+
−% MCMC estimates paramters using a Monte Carlo Markov Chain.
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−%
+
−% DESCRIPTION: MCMC estimate the parameters of a given model given
+
−%              inputs, outputs and noise using a Metropolis algorithm.
+
−%              It handles (1 input / 1 output) systems, (2 input / 1 output) systems,
+
−%              and (2 input / 2 output) systems.
+
−%
+
−% CALL:        b = mcmc(in,out,pl)
+
−%
+
−% INPUTS:      out     - analysis objects with measured outputs
+
−%
+
−%              pl      - parameter list
+
−%
+
−% OUTPUTS:     b   - pest object contatining estimate information
+
−%
+
−% <a href="matlab:utils.helper.displayMethodInfo('ao', 'mcmc')">Parameters Description</a>
+
−%
+
−% VERSION:    $Id: mcmc.m,v 1.24 2011/11/16 15:21:13 nikos Exp $
+
−%
+
−% References:  "Catching supermassive black holes binaries without a net"
+
−%              N.J. Cornish, E.K. Porter, Phys.Rev.D 75, 021301, 2007
+
−%
+
−% TODO: multiple chain option not implemented yet
+
−%       metropolis/hastings not implemented
+
−%
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−
+
−function varargout = mcmc(varargin)
+
−  
+
−  % Check if this is a call for parameters
+
−  if utils.helper.isinfocall(varargin{:})
+
−    varargout{1} = getInfo(varargin{3});
+
−    return
+
−  end
+
−  
+
−  import utils.const.*
+
−  utils.helper.msg(msg.PROC3, 'running %s/%s', mfilename('class'), mfilename);
+
−  
+
−  % Method can not be used as a modifier
+
−  if nargout == 0
+
−    error('### mcmc cannot be used as a modifier. Please give an output variable.');
+
−  end
+
−  
+
−  % Collect input variable names
+
−  in_names = cell(size(varargin));
+
−  for ii = 1:nargin,in_names{ii} = inputname(ii);end
+
−  
+
−  % Collect all AOs smodels and plists
+
−  [as, ao_invars] = utils.helper.collect_objects(varargin(:), 'ao', in_names);
+
−  pl              = utils.helper.collect_objects(varargin(:), 'plist', in_names);
+
−  
+
−  % Decide on a deep copy or a modify
+
−  out = copy(as, nargout);
+
−  
+
−  % Combine plists
+
−  pl = parse(pl, getDefaultPlist);
+
−  
+
−  
+
−  % Get parameters from plist
+
−  mtxin = find(pl,'input');
+
−  noi = find(pl,'noise');
+
−  mdlin = find(pl,'model');
+
−  
+
−  % Decide on a deep copy or a modify
+
−  in  = copy(mtxin, nargout);
+
−  mdl = copy(mdlin, nargout);
+
−
+
−  numexp = numel(in(1,:));
+
−  numchannels_in = numel(in(:,1));
+
−  numchannels_out = numel(out(:,1));
+
−
+
−  if (numel(in) ~= numel(out))
+
−      error('### Dimensions of input and output must be equal.');
+
−  end
+
−
+
−  % Redefining the ao inputs as matrix objects 
+
−  for ii = 1:numexp
+
−    matin(ii) = matrix(in(:,ii),plist('shape',[numchannels_in 1]));
+
−    matout(ii) = matrix(out(:,ii),plist('shape',[numchannels_in 1]));
+
−    matnoise(ii) = matrix(noi(:,ii),plist('shape',[numchannels_in 1]));
+
−  end
+
−    
+
−  switch class(mdl)
+
−    case 'smodel'
+
−        matmodel = matrix(mdl);
+
−    case 'ssm'
+
−        matmodel = mdl;
+
−    case 'matrix'
+
−        matmodel = mdl;
+
−  end
+
−
+
−  pl = pset(pl,'model',matmodel,'input',matin,'noise',matnoise);
+
−  mcmc_obj = mcmc(matout,pl);
+
−
+
−
+
−  % Set output
+
−  varargout{1} = mcmc_obj;
+
−  
+
−end
+
−
+
−
+
−
+
−%--------------------------------------------------------------------------
+
−% Get Info Object
+
−%--------------------------------------------------------------------------
+
−function ii = getInfo(varargin)
+
−  if nargin == 1 && strcmpi(varargin{1}, 'None')
+
−    sets = {};
+
−    pl   = [];
+
−  else
+
−    sets = {'Default'};
+
−    pl   = getDefaultPlist;
+
−  end
+
−  % Build info object
+
−  ii = minfo(mfilename, 'ao', 'ltpda', utils.const.categories.sigproc, '$Id: mcmc.m,v 1.24 2011/11/16 15:21:13 nikos Exp $', sets, pl);
+
−end
+
−
+
−%--------------------------------------------------------------------------
+
−% Get Default Plist
+
−%--------------------------------------------------------------------------
+
−function plout = getDefaultPlist()
+
−  persistent pl;  
+
−  if exist('pl', 'var')==0 || isempty(pl)
+
−    pl = buildplist();
+
−  end
+
−  plout = pl;  
+
−end
+
−
+
−function pl = buildplist()
+
−  pl = plist();
+
−  
+
−  % N
+
−  p = param({'N','number of samples of the chain.'}, paramValue.DOUBLE_VALUE(1000));
+
−  pl.append(p);
+
−  
+
−  % Sigma
+
−  p = param({'cov','covariance of the gaussian jumping distribution.'}, paramValue.DOUBLE_VALUE(1e-4));
+
−  pl.append(p);
+
−  
+
−  % Param
+
−  p = param({'Fitparams','A cell array of evaluated parameters.'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  % Input
+
−  p = param({'input','A matrix array of input signals.'}, paramValue.EMPTY_STRING);
+
−  pl.append(p);
+
−  
+
−  % Frequencies
+
−  p = param({'frequencies','Range of frequencies where the analysis is performed. If an array, only first and last are used'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  % Noise
+
−  p = param({'noise','An array of noise spectrum (PSD) used to compute the likelihood.<ul>', ...
+
−    '<li>1 channel - Input one object</li>', ...
+
−    '<li>2 channel - Input four objects defining the power spectrum matrix </li>',...
+
−    '</ul>'}, paramValue.EMPTY_STRING);
+
−  pl.append(p);
+
−  
+
−  % Model
+
−  p = param({'model','An array of models.',...
+
−    '<li>1 input / 1 output - Input one object</li>', ...
+
−    '<li>2 input / 1 output - Input two objects</li>', ...
+
−    '<li>2 channel (2 input/ 2 output) - Input four objects defining the transfer function matrix </li>',...
+
−    '</ul>'}, paramValue.EMPTY_STRING);
+
−  pl.append(p);
+
−  
+
−  % Search
+
−  p = param({'search','Set to true to use bigger jumps in parameter space during annealing and cool down.'}, paramValue.TRUE_FALSE);
+
−  pl.append(p);
+
−  
+
−  % Simplex
+
−  p = param({'simplex','Set to true to perform a simplex search to find the starting parameters of the MCMC chain.'}, paramValue.TRUE_FALSE);
+
−  pl.append(p);
+
−  
+
−  % heat
+
−  p = param({'heat','The heat index flattening likelihood surface during annealing.'}, paramValue.DOUBLE_VALUE(1));
+
−  pl.append(p);
+
−  
+
−  % Tc
+
−  p = param({'Tc','An array of two values setting the initial and final value for the cooling down.'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  % x0
+
−  p = param({'x0','The proposed initial values.'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  % jumps
+
−  p = param({'jumps','An array of four numbers setting the rescaling of the covariance matrix during the search phase.',...
+
−    'The first value is the one applied by default, the following thhree apply just when the chain sample is',...
+
−    'mod(10), mod(25) and mod(100) respectively.'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  % plot
+
−  p = param({'plot','Select indexes of the parameters to be plotted.'}, paramValue.EMPTY_DOUBLE);
+
−  pl.append(p);
+
−  
+
−  % debug
+
−  p = param({'debug','Set to true to get debug information of the MCMC process.'}, paramValue.FALSE_TRUE);
+
−  pl.append(p);
+
−  
+
−  p = param({'prior','Mean, sigma and normalization factor for priors. Still under test'}, paramValue.EMPTY_STRING);
+
−  pl.append(p);
+
−
+
−  p = param({'anneal',['Choose type of annealing during sampling. Default value is ',...
+
−    'simulated annealing. Choose "thermo" for annealing with a thermostat.',...
+
−    ' SNR is computed and if it is larger than a fixed value SNR0 (provided also in the plist), ',...
+
−    'then the chains are heated by a factor of (SNR(1)/SNR0)^2. Choosing "simple" ',...
+
−    'the deviation of the loglikelihood of every 10 points in the chains is stored. If this deviation ',...
+
−    'is larger or smaller than two fixed values the chains are cooled or heated respectively.']}, {1, {'simul','thermo', 'simple'}, paramValue.SINGLE});
+
−  pl.append(p);
+
−
+
−  p = param({'SNR0','Fixed value for thermostated annealing.'},   {1, {200}, paramValue.OPTIONAL});
+
−  pl.append(p);
+
−          
+
−  p = param({'DeltaL',['Deviation of Loglikelihood for 10 points of the chains. Used for',...
+
−    'the "simple" choice of annealing with a thermostat.']},   {1, {[100 600 2 3]}, paramValue.OPTIONAL});
+
−  pl.append(p);
+
−  
+
−end
+
−
+
−
+
−% PARAMETERS:  J     - number of chains to compute.
+
−%              sigma - dispersion of the jumping distribution.
+
−%              range - range where the parameteters are sampled.
+
−%              param - a cell array of evaluated parameters (from the
+
−%                      smodel).
+
−%              Tc    - an array with two values (default: 0, i.e. no annealing).
+
−%              heat  - heat index flattening likelihood surface (default: 1)
+
−%              x0    - proposed initial values, if empty selected randomly.
+
−%                      (default: empty)
+
−
+
−