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MCMC software for metrology applications

MCM2MCMC is software developed at NPL to convert a sample from a Bayesian posterior distribution corresponding to a particular choice of prior distribution derived using the Monte Carlo method, to a Bayesian posterior corresponding to a preferred prior distribution. A Metropolis-Hastings Markov chain Monte Carlo algorithm is used to achieve this conversion.

The software, developed in MATLAB, is provided in the form of M-files, and as HTML files published using MATLAB Version R2017b. The software demonstrates five examples – three relating to Gauge block measurements and two relating to measurements along an exponential curve. There is a script for each example that may be run directly. The scripts may be modified to run the software for different measurement scenarios. The source code is provided with commenting to help practitioners develop their own implementations of the software. For users who do not have access to MATLAB, or who are interested in reading about the examples, the software may be viewed in the supplied HTML files. There is an HTML file for each example.

The software is intended to help users easily convert samples obtained based on the GUM Supplement 1 approach to that from a Bayesian posterior distribution corresponding to a specified prior distribution.

MCMCMH is software developed at NPL to generate a sample from a user defined target distribution using the Metropolis-Hastings Markov chain Monte Carlo algorithm.

The software, developed in MATLAB, is provided in the form of M-files, and as HTML files published using MATLAB Version R2017b. The software demonstrates two examples – one implements a random walk algorithm and the other an independence chain algorithm. There is a script for each example that may be run directly. The scripts may be modified to run the software for different measurement scenarios. The source code is provided with commenting to help practitioners develop their own implementations of the software. For users who do not have access to MATLAB, or who are interested in reading about the examples, the software may be viewed in the supplied HTML files. There is an HTML file for each example.

The software is intended to help users sample from a Bayesian posterior distribution and evaluate convergence of the samples to the user defined target distribution. Summary information can also be computed based on the samples.

NLLSMH is software developed at NPL to generate samples from a Bayesian posterior distribution for parameters of a non-linear model. The Metropolis-Hastings Markov chain Monte Carlo algorithm is used for this purpose.

The software, developed in MATLAB, is provided in the form of M-files. The software demonstrates two examples – an exponential decay example and an arc fitting example. There is a script for each example that may be run directly. The scripts may be modified to run the software for different measurement scenarios. The source code is provided with commenting to help practitioners develop their own implementations of the software. This software calls NPL's MCMCMH software to generate samples from a Bayesian posterior distribution for parameters of the non-linear model.

For non-linear models, the Bayesian posterior distribution associated with model parameters will in general not be analytically defined. Therefore, computational techniques are required to provide summary information about the posterior distribution. This software is intended to help users sample from such a Bayesian posterior distribution and evaluate convergence of the samples to the user defined target distribution. Summary information can also be computed based on the samples.


MCM2MCMC, MCMCMH and NLLSMH are downloaded together as a compressed ZIP folder. Please start by reading the readme.txt files within that folder. The software comes with supporting documentation, including user manuals.


02 May 2018
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