factorize some codes across options and modify the definition of mixtures.
parent
ffd62a5923
commit
2858470942
|
@ -3,28 +3,24 @@ function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, Thr
|
|||
% predictive (prior) and filtered (posterior) densities for state variables
|
||||
% by gaussian distributions.
|
||||
% Gaussian approximation is done by:
|
||||
% - a Kronrod-Paterson gaussian quadrature with a limited number of nodes.
|
||||
% Multidimensional quadrature is obtained by the Smolyak operator (ref: Winschel & Kratzig, 2010).
|
||||
% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2008,2009).
|
||||
% - a scaled unscented transform cubature (ref: )
|
||||
% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2009).
|
||||
% - a scaled unscented transform cubature (ref: Julier & Uhlmann 1995)
|
||||
% - Monte-Carlo draws from a multivariate gaussian distribution.
|
||||
% First and second moments of prior and posterior state densities are computed
|
||||
% from the resulting nodes/particles and allows to generate new distributions at the
|
||||
% following observation.
|
||||
% => The use of nodes is much faster than Monte-Carlo Gaussian particle and standard particles
|
||||
% filters since it treats a lesser number of particles and there is no need
|
||||
% Pros: The use of nodes is much faster than Monte-Carlo Gaussian particle and standard particles
|
||||
% filters since it treats a lesser number of particles. Furthermore, in all cases, there is no need
|
||||
% of resampling.
|
||||
% However, estimations may reveal biaised if the model is truly non-gaussian
|
||||
% Cons: estimations may be biaised if the model is truly non-gaussian
|
||||
% since predictive and filtered densities are unimodal.
|
||||
%
|
||||
% INPUTS
|
||||
% reduced_form_model [structure] Matlab's structure describing the reduced form model.
|
||||
% reduced_form_model.measurement.H [double] (pp x pp) variance matrix of measurement errors.
|
||||
% reduced_form_model.state.Q [double] (qq x qq) variance matrix of state errors.
|
||||
% reduced_form_model.state.dr [structure] output of resol.m.
|
||||
% Y [double] pp*smpl matrix of (detrended) data, where pp is the maximum number of observed variables.
|
||||
% start [integer] scalar, likelihood evaluation starts at 'start'.
|
||||
% smolyak_accuracy [integer] scalar.
|
||||
% Reduced_Form [structure] Matlab's structure describing the reduced form model.
|
||||
% Y [double] matrix of original observed variables.
|
||||
% start [double] structural parameters.
|
||||
% ParticleOptions [structure] Matlab's structure describing options concerning particle filtering.
|
||||
% ThreadsOptions [structure] Matlab's structure.
|
||||
%
|
||||
% OUTPUTS
|
||||
% LIK [double] scalar, likelihood
|
||||
|
@ -34,7 +30,7 @@ function [LIK,lik] = gaussian_filter(ReducedForm, Y, start, ParticleOptions, Thr
|
|||
%
|
||||
% NOTES
|
||||
% The vector "lik" is used to evaluate the jacobian of the likelihood.
|
||||
% Copyright (C) 2009-2013 Dynare Team
|
||||
% Copyright (C) 2009-2015 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
|
@ -110,12 +106,7 @@ const_lik = (2*pi)^(number_of_observed_variables/2) ;
|
|||
lik = NaN(sample_size,1);
|
||||
LIK = NaN;
|
||||
|
||||
SampleWeights = 1/number_of_particles ;
|
||||
ks = 0 ;
|
||||
%Estimate = zeros(number_of_state_variables,sample_size) ;
|
||||
%V_Estimate = zeros(number_of_state_variables,number_of_state_variables,sample_size) ;
|
||||
for t=1:sample_size
|
||||
% build the proposal
|
||||
[PredictedStateMean,PredictedStateVarianceSquareRoot,StateVectorMean,StateVectorVarianceSquareRoot] = ...
|
||||
gaussian_filter_bank(ReducedForm,Y(:,t),StateVectorMean,StateVectorVarianceSquareRoot,Q_lower_triangular_cholesky,H_lower_triangular_cholesky,H,ParticleOptions,ThreadsOptions) ;
|
||||
if ParticleOptions.distribution_approximation.cubature || ParticleOptions.distribution_approximation.unscented
|
||||
|
@ -126,40 +117,21 @@ for t=1:sample_size
|
|||
PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
|
||||
weights2,weights_c2,ReducedForm,ThreadsOptions) ;
|
||||
SampleWeights = weights2.*IncrementalWeights ;
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
StateVectorMean = StateParticles*SampleWeights ;
|
||||
temp = bsxfun(@minus,StateParticles,StateVectorMean) ;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky( bsxfun(@times,SampleWeights',temp)*temp' )';
|
||||
else % Monte-Carlo draws
|
||||
else
|
||||
StateParticles = bsxfun(@plus,StateVectorVarianceSquareRoot*randn(state_variance_rank,number_of_particles),StateVectorMean) ;
|
||||
IncrementalWeights = ...
|
||||
gaussian_densities(Y(:,t),StateVectorMean,...
|
||||
StateVectorVarianceSquareRoot,PredictedStateMean,...
|
||||
PredictedStateVarianceSquareRoot,StateParticles,H,const_lik,...
|
||||
1/number_of_particles,1/number_of_particles,ReducedForm,ThreadsOptions) ;
|
||||
%SampleWeights = SampleWeights.*IncrementalWeights ;
|
||||
SampleWeights = IncrementalWeights/number_of_particles ;
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
%VarSampleWeights = IncrementalWeights-SumSampleWeights ;
|
||||
%VarSampleWeights = VarSampleWeights*VarSampleWeights'/(number_of_particles-1) ;
|
||||
lik(t) = log(SumSampleWeights) ; %+ .5*VarSampleWeights/(number_of_particles*(SumSampleWeights*SumSampleWeights)) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
% Neff = neff(SampleWeights) ;
|
||||
% if (Neff<0.5*sample_size && ParticleOptions.resampling.status.generic) || ParticleOptions.resampling.status.systematic
|
||||
% ks = ks + 1 ;
|
||||
% StateParticles = resample(StateParticles',SampleWeights,ParticleOptions)' ;
|
||||
% StateVectorMean = mean(StateParticles,2) ;
|
||||
% StateVectorVarianceSquareRoot = reduced_rank_cholesky( (StateParticles*StateParticles')/(number_of_particles-1) - StateVectorMean*(StateVectorMean') )';
|
||||
% SampleWeights = 1/number_of_particles ;
|
||||
% elseif ParticleOptions.resampling.status.none
|
||||
StateVectorMean = StateParticles*SampleWeights ;
|
||||
temp = bsxfun(@minus,StateParticles,StateVectorMean) ;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky( bsxfun(@times,SampleWeights',temp)*temp' )';
|
||||
%disp(StateVectorVarianceSquareRoot)
|
||||
% end
|
||||
end
|
||||
SumSampleWeights = sum(SampleWeights) ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
StateVectorMean = StateParticles*SampleWeights ;
|
||||
temp = bsxfun(@minus,StateParticles,StateVectorMean) ;
|
||||
StateVectorVarianceSquareRoot = reduced_rank_cholesky( bsxfun(@times,SampleWeights',temp)*temp' )';
|
||||
end
|
||||
|
||||
LIK = -sum(lik(start:end));
|
||||
|
|
|
@ -52,8 +52,7 @@ function [LIK,lik] = gaussian_mixture_filter(ReducedForm,Y,start,ParticleOptions
|
|||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
|
||||
persistent init_flag mf0 mf1 Gprime Gsecond
|
||||
persistent init_flag mf0 mf1
|
||||
persistent nodes weights weights_c I J G number_of_particles
|
||||
persistent sample_size number_of_state_variables number_of_observed_variables number_of_structural_innovations
|
||||
|
||||
|
@ -71,16 +70,10 @@ if isempty(init_flag)
|
|||
number_of_observed_variables = length(mf1);
|
||||
number_of_structural_innovations = length(ReducedForm.Q);
|
||||
G = ParticleOptions.mixture_state_variables; % number of GM components in state
|
||||
I = 1 ; %ParticleOptions.mixture_structural_shocks ; % number of GM components in structural noise
|
||||
J = 1 ; %ParticleOptions.mixture_measurement_shocks ; % number of GM components in observation noise
|
||||
Gprime = G*I ;
|
||||
Gsecond = G*I*J ;
|
||||
number_of_particles = ParticleOptions.number_of_particles;
|
||||
init_flag = 1;
|
||||
end
|
||||
|
||||
SampleWeights = ones(Gsecond,1)/Gsecond ;
|
||||
|
||||
% compute gaussian quadrature nodes and weights on states and shocks
|
||||
if isempty(nodes)
|
||||
if ParticleOptions.distribution_approximation.cubature
|
||||
|
@ -111,29 +104,54 @@ else
|
|||
end
|
||||
Q_lower_triangular_cholesky = reduced_rank_cholesky(Q)';
|
||||
|
||||
% Initialize all matrices
|
||||
% Initialize mixtures
|
||||
StateWeights = ones(1,G)/G ;
|
||||
StateMu = ReducedForm.StateVectorMean*ones(1,G) ;
|
||||
StateMu = ReducedForm.StateVectorMean ;
|
||||
StateSqrtP = zeros(number_of_state_variables,number_of_state_variables,G) ;
|
||||
temp = reduced_rank_cholesky(ReducedForm.StateVectorVariance)' ;
|
||||
StateMu = bsxfun(@plus,StateMu,bsxfun(@times,diag(temp),(-(G-1)/2:1:(G-1)/2))/10) ;
|
||||
for g=1:G
|
||||
StateSqrtP(:,:,g) = temp ;
|
||||
end
|
||||
|
||||
StructuralShocksWeights = ones(1,I)/I ;
|
||||
StructuralShocksMu = zeros(number_of_structural_innovations,I) ;
|
||||
if ParticleOptions.proposal_approximation.cubature
|
||||
[StructuralShocksMu,StructuralShocksWeights] = spherical_radial_sigma_points(number_of_structural_innovations);
|
||||
StructuralShocksWeights = ones(size(StructuralShocksMu,1),1)*StructuralShocksWeights ;
|
||||
elseif ParticleOptions.proposal_approximation.unscented
|
||||
[StructuralShocksMu,StructuralShocksWeights,raf] = unscented_sigma_points(number_of_structural_innovations,ParticleOptions);
|
||||
else
|
||||
if ~ParticleOptions.distribution_approximation.montecarlo
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
end
|
||||
end
|
||||
I = size(StructuralShocksWeights,1) ;
|
||||
StructuralShocksMu = Q_lower_triangular_cholesky*(StructuralShocksMu') ;
|
||||
StructuralShocksSqrtP = zeros(number_of_structural_innovations,number_of_structural_innovations,I) ;
|
||||
for i=1:I
|
||||
StructuralShocksSqrtP(:,:,i) = Q_lower_triangular_cholesky ;
|
||||
end
|
||||
|
||||
ObservationShocksWeights = ones(1,J)/J ;
|
||||
ObservationShocksMu = zeros(number_of_observed_variables,J) ;
|
||||
if ParticleOptions.proposal_approximation.cubature
|
||||
[ObservationShocksMu,ObservationShocksWeights] = spherical_radial_sigma_points(number_of_observed_variables);
|
||||
ObservationShocksWeights = ones(size(ObservationShocksMu,1),1)*ObservationShocksWeights;
|
||||
elseif ParticleOptions.proposal_approximation.unscented
|
||||
[ObservationShocksMu,ObservationShocksWeights,raf] = unscented_sigma_points(number_of_observed_variables,ParticleOptions);
|
||||
else
|
||||
if ~ParticleOptions.distribution_approximation.montecarlo
|
||||
error('Estimation: This approximation for the proposal is not implemented or unknown!')
|
||||
end
|
||||
end
|
||||
J = size(ObservationShocksWeights,1) ;
|
||||
ObservationShocksMu = H_lower_triangular_cholesky*(ObservationShocksMu') ;
|
||||
ObservationShocksSqrtP = zeros(number_of_observed_variables,number_of_observed_variables,J) ;
|
||||
for j=1:J
|
||||
ObservationShocksSqrtP(:,:,j) = H_lower_triangular_cholesky ;
|
||||
end
|
||||
|
||||
Gprime = G*I ;
|
||||
Gsecond = G*I*J ;
|
||||
SampleWeights = ones(Gsecond,1)/Gsecond ;
|
||||
|
||||
StateWeightsPrior = zeros(1,Gprime) ;
|
||||
StateMuPrior = zeros(number_of_state_variables,Gprime) ;
|
||||
StateSqrtPPrior = zeros(number_of_state_variables,number_of_state_variables,Gprime) ;
|
||||
|
@ -142,10 +160,8 @@ StateWeightsPost = zeros(1,Gsecond) ;
|
|||
StateMuPost = zeros(number_of_state_variables,Gsecond) ;
|
||||
StateSqrtPPost = zeros(number_of_state_variables,number_of_state_variables,Gsecond) ;
|
||||
|
||||
%estimate = zeros(sample_size,number_of_state_variables,3) ;
|
||||
const_lik = (2*pi)^(.5*number_of_observed_variables) ;
|
||||
|
||||
ks = 0 ;
|
||||
lik = NaN(sample_size,1);
|
||||
LIK = NaN;
|
||||
for t=1:sample_size
|
||||
|
@ -154,13 +170,13 @@ for t=1:sample_size
|
|||
for i=1:I
|
||||
for j=1:J
|
||||
for g=1:G ;
|
||||
a = g + (j-1)*G ;
|
||||
b = a + (i-1)*Gprime ;
|
||||
[StateMuPrior(:,a),StateSqrtPPrior(:,:,a),StateWeightsPrior(1,a),...
|
||||
StateMuPost(:,b),StateSqrtPPost(:,:,b),StateWeightsPost(1,b)] =...
|
||||
gaussian_mixture_filter_bank(ReducedForm,Y(:,t),StateMu(:,g),StateSqrtP(:,:,g),StateWeights(1,g),...
|
||||
StructuralShocksMu(:,i),StructuralShocksSqrtP(:,:,i),StructuralShocksWeights(1,i),...
|
||||
ObservationShocksMu(:,j),ObservationShocksSqrtP(:,:,j),ObservationShocksWeights(1,j),...
|
||||
gprime = g + (i-1)*G ;
|
||||
gsecond = gprime + (j-1)*Gprime ;
|
||||
[StateMuPrior(:,gprime),StateSqrtPPrior(:,:,gprime),StateWeightsPrior(1,gprime),...
|
||||
StateMuPost(:,gsecond),StateSqrtPPost(:,:,gsecond),StateWeightsPost(1,gsecond)] =...
|
||||
gaussian_mixture_filter_bank(ReducedForm,Y(:,t),StateMu(:,g),StateSqrtP(:,:,g),StateWeights(g),...
|
||||
StructuralShocksMu(:,i),StructuralShocksSqrtP(:,:,i),StructuralShocksWeights(i),...
|
||||
ObservationShocksMu(:,j),ObservationShocksSqrtP(:,:,j),ObservationShocksWeights(j),...
|
||||
H,H_lower_triangular_cholesky,const_lik,ParticleOptions,ThreadsOptions) ;
|
||||
end
|
||||
end
|
||||
|
@ -197,29 +213,11 @@ for t=1:sample_size
|
|||
StateParticles,H,const_lik,1/number_of_particles,...
|
||||
1/number_of_particles,ReducedForm,ThreadsOptions) ;
|
||||
% calculate importance weights of particles
|
||||
% SampleWeights = SampleWeights.*IncrementalWeights ;
|
||||
SampleWeights = IncrementalWeights/number_of_particles ;
|
||||
SumSampleWeights = sum(SampleWeights,1) ;
|
||||
SampleWeights = SampleWeights./SumSampleWeights ;
|
||||
lik(t) = log(SumSampleWeights) ;
|
||||
% First possible state point estimates
|
||||
%estimate(t,:,1) = SampleWeights*StateParticles' ;
|
||||
% Resampling if needed of required
|
||||
% Neff = neff(SampleWeights) ;
|
||||
% if (ParticleOptions.resampling.status.generic && Neff<.5*sample_size) || ParticleOptions.resampling.status.systematic
|
||||
% ks = ks + 1 ;
|
||||
% StateParticles = resample(StateParticles',SampleWeights,ParticleOptions)' ;
|
||||
% StateVectorMean = mean(StateParticles,2) ;
|
||||
% StateVectorVarianceSquareRoot = reduced_rank_cholesky( (StateParticles*StateParticles')/number_of_particles - StateVectorMean*(StateVectorMean') )';
|
||||
% SampleWeights = 1/number_of_particles ;
|
||||
% elseif ParticleOptions.resampling.status.none
|
||||
% StateVectorMean = StateParticles*sampleWeights ;
|
||||
% temp = sqrt(SampleWeights').*StateParticles ;
|
||||
% StateVectorVarianceSquareRoot = reduced_rank_cholesky( temp*temp' - StateVectorMean*(StateVectorMean') )';
|
||||
% end
|
||||
% Use the information from particles to update the gaussian mixture on state variables
|
||||
[StateMu,StateSqrtP,StateWeights] = fit_gaussian_mixture(StateParticles,StateMu,StateSqrtP,StateWeights,0.001,10,1) ;
|
||||
%estimate(t,:,3) = StateWeights*StateMu' ;
|
||||
end
|
||||
end
|
||||
|
||||
|
|
Loading…
Reference in New Issue