Markov Chain Monte Carlo

ao/mcmc MCMC - single/multiple experiments with AOs as inputs.
matrix/mcmc MCMC - single/multiple experiments with matrix objects as inputs.

The following section is dedicated to Bayesian parameter estimation techniques. Theoretical aspects are explained and some usefull examples are provided.

A little bit of theory.

The MCMC is a statistical method that is based on random sampling from the parameter space and it is considered suitable and efficient when the parameter space is multidimensional. New samples are generated using a Markov Chain mechanism and in each jump (or step) in the parameter space, the likelihood is calculated. After a sufficient number of samples, one can investigate the shape of the likelihood surface.


% call the method p = mcmc(out,plist);

Where, out is an AO or matrix object of the measured signal (output of the system).


The parameter list plist includes the following parameters:

Extra attention is needed when filling the input, noise and out fields. The objects must be organized in a arrays or matrices with a special way. The columns of a matrix are the numbers of experiments and the rows are the number of channels. In the case of LTP we have two channels. If we want to import two experiments, then for each key we specify a 2x2 AOs object or a 2x2 matrix object.

If the user doesn't specify the value of a given parameter, the default value is used.


There is one simple example for the use of mcmc method estimating parameters of a simple harmonic oscillator ssm model. For a more complex application (full LTP ssm model) refer to the LTPDA training 2, Topic 5.


  1. M Nofrarias et al, Bayesian parameter estimation in the second LISA Pathfinder mock data challenge, PHYSICAL REVIEW D 82, 122002 (2010)
  2. M Nofrarias, L Ferraioli, G Congedo, Comparison of parameter estimates results in STOC Exercise 6, S2-AEI-TN-3070.

©LTP Team