.. _api-mcmc-goodman_weare:
.. role::  raw-html(raw)
    :format: html

mcmc.goodman_weare
==================

Usage
-----

.. code-block::

    obj = mcmc;
    xPosterior = obj.goodman_weare(y,x0,weights,fitting,modelFWD,varargin)

I/O overview
------------

+---------------------------+--------------------------------------------------------------------------------------------------------------+
| Input                     | Description                                                                                                  |
+===========================+==============================================================================================================+
| y                         | measurements, [Nmeas, Nvoxels]                                                                               |
+---------------------------+--------------------------------------------------------------------------------------------------------------+
| x0                        | structure variable containing starting points of all model parameters to be estimated                        |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| weights                   | N-D wieghts, same dimension as 'data' (optional)                                                             |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting                   | structure contains fitting algorithm parameters                                                              |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.model_params      | 1xM cell variable,    name of the model parameters, e.g. {'S0','R2star','noise'};                            |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.lb                | 1xM numeric variable, fitting lower bound, same order as field 'model_params', e.g. [0.5, 0, 0.001];         |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.ub                | 1xM numeric variable, fitting upper bound, same order as field 'model_params', e.g. [2, 1, 0.1];             |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.iteration         | # MCMC iterations                                                                                            |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.repetition        | # repetition of MCMC proposal                                                                                |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.thinning          | sampling interval between iterations                                                                         |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.burnin            | iterations to be discarded at the beginning, if >1, the exact number will be used; else iteration*burnin     |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.StepSize          | step size for 'GW' in MCMC proposal ('GW' only)                                                              |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| fitting.Nwalker           | # random walkers ('GW' only)                                                                                 |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| FWDfunc                   | function handle for forward signal generation; size of the output must match size of 'data'                  |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 
| varargin                  | additional input for FWDfunc other than 'parameter' and 'mask' (same order as FWDfunc)                       |
+---------------------------+--------------------------------------------------------------------------------------------------------------+ 

+-----------------------------------+--------------------------------------------------------------------------------------------------------------+
| Output                            | Description                                                                                                  |
+===================================+==============================================================================================================+
| xPosterior                        | structure contains MCMC posterior samples                                                                    |
+-----------------------------------+--------------------------------------------------------------------------------------------------------------+
| xPosterior.(model_params{k})      | Model parameter MCMC posterior samples                                                                       |
+-----------------------------------+--------------------------------------------------------------------------------------------------------------+

.. note::
    'noise' is always required in fitting.model_params.

See also :ref:`gettingstarted-mcmc_affineinvariantensemble_tutorial`.