Added new option mh_tune_jscale.

Works only with the Random Walk Metropolis Hastings algorithm.

Closes #1598

doc/dynare.texi

@@ -5595,12 +5595,17 @@ variance if the acceptance ratio is too low. In some situations it may
 help to consider parameter-specific values for this scale parameter. 
 This  can  be  done  in  the  @ref{estimated_params}- block.  
 
-Note that @code{mode_compute=6} will tune the scale parameter to achieve an acceptance rate of 
+Note that @code{mode_compute=6} will tune the scale parameter to achieve an
-@ref{AcceptanceRateTarget}. The resulting scale parameter will be saved into a file
+acceptance rate of @ref{AcceptanceRateTarget}. The resulting scale parameter
-named @file{@var{MODEL_FILENAME}_mh_scale.mat}. This file can be loaded in subsequent runs
+will be saved into a file named @file{@var{MODEL_FILENAME}_mh_scale.mat}. This
-via the @code{posterior_sampler_options}-option @ref{scale_file}. Both @code{mode_compute=6}
+file can be loaded in subsequent runs via the
-and @code{scale_file} will overwrite any value specified in @code{estimated_params} with the tuned value.  
+@code{posterior_sampler_options}-option @ref{scale_file}. Both
-Default: @code{0.2}
+@code{mode_compute=6} and @code{scale_file} will overwrite any value specified
+in @code{estimated_params} with the tuned value.  Default: @code{0.2}
+
+Note also that for the Random Walk Metropolis Hastings algorithm, it is
+possible to use option @ref{mh_tune_jscale}, to automatically tune the value of
+@code{mh_jscale}.
 
 @item mh_init_scale = @var{DOUBLE}
 The scale to be used for drawing the initial value of the
@@ -5617,6 +5622,16 @@ If the @ref{nointeractive}-option has been invoked, the program will instead aut
 @code{mh_init_scale} by 10 percent after 100 futile draws and try another 100 draws. This iterative 
 procedure will take place at most 10 times, at which point Dynare will abort with an error message.
 
+@item mh_tune_jscale [= @var{DOUBLE}]
+@anchor{mh_tune_jscale} Automatically tunes the scale parameter of the jumping
+distribution's covariance matrix (Metropolis-Hastings), so that the overall
+acceptance ratio is close to the desired level. Default value is
+@code{0.33}. It is not possible to match exactly the desired
+acceptance ratio because of the stochastic nature of the algoirithm (the
+proposals and the initialial conditions of the markov chains if
+@code{mh_nblocks>1}). This option is only available for the Random Walk
+Metropolis Hastings algorithm.
+
 @item mh_recover
 @anchor{mh_recover} Attempts to recover a Metropolis-Hastings
 simulation that crashed prematurely, starting with the last available saved 

matlab/calibrate_mh_scale_parameter.m

@@ -0,0 +1,111 @@
+function Scale = calibrate_mh_scale_parameter(ObjectiveFunction, CovarianceMatrix, Parameters, MhBounds, options, varargin)
+
+% Tune the MH scale parameter so that the overall acceptance ratio is close to AcceptanceTarget.
+%
+% INPUTS
+% - ObjectiveFunction             [fhandle]      Function (posterior kernel).
+% - CovarianceMatrix              [double]       n*n matrix, covariance matrix of the jumping distribution.
+% - Parameters                    [double]       n*1 vector, parameter values.
+% - MhBounds                      [double]       n*2 matrix, bounds on the possible values for the parameters.
+% - options                       [structure]    content of options_.tune_mh_jscale.
+% - varargin                      [cell]         Additional arguments to be passed to ObjectiveFunction.
+%
+% OUTPUTS
+% - Scale                         [double]       scalar, optimal scale parameter for teh jumping distribution.
+
+% Fire up the wait bar
+hh = dyn_waitbar(0,'Tuning of the scale parameter...');
+set(hh,'Name','Tuning of the scale parameter.');
+
+% Intilialize various counters.
+j = 1; jj  = 1; isux = 0; jsux = 0; i = 0;
+
+% Evaluate the objective function.
+logpo0 = - feval(ObjectiveFunction, Parameters, varargin{:});
+logpo1 = logpo0;
+
+% Get the dimension of the problem.
+n = length(Parameters);
+
+% Initialize the correction on the scale factor.
+correction = 1.0;
+
+% Set the initial value of the scale parameter
+Scale = options.guess;
+
+% Transposition of some arrays.
+MhBounds = MhBounds';
+Parameters = Parameters';
+
+% Compute the Cholesky of the covariance matrix, return an error if the
+% matrix is not positive definite.
+try
+    dd = chol(CovarianceMatrix);
+catch
+    error('The covariance matrix has to be a symetric positive definite matrix!')
+end
+
+% Set parameters related to the proposal distribution
+if options.rwmh.proposal_distribution=='rand_multivariate_normal'
+    nu = n;
+elseif options.rwmh.proposal_distribution=='rand_multivariate_student'
+    nu = options.rwmh.student_degrees_of_freedom;
+end
+
+% Random Walk Metropolis Hastings iterations...
+while j<=options.maxiter
+    % Obtain a proposal (jump)
+    proposal = feval(options.rwmh.proposal_distribution, Parameters, Scale*dd, nu);
+    % If out of boundaries set the posterior kernel equal to minus infinity
+    % so that the proposal will be rejected with probability one.
+    if all(proposal > MhBounds(1,:)) && all(proposal < MhBounds(2,:))
+        logpo0 = -feval(ObjectiveFunction, proposal(:), varargin{:});
+    else
+        logpo0 = -inf;
+    end
+    % Move if the proposal is enough likely...
+    if logpo0>-inf && log(rand)<logpo0-logpo1
+        Parameters = proposal;
+        logpo1 = logpo0;
+        isux = isux + 1;
+        jsux = jsux + 1;
+    end% ... otherwise I don't move.
+    prtfrc = j/options.maxiter;
+    % Update the waitbar
+    if ~mod(j, 10)
+        dyn_waitbar(prtfrc, hh, sprintf('Acceptance ratio [during last 500]: %f [%f]', isux/j, jsux/jj));
+    end
+    % Adjust the value of the scale parameter.
+    if ~mod(j, options.stepsize)
+        r1 = jsux/jj;    % Local acceptance ratio
+        r2 = isux/j;     % Overall acceptance ratio
+        % Set correction for the scale factor
+        c1 = r1/options.target;
+        if abs(c1-1)>.05
+            correction = correction^options.rho*c1^(1-options.rho);
+        else
+            correction = c1;
+        end
+        % Apply correction
+        if c1>0
+            Scale = Scale*correction;
+        else
+            Scale = Scale/10;
+        end
+        % Update some counters.
+        jsux = 0; jj = 0;
+        if abs(r2-options.target)<options.c2 && abs(r1-options.target)<options.c1
+            i = i+1;
+        else
+            i = 0;
+        end
+        % Test convergence.
+        if i>options.c3
+            break
+        end
+    end
+    j = j+1;
+    jj = jj + 1;
+end
+
+dyn_waitbar_close(hh);

matlab/dynare_estimation_1.m

@@ -228,7 +228,7 @@ if ~isequal(options_.mode_compute,0) && ~options_.mh_posterior_mode_estimation
     elseif isnumeric(options_.mode_compute) && options_.mode_compute==6 %save scaling factor
         save([M_.fname '_optimal_mh_scale_parameter.mat'],'Scale');
         options_.mh_jscale = Scale;
-        bayestopt_.jscale = ones(length(xparam1),1)*Scale;
+        bayestopt_.jscale(:) = options_.mh_jscale;
     end
     if ~isnumeric(options_.mode_compute) || ~isequal(options_.mode_compute,6) %always already computes covariance matrix
         if options_.cova_compute == 1 %user did not request covariance not to be computed
@@ -438,6 +438,21 @@ if (any(bayestopt_.pshape  >0 ) && options_.mh_replic) || ...
             error(['Estimation:: Mode value(s) of ', disp_string ,' are outside parameter bounds.'])
         end
     end
+    % Tunes the jumping distribution's scale parameter
+    if options_.mh_tune_jscale.status
+        if options_.posterior_sampler_options.posterior_sampling_method=='random_walk_metropolis_hastings'
+            options = options_.mh_tune_jscale;
+            options.rwmh = options_.posterior_sampler_options.rwmh;
+            options_.mh_jscale = calibrate_mh_scale_parameter(objective_function, ...
+                                                                  invhess, xparam1, [bounds.lb,bounds.ub], ...
+                                                                  options, dataset_, dataset_info, options_, M_, estim_params_, bayestopt_, bounds, oo_);
+                bayestopt_.jscale(:) = options_.mh_jscale;
+                disp(sprintf('mh_jscale has been set equal to %s', num2str(options_.mh_jscale)))
+                skipline()
+        else
+            warning('mh_tune_jscale is only available with Random Walk Metropolis Hastings!')
+        end
+    end
     % runs MCMC
     if options_.mh_replic || options_.load_mh_file
         posterior_sampler_options = options_.posterior_sampler_options.current_options;

matlab/global_initialization.m

@@ -442,6 +442,15 @@ options_.mh_conf_sig = 0.90;
 options_.prior_interval = 0.90;
 options_.mh_drop = 0.5;
 options_.mh_jscale = 0.2;
+options_.mh_tune_jscale.status = false;
+options_.mh_tune_jscale.guess = .2;
+options_.mh_tune_jscale.target = .33;
+options_.mh_tune_jscale.maxiter = 200000;
+options_.mh_tune_jscale.rho = .7;
+options_.mh_tune_jscale.stepsize = 1000;
+options_.mh_tune_jscale.c1 = .02;
+options_.mh_tune_jscale.c2 = .05;
+options_.mh_tune_jscale.c3 = 4;
 options_.mh_init_scale = 2*options_.mh_jscale;
 options_.mh_mode = 1;
 options_.mh_nblck = 2;

preprocessor

@@ -1 +1 @@
-Subproject commit d686275da142e2d1e1afcdb32785c25f25b5a5a7
+Subproject commit 1ba023e37d6ee7fc8d393840e42a4542274efbb7

tests/Makefile.am

@@ -41,6 +41,7 @@ MODFILES = \
 	estimation/MH_recover/fs2000_recover_2.mod \
 	estimation/MH_recover/fs2000_recover_3.mod \
 	estimation/t_proposal/fs2000_student.mod \
+	estimation/tune_mh_jscale/fs2000.mod \
 	moments/example1_var_decomp.mod \
 	moments/example1_bp_test.mod \
 	moments/test_AR1_spectral_density.mod \

tests/estimation/tune_mh_jscale/fs2000.mod

@@ -0,0 +1,105 @@
+/*
+ * Copyright (C) 2004-2018 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/>.
+ */
+
+var m P c e W R k d n l gy_obs gp_obs y dA;
+varexo e_a e_m;
+
+parameters alp bet gam mst rho psi del;
+
+alp = 0.33;
+bet = 0.99;
+gam = 0.003;
+mst = 1.011;
+rho = 0.7;
+psi = 0.787;
+del = 0.02;
+
+model;
+dA = exp(gam+e_a);
+log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
+-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
+W = l/n;
+-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
+R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
+1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
+c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
+P*c = m;
+m-1+d = l;
+e = exp(e_a);
+y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
+gy_obs = dA*y/y(-1);
+gp_obs = (P/P(-1))*m(-1)/dA;
+end;
+
+shocks;
+var e_a; stderr 0.014;
+var e_m; stderr 0.005;
+end;
+
+steady_state_model;
+  dA = exp(gam);
+  gst = 1/dA;
+  m = mst;
+  khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
+  xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
+  nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
+  n  = xist/(nust+xist);
+  P  = xist + nust;
+  k  = khst*n;
+
+  l  = psi*mst*n/( (1-psi)*(1-n) );
+  c  = mst/P;
+  d  = l - mst + 1;
+  y  = k^alp*n^(1-alp)*gst^alp;
+  R  = mst/bet;
+  W  = l/n;
+  ist  = y-c;
+  q  = 1 - d;
+
+  e = 1;
+
+  gp_obs = m/dA;
+  gy_obs = dA;
+end;
+
+steady;
+
+check;
+
+estimated_params;
+alp, beta_pdf, 0.356, 0.02;
+bet, beta_pdf, 0.993, 0.002;
+gam, normal_pdf, 0.0085, 0.003;
+mst, normal_pdf, 1.0002, 0.007;
+rho, beta_pdf, 0.129, 0.100;
+psi, beta_pdf, 0.65, 0.05;
+del, beta_pdf, 0.01, 0.005;
+stderr e_a, inv_gamma_pdf, 0.035449, inf;
+stderr e_m, inv_gamma_pdf, 0.008862, inf;
+end;
+
+varobs gp_obs gy_obs;
+
+estimation(order=1, datafile='../fsdat_simul', nobs=192, loglinear, mh_replic=20000, mh_nblocks=2, mh_tune_jscale=0.33);
+
+mhdata = load('fs2000/metropolis/fs2000_mh_history_0.mat');
+
+if any(abs(mhdata.record.AcceptanceRatio-options_.mh_tune_jscale.target)>options_.mh_tune_jscale.c1)
+    error('Automagic tuning of the MCMC proposal scale parameter did not work as expected!')
+end