Parallel Tempering


This is a Fortran90 source code for multi-dimensional optimization (derivative free) and probabilistic sampling. Parallel tempering is a technique for accelerating convergence of Markov chains in multi-dimensional sampling. It can be used for Bayesian probabilistic sampling or optimization (misfit function fitting). This software is intended as a wrapper code to be used in conjunction with the users own Markov chain code, or using the internal MCMC algorithm supplied. It can be used for general Bayesian sampling or optimization. Examples of both appear in Sambridge (2013) along with full details of the implementation used here. Examples of driver routines calling the PT library are supplied with the code.

Example of Parallel Tempering applied to sampling a bi-modal PDF (left panel) as a function f a single variable. The standard McMC chain samples the original distribution and is trapped in the peak at x=0 and unable to visit the the one at x=100. With Tempering the chain can traverse the low probability region a x=50 many times and explore both peaks. See manual for details.

A pdf manual is available here and provides information on installation and usage. A copy of the manual is included in the download package.

Figure illustrating a Parallel Tempering algorithm perform exchange swaps between Markov chains a different temperatures (From Sambridge 2013).

An example of the Fit of 18 Receiver functions simultaneously fit by seeking a best fit 2-D seismic model using the Parallel Tempering software in optimization mode (From Sambridge 2013).

Figure illustrating 2-D sampling.


The code can be downloaded here. The package includes the above pdf manual and some examples. You will need to register with iEarth prior to download.

The contents of this package is provided under the terms of the GPL licence

Enquires should be directed to the author Malcolm Sambridge.


    Sambridge, M., 2013. A Parallel Tempering algorithm for probabilistic sampling and multi-modal optimization, Geophys. J. Int., doi: 10.1093/gji/ggt342

    Dosso, S. E., Holland, C. W. and Sambridge, M., 2012. Parallel tempering in strongly nonlinear geoacoustic inversion, J. Acoust. Soc. Am., 132, Issue 5, 3030-3040. doi:10.1121/1.4757639