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 :doc:`uq` 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: :doc:`Monte Carlo filtering <mcf>`
  -- map the input space into the region that produces a given behaviour and
  see which parameters separate "behave" from "non-behave" -- and the
  :doc:`high-dimensional model representation <hdmr>` -- 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 :doc:`polynomial-chaos emulator <surrogates>` 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.

.. toctree::
   :maxdepth: 2

   uq
   mcf
   hdmr
   surrogates