Examples

All examples listed here are part of the MUQ source code. Refer to the documentation for installation instructions.

c++Gaussian Process

Mauna Loa CO2

Regression of CO2 observations with a statespace representation of a Gaussian process.

c++Regression

Monotone Regression

Regression of stress-strain data with guaranteed monotonocity of the learned relationship.

pythonPCE

Mixed PCE Construction

Construction of polynomial chaos expansions with inputs that have different distributions.

pythonPCE

Basic PCE Construction

Basic construction of polynomial chaos expansions with adaptive Smolyak algorithm.

pythonMCMC

Analyzing Groundwater Pump Tests with Hierarchical Models

Characterizes the properties of a confined aquifer by solving a hierarchical Bayesian inference problem involving the Theis model of groundwater flow.

c++MCMC

MC using MCMC components

Shows how to implement Monte Carlo type methods using the modular MCMC stack. Allows easily running MC and MCMC on the same model.

c++MCMC

MLMC using MLMCMC components

Shows how to implement Multilevel Monte Carlo type methods using the modular MCMC stack. Allows easily running MLMC and MLMCMC on the same model.

c++MCMC

Parallelized MLMC using MCMC components

Shows how to implement parallelized Multilevel Monte Carlo type methods using the modular parallel MIMCMC stack. Allows easily runningMultilevel MC and Multilevel / Multiindex MCMC on the same model, using a common parallel architecture.

c++MCMC

Random walk Metropolis MCMC using a custom proposal covariance

Implement a simple Metropolis-Hastings MCMC method, choosing a custom covariance for a Gaussian proposal.

pythonMCMC

MCMC with pCN proposal

Implement a simple MCMC method with preconditioned Crank-Nicolson proposal.

pythonMCMC

DILI MCMC

Demonstrates the basic usage of the Dimension Independent Likelihood Informed (DILI) MCMC algorithm.

pythonMCMC

Delayed Rejection MCMC

Illustrates thee use of delayed rejection MCMC on a Bayesian inverse problem constructed from an elliptic PDE forward model.

c++MCMC

Simple MCMC

MCMC sampling from a simple Gaussian distribution. Custom target distributions can be supplied.

pythonMCMC

Simple MCMC

Introduces MUQ's MCMC capabilities using a random walk proposal on a Gaussian target densityl.

c++MCMC

Basic Metropolis-in-Gibbs Sampling

Metropolis-in-Gibbs sampling of a simple hierarchical Bayesian model with Gaussian-Inverse Gamma target density.

pythonMCMC

Basic Metropolis-in-Gibbs Sampling

Metropolis-in-Gibbs sampling of a simple hierarchical Bayesian model with Gaussian-Inverse target density.

c++MCMC

Parallel Multilevel MCMC with parallel model

Defines a hierarchy of simple Gaussian models and applies Multilevel MCMC to it. The MLMCMC method itself allows massive parallelization, and the forward model may be parallelized as well. We use simple Gaussian target densities here, but the example can serve as a template for actually parallel models.

c++MCMC

Multilevel MCMC with parallel model

Defines a hierarchy of simple Gaussian models and applies Multilevel MCMC to it. The UQ method is sequential. However, the models themselves may exploit MPI parallelism. We use simple Gaussian target densities here, but the example can serve as a template for actually parallel models.

pythonMCMC

Multilevel MCMC

Defines a hierarchy of simple Gaussian models and applies Multilevel MCMC to it.

c++MCMC

Parallel Multiindex MCMC with parallel model

Defines a two-dimensional hierarchy of simple Gaussian models and applies Multilevel MCMC to it. The MIMCMC method itself allows massive parallelization, and the forward model may be parallelized as well. We use simple Gaussian target densities here, but the example can serve as a template for actually parallel models.

c++MCMC

Multiindex MCMC

Defines a two-dimensional hierarchy of simple Gaussian models and applies Multiindex MCMC to it.

pythonMCMC

Multiindex MCMC

Defines a two dimensional hierarchy of simple Gaussian models and applies Multiindex MCMC to it.

c++HDF5

Block Operations in HDF5

Demonstrates slicing and other block operations for reading and writing parts of a dataset stored in an HDF5 file.

c++HDF5

Introduction to MUQ's HDF5 wrapper

Demonstrates the use of MUQ's HDF5 wrapper for reading and writing binary HDF5 files.

MUQ is on Slack!

Join our slack workspace to connect with other users, get help, and discuss new features.

Test Status

Acknowledgments

NSF Logo

This material is based upon work supported by the National Science Foundation under Grant No. 1550487.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

DOE Logo

This material is based upon work supported by the US Department of Energy, Office of Advanced Scientific Computing Research, SciDAC (Scientific Discovery through Advanced Computing) program under awards DE-SC0007099 and DE-SC0021226, for the QUEST and FASTMath SciDAC Institutes.

MUQ

The MIT Uncertainty Quantification Library

Examples

Mauna Loa CO2

Monotone Regression

Mixed PCE Construction

Basic PCE Construction

Analyzing Groundwater Pump Tests with Hierarchical Models

MC using MCMC components

MLMC using MLMCMC components

Parallelized MLMC using MCMC components

Random walk Metropolis MCMC using a custom proposal covariance

MCMC with pCN proposal

DILI MCMC

Delayed Rejection MCMC

Simple MCMC

Simple MCMC

Basic Metropolis-in-Gibbs Sampling

Basic Metropolis-in-Gibbs Sampling

Parallel Multilevel MCMC with parallel model

Multilevel MCMC with parallel model

Multilevel MCMC

Parallel Multiindex MCMC with parallel model

Multiindex MCMC

Multiindex MCMC

Block Operations in HDF5

Introduction to MUQ's HDF5 wrapper