1. Global Sensitivity Analysis and Uncertainty Quantification

These tools answer two related questions about a model whose inputs (parameters and, where relevant, shocks) are uncertain:

• Uncertainty quantification (UQ) – how uncertain are the model’s outputs (steady states, impulse responses, moments, forecasts, decompositions) given that uncertainty? This is forward propagation, covered on the Uncertainty Quantification page.

• Global sensitivity analysis (GSA) – which inputs are responsible for that output uncertainty (or for some qualitative behaviour of the model)? RISE offers two complementary GSA approaches: Monte Carlo filtering – map the input space into the region that produces a given behaviour and see which parameters separate “behave” from “non-behave” – and the high-dimensional model representation – fit a low-order surrogate of the input-to-output map, from which variance-based (Sobol-type) sensitivity indices and a cheap emulator follow.

• Surrogates – the polynomial-chaos emulator fits a fast stand-in for an expensive function of the parameters (typically the log posterior), with the polynomial basis derived from the priors; Sobol’ indices come out of the fit analytically. This is also the foundation of the surrogate-accelerated estimation roadmap.

All three rely on sampling the input space; RISE uses the posterior sampler after estimation, draws from the prior, or quasi-Monte-Carlo low-discrepancy sequences (Sobol, Halton, …) over a calibration range.

• 1.1. Uncertainty Quantification
  • 1.1.1. Where the parameter draws come from
  • 1.1.2. Propagating uncertainty through the model
  • 1.1.3. From propagation to sensitivity
• 1.2. Monte Carlo Filtering
  • 1.2.1. Description
  • 1.2.2. Quick start examples
  • 1.2.3. Details on the mcf class
  • 1.2.4. Support facility for filtration : the mcfprop class
• 1.3. High Dimensional Model Representation
  • 1.3.1. Description
  • 1.3.2. Quick-start examples
  • 1.3.3. Details
• 1.4. Surrogates: polynomial chaos, analytic Sobol’ indices
  • 1.4.1. Quick start
  • 1.4.2. The prior chooses the polynomials
  • 1.4.3. The Gaussian-process emulator: calibrated pointwise uncertainty
  • 1.4.4. Fitting on your own function
  • 1.4.5. Options
  • 1.4.6. Trust, but verify
  • 1.4.7. Delayed-acceptance MCMC: exact posterior, fraction of the cost
  • 1.4.8. Adaptive tools on top of the emulators
  • 1.4.9. One call, three views: the sensitivity front-end