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function [theta, fxsim, neval] = slice_sampler(objective_function,theta,thetaprior,sampler_options,varargin)
% function [theta, fxsim, neval] = slice_sampler(objective_function,theta,thetaprior,sampler_options,varargin)
% ----------------------------------------------------------
% UNIVARIATE SLICE SAMPLER - stepping out (Neal, 2003)
% W: optimal value in the range (3,10)*std(x)
% - see C.Planas and A.Rossi (2014)
% objective_function(theta,varargin): -log of any unnormalized pdf
% with varargin (optional) a vector of auxiliaty parameters
% to be passed to f( ).
% ----------------------------------------------------------
%
% INPUTS
% objective_function: objective function (expressed as minus the log of a density)
% theta: last value of theta
% thetaprior: bounds of the theta space
% sampler_options: posterior sampler options
% varargin: optional input arguments to objective function
%
% OUTPUTS
% theta: new theta sample
% fxsim: value of the objective function for the new sample
% neval: number of function evaluations
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2015-2017 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/>.
if sampler_options.rotated %&& ~isempty(sampler_options.V1),
[theta, fxsim, neval] = rotated_slice_sampler(objective_function,theta,thetaprior,sampler_options,varargin{:});
if isempty(sampler_options.mode) % jumping
return
else
nevalR=sum(neval);
end
end
theta=theta(:);
npar = length(theta);
W1 = sampler_options.W1;
neval = zeros(npar,1);
for it=1:npar
neval(it) = 0;
W = W1(it);
xold = theta(it);
% XLB = thetaprior(3);
% XUB = thetaprior(4);
XLB = thetaprior(it,1);
XUB = thetaprior(it,2);
% -------------------------------------------------------
% 1. DRAW Z = ln[f(X0)] - EXP(1) where EXP(1)=-ln(U(0,1))
% THIS DEFINES THE SLICE S={x: z < ln(f(x))}
% -------------------------------------------------------
fxold = -feval(objective_function,theta,varargin{:});
neval(it) = neval(it) + 1;
Z = fxold + log(rand(1,1));
% -------------------------------------------------------------
% 2. FIND I=(L,R) AROUND X0 THAT CONTAINS S AS MUCH AS POSSIBLE
% STEPPING-OUT PROCEDURE
% -------------------------------------------------------------
u = rand(1,1);
L = max(XLB,xold-W*u);
R = min(XUB,L+W);
while(L > XLB)
xsim = L;
theta(it) = xsim;
fxl = -feval(objective_function,theta,varargin{:});
neval(it) = neval(it) + 1;
if (fxl <= Z)
break
end
L = max(XLB,L-W);
end
while(R < XUB)
xsim = R;
theta(it) = xsim;
fxr = -feval(objective_function,theta,varargin{:});
neval(it) = neval(it) + 1;
if (fxr <= Z)
break
end
R = min(XUB,R+W);
end
% ------------------------------------------------------
% 3. SAMPLING FROM THE SET A = (I INTERSECT S) = (LA,RA)
% ------------------------------------------------------
fxsim = Z-1;
while (fxsim < Z)
u = rand(1,1);
xsim = L + u*(R - L);
theta(it) = xsim;
fxsim = -feval(objective_function,theta,varargin{:});
neval(it) = neval(it) + 1;
if (xsim > xold)
R = xsim;
else
L = xsim;
end
end
end
if sampler_options.rotated && ~isempty(sampler_options.mode) % jumping
neval=sum(neval)+nevalR;
end
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