110 lines
4.2 KiB
Matlab
110 lines
4.2 KiB
Matlab
function [LIK,lik] = conditional_particle_filter(ReducedForm, Y, s, ParticleOptions, ThreadsOptions, options_, M_)
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% Evaluates the likelihood of a non-linear model with a particle filter
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%
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% INPUTS
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% - ReducedForm [structure] Matlab's structure describing the reduced form model.
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% - Y [double] p×T matrix of (detrended) data, where p is the number of observed variables.
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% - s [integer] scalar, likelihood evaluation starts at s (has to be smaller than T, the sample length provided in Y).
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% - ParticlesOptions [struct]
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% - ThreadsOptions [struct]
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% - options_ [struct]
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% - M_ [struct]
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%
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% OUTPUTS
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% - LIK [double] scalar, likelihood
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% - lik [double] (T-s+1)×1 vector, density of observations in each period.
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%
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% REMARKS
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% - The proposal is built using the Kalman updating step for each particle.
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% - we need draws in the errors distributions
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% Whether we use Monte-Carlo draws from a multivariate gaussian distribution
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% as in Amisano & Tristani (JEDC 2010).
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% Whether we use multidimensional Gaussian sparse grids approximations:
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% - a univariate Kronrod-Paterson Gaussian quadrature combined by the Smolyak
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% operator (ref: Winschel & Kratzig, 2010).
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% - a spherical-radial cubature (ref: Arasaratnam & Haykin, 2009a,2009b).
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% - a scaled unscented transform cubature (ref: Julier & Uhlmann 1997, van der
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% Merwe & Wan 2003).
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%
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% Pros:
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% - Allows using current observable information in the proposal
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% - The use of sparse grids Gaussian approximation is much faster than the Monte-Carlo approach
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% Cons:
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% - The use of the Kalman updating step may biais the proposal distribution since
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% it has been derived in a linear context and is implemented in a nonlinear
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% context. That is why particle resampling is performed.
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% Copyright © 2009-2020 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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% Set default for third input argument.
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if isempty(s)
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s = 1;
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end
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T = size(Y,2);
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p = length(ReducedForm.mf1);
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n = ParticleOptions.number_of_particles;
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% Get covariance matrices
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Q = ReducedForm.Q;
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H = ReducedForm.H;
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if isempty(H)
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H = 0;
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H_lower_triangular_cholesky = 0;
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else
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H_lower_triangular_cholesky = chol(H)';
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end
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% Get initial condition for the state vector.
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StateVectorMean = ReducedForm.StateVectorMean;
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StateVectorVarianceSquareRoot = chol(ReducedForm.StateVectorVariance)';
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state_variance_rank = size(StateVectorVarianceSquareRoot, 2);
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Q_lower_triangular_cholesky = chol(Q)';
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% Set seed for randn().
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options_=set_dynare_seed_local_options(options_,'default');
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% Initialization of the likelihood.
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lik = NaN(T, 1);
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ks = 0;
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StateParticles = bsxfun(@plus, StateVectorVarianceSquareRoot*randn(state_variance_rank, n), StateVectorMean);
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SampleWeights = ones(1, n)/n;
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for t=1:T
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flags = false(n, 1);
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for i=1:n
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[StateParticles(:,i), SampleWeights(i), flags(i)] = ...
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conditional_filter_proposal(ReducedForm, Y(:,t), StateParticles(:,i), SampleWeights(i), Q_lower_triangular_cholesky, H_lower_triangular_cholesky, H, ParticleOptions, ThreadsOptions, options_, M_);
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end
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if any(flags)
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LIK = -Inf;
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lik(t) = -Inf;
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return
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end
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SumSampleWeights = sum(SampleWeights);
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lik(t) = log(SumSampleWeights);
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SampleWeights = SampleWeights./SumSampleWeights;
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if (ParticleOptions.resampling.status.generic && neff(SampleWeights)<ParticleOptions.resampling.threshold*T) || ParticleOptions.resampling.status.systematic
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ks = ks + 1;
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StateParticles = resample(StateParticles', SampleWeights', ParticleOptions)';
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SampleWeights = ones(1, n)/n;
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end
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end
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LIK = -sum(lik(s:end)); |