Linear Least Squares inversion: sippi_least_squares.m

If the prior is defined using a pure (no histogram reproduction) Gaussian type prior model, a Gaussian likelihood/noise for the data, and a linear forward model, then the a posteriori probability density will also be Gaussian.

In this case the Gaussian a posterior probability density can be directly estimated using Linear Least Squares inversion (see e.g. Tarantola and Valette (1982) or Tarantola (2005)), which is available through sippi_least_squares.m, which can be called using

[m_est,Cm_est,m_reals,,options,data,prior,forward]=sippi_least_squares(data,prior,forward,options);

To compute posterior mean and covariance only use e.g.

[m_est,Cm_est]=sippi_least_squares(data,prior,forward);

A number of realizations from the posterior distribution can also be computed using

[m_est,Cm_est,m_reals,options]=sippi_least_squares(data,prior,forward);

In this case the computed realizations, as well as all computed data, will be stored in the folder options.txt, similar to when using sippi_metropolis.m and sippi_rejection. Some figures analyzing the posterior distrbibution can then be generated using e.g. sippi_plot_posterior.m.

options.lsq contains all the operators that is used for the least squares inversion (d0,Cd,m0,Cm,G).