulators
- Procedure: Recursively update the dynamic emulator mean and variance in the approximation method
- Procedure: Validate a Gaussian process emulator
- Procedure: Variance Based Sensitivity Analysis using a GP emulator
- Procedure: Variogram estimation of covariance function hyperparameters
- Procedure: Generate a Weyl design

- Example: 1 Dimensional History Matching
- Example: A one dimensional emulator
- Example: A two dimensional emulator with uncertainty and sensitivity analysis
- Example: Illustrations of decision-based sensitivity analysis
- Example: A one-input, two-output emulator
- Example: Multi-output emulator with separable covariance and dimension reduction
- Example: Using Automatic Relevance Determination (ARD)
- Example: Using the Morris method
- Example: A one dimensional emulator built with function output and derivatives

- Discussion: Active and inactive inputs
- Discussion: Adjusting Exchangeable Beliefs
- Discussion: Theoretical aspects of Bayes linear
- Discussion: The Best Input Approach.
- Discussion: Computational issues in building a Gaussian process emulator for the core problem
- Discussion: The core problem
- Discussion: Technical issues in training sample design for the core problem
- Discussion: Design of a validation sample
- Discussion: The GP covariance function
- Discussion: Decision-based Sensitivity Analysis
- Discussion: Exchangeable Computer Models
- Discussion: Expert Assessment of Model Discrepancy
- Discussion: Factorial design
- Discussion: Formal Assessment of Model Discrepancy
- Discussion: Forms of GP-Based Emulators
- Discussion: The Gaussian assumption
- Discussion: Implausibility Cutoffs
- Discussion: Informal Assessment of Model Discrepancy
- Discussion: Iterative Refocussing
- Discussion: the Karhunen-Loeve expansion for Gaussian processes
- Discussion: Monte Carlo estimation, sample sizes and emulator hyperparameter sets
- Discussion: The Observation Equation
- Discussion: Finding the posterior mode of correlation lengths
- Discussion: Design for generating emulator realisations
- Discussion: Reification
- Discussion: Reification Theory
- Discussion: Sensitivity measures for decision uncertainty
- Discussion: Sensitivity measures for output uncertainty
- Discussion: Sensitivity analysis measures for simplification
- Discussion: Sobol sequence
- Discussion: Structured Forms for Model Discrepancy
- Discussion: Use of a structured mean function
- Discussion: Sensitivity analysis in the toolkit
- Discussion: Nugget effects in uncertainty and sensitivity analyses
- Discussion: Uncertainty analysis
- Discussion: Variance-based Sensitivity Analysis
- Discussion: Theory of variance-based sensitivity analysis
- Discussion: Why Model Discrepancy?
- Discussion: Why Probabilistic Sensitivity Analysis?

- Alternatives: Prior specification for BL hyperparameters
- Alternatives: Basis functions for the emulator mean
- Alternatives: Training Sample Design for the Core Problem
- Alternatives: Emulator prior correlation function
- Alternatives: Dynamic Emulation Approaches
- Alternatives: Estimators of correlation hyperparameters
- Alternatives: Prior distributions for GP hyperparameters
- Alternatives: Gaussian Process or Bayes Linear Emulators
- Alternatives: Implausibility Measures
- Alternatives: Iterating single step emulators
- Alternatives: Emulator prior mean function
- Alternatives: Multivariate emulator prior mean function
- Alternatives: Approaches to emulating multiple outputs
- Alternatives: Choice of covariance function in the multivariate Gaussian process emulator
- Alternatives: Prior distributions for multivariate GP hyperparameters
- Alternatives: Numerical solution for Karhunen Loeve expansion
- Alternatives: Optimal design criteria
- Alternatives: Optimal Design Algorithms
- Alternatives: Deciding which screening method to use

- Definition of Term: Active input
- Definition of Term: Adjoint
- Definition of Term: Assessment
- Definition of Term: Bayes linear adjustment
- Definition of Term: Bayes linear variance learning
- Definition of Term: Basis functions
- Definition of Term: Bayes linear
- Definition of Term: Bayesian
- Definition of Term: Best Input
- Definition of Term: Calibration
- Definition of Term: Code uncertainty
- Definition of Term: Conjugate prior
- Definition of Term: Correlation length
- Definition of Term: Data Assimilation
- Definition of Term: Decision-based sensitivity analysis
- Definition of Term: Design
- Definition of Term: Deterministic
- Definition of Term: Dynamic simulator
- Definition of Term: Elicitation
- Definition of Term: Emulator
- Definition of Term: Exchangeability
- Definition of Term: Forcing Input
- Definition of Term: Gaussian process
- Definition of Term: History Matching
- Definition of Term: Hyperparameter
- Definition of Term: Implausibility Measure
- Definition of Term: Inactive input
- Definition of Term: MUCM
- Definition of Term: Model Based Design
- Definition of Term: Model Discrepancy
- Definition of Term: Multilevel Emulation
- Definition of Term: Multivariate Gaussian process
- Definition of Term: Multivariate t-process
- Definition of Term: Nugget
- Definition of Term: Principal Component Analysis
- Definition of Term: Proper (or improper) distribution
- Definition of Term: Regularity
- Definition of Term: Reification
- Definition of Term: Screening
- Definition of Term: Second-order Exchangeability
- Definition of Term: Second-order belief specification
- Definition of Term: Sensitivity analysis
- Definition of Term: Separable
- Definition of Term: Simulator
- Definition of Term: Single step function
- Definition of term: Smoothing kernel
- Definition of Term: Smoothness
- Definition of Term: Space filling design
- Definition of Term: State Vector
- Definition of Term: Stochastic
- Definition of Term: T-process
- Definition of Term: Training sample
- Definition of Term: Uncertainty analysis
- Definition of Term: Validation
- Definition of Term: Variance-based sensitivity analysis
- Definition of Term: Weak prior distribution