adaptive_metropolis_hastings.m

function record=adaptive_metropolis_hastings(TargetFun,ProposalFun,xparam1,vv,mh_bounds,varargin)
%function adaptive_metropolis_hastings(TargetFun,ProposalFun,xparam1,vv,mh_bounds,varargin)
% Random walk Metropolis-Hastings algorithm. 
% 
% INPUTS 
%   o TargetFun  [char]     string specifying the name of the objective
%                           function (posterior kernel).
%   o xparam1    [double]   (p*1) vector of parameters to be estimated (initial values).
%   o vv         [double]   (p*p) matrix, posterior covariance matrix (at the mode).
%   o mh_bounds  [double]   (p*2) matrix defining lower and upper bounds for the parameters. 
%   o varargin              list of argument following mh_bounds
%  
% OUTPUTS 
%   o record     [struct]   structure describing the iterations
%
% ALGORITHM 
%   Metropolis-Hastings.       
%
% SPECIAL REQUIREMENTS
%   None.
%
% PARALLEL CONTEXT
% The most computationally intensive part of this function may be executed
% in parallel. The code sutable to be executed in
% parallel on multi core or cluster machine (in general a 'for' cycle),
% is removed from this function and placed in random_walk_metropolis_hastings_core.m funtion.
% Then the DYNARE parallel package contain a set of pairs matlab functions that can be executed in
% parallel and called name_function.m and name_function_core.m. 
% In addition in parallel package we have second set of functions used
% to manage the parallel computation.
%
% This function was the first function to be parallelized, later other
% functions have been parallelized using the same methodology.
% Then the comments write here can be used for all the other pairs of
% parallel functions and also for management funtions.

% Copyright (C) 2006-2013 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.

global M_ options_ bayestopt_ estim_params_ oo_


old_options = options_;

accept_target = options_.amh.accept_target;
m_directory = [M_.fname '/metropolis/']; 

if options_.load_mh_file == 0
    delete([m_directory 'adaptive_metropolis_proposal_*.mat']);
    nP = 0;
else
    D = dir([m_directory 'adaptive_metropolis_proposal_*.mat']);
    nP = size(D,1);
end;

if nP == 0
    jscale = options_.mh_jscale;
    bayestopt_.jscale = jscale;
    save([m_directory 'adaptive_metropolis_proposal_0'],'vv','jscale');
    nP = 1;
else
    tmp = load([m_directory 'adaptive_metropolis_proposal_' ...
                int2str(nP-1)],'vv','jscale');
    vv = tmp.vv;
    bayestopt_.jscale = tmp.jscale;
end

if options_.amh.cova_steps
    bayestopt_.jscale = tune_scale_parameter(TargetFun, ...
                                              ProposalFun,xparam1,vv,mh_bounds,varargin{:});
end

for i=1:options_.amh.cova_steps
    options_.mh_replic = options_.amh.cova_replic;
    random_walk_metropolis_hastings(TargetFun,ProposalFun, ...
                                    xparam1,vv,mh_bounds,varargin{:});
    tot_draws = total_draws(M_);
    options_.mh_drop = (tot_draws-options_.amh.cova_replic)/tot_draws;
    CutSample(M_,options_,estim_params_);
    [junk,vv] = compute_mh_covariance_matrix();
    jscale = tune_scale_parameter(TargetFun,ProposalFun,xparam1,vv,mh_bounds,varargin{:});
    bayestopt_.jscale = jscale;
    save([m_directory 'adaptive_metropolis_proposal_' ...
          int2str(nP)],'vv','jscale');
    nP = nP + 1;
end

options_.mh_replic = old_options.mh_replic;
options_.mh_drop = old_options.mh_drop;
record = random_walk_metropolis_hastings(TargetFun,ProposalFun, ...
                                         xparam1,vv,mh_bounds,varargin{:});
                


function selected_scale = tune_scale_parameter(TargetFun,ProposalFun,xparam1,vv,mh_bounds,varargin)
global options_ bayestopt_

selected_scale = [];

maxit = options_.amh.scale_tuning_maxit;
accept_target = options_.amh.accept_target;
test_runs = options_.amh.scale_tuning_test_runs;
tolerance = options_.amh.scale_tuning_tolerance;
Scales = zeros(maxit,1);
AvRates = zeros(maxit,1);
Scales(1) = bayestopt_.jscale;

for i=1:maxit
    options_.mh_replic = options_.amh.scale_tuning_blocksize;
    bayestopt_.jscale = Scales(i);
    record = random_walk_metropolis_hastings(TargetFun,ProposalFun, ...
                                             xparam1,vv, ...
                                             mh_bounds,varargin{:});
    AvRates(i) = mean(record.AcceptanceRatio);

    if i < test_runs
        i_kept_runs = 1:i;
    else
        i_kept_runs = i_kept_runs+1;
    end
    
    kept_runs_s = Scales(i_kept_runs);
    kept_runs_a = AvRates(i_kept_runs);
    
    if i > test_runs
        a_mean = mean(kept_runs_a);
        if (a_mean > (1-tolerance)*accept_target) && ...
                (a_mean < (1+tolerance)*accept_target) && ...
                all(kept_runs_a > (1-test_runs*tolerance)*accept_target) && ...
                all(kept_runs_a < (1+test_runs*tolerance)*accept_target)
            selected_scale = mean(Scales((i-test_runs+1):i));
            disp(['Selected scale: ' num2str(selected_scale)])
            return
        end
    end
    
    mean_kept_runs_a = mean(kept_runs_a);
    if (mean_kept_runs_a/accept_target < 1-test_runs*tolerance) ...
            || (mean_kept_runs_a/accept_target > 1+test_runs*tolerance)
        damping_factor = 1
    else
        damping_factor = 1/3
    end
    Scales(i+1) = mean(kept_runs_s)*(mean(kept_runs_a)/ ...
                                     accept_target)^damping_factor;


    options_.load_mh_file = 1;
    
    disp(100*kept_runs_s')
    disp(100*kept_runs_a')
    disp(['Selected scale ' num2str(Scales(i+1))])    
end

error('AMH scale tuning: tuning didn''t converge')

function y = total_draws(M_)
load_last_mh_history_file([M_.dname filesep 'metropolis'],M_.fname);
y = sum(record.MhDraws(:,1));