From 5515da191ab9c71edf8f2d790b48f728b13435cd Mon Sep 17 00:00:00 2001 From: Johannes Pfeifer Date: Tue, 22 Nov 2016 10:47:09 +0100 Subject: [PATCH] Add Raftery/Lewis (1992) convergence diagnostics --- doc/dynare.texi | 19 ++ license.txt | 5 + .../convergence_diagnostics/McMCDiagnostics.m | 29 ++- .../convergence_diagnostics/raftery_lewis.m | 179 ++++++++++++++++++ matlab/global_initialization.m | 3 + preprocessor/DynareBison.yy | 6 +- preprocessor/DynareFlex.ll | 2 + tests/TeX/fs2000_corr_ME.mod | 2 +- tests/estimation/fs2000.mod | 9 +- 9 files changed, 250 insertions(+), 4 deletions(-) create mode 100644 matlab/convergence_diagnostics/raftery_lewis.m diff --git a/doc/dynare.texi b/doc/dynare.texi index eccf5096d..aee146dd2 100644 --- a/doc/dynare.texi +++ b/doc/dynare.texi @@ -6189,6 +6189,21 @@ Percentage of MCMC draws at the beginning and end of the MCMC chain taken to compute the @cite{Geweke (1992,1999)} convergence diagnostics (requires @ref{mh_nblocks}=1) after discarding the first @ref{mh_drop} percent of draws as a burnin. Default: @code{[0.2 0.5]}. +@item raftery_lewis_diagnostics +@anchor{raftery_lewis_diagnostics} +Triggers the computation of the @cite{Raftery and Lewis (1992)} convergence diagnostics. The goal is deliver the number of draws +required to estimate a particular quantile of the CDF @code{q} with precision @code{r} with a probability @code{s}. Typically, one wants to estimate +the @code{q=0.025} percentile (corresponding to a 95 percent HPDI) with a precision of 0.5 percent (@code{r=0.005}) with 95 percent +certainty (@code{s=0.95}). The defaults can be changed via @ref{raftery_lewis_qrs}. Based on the +theory of first order Markov Chains, the diagnostics will provide a required burn-in (@code{M}), the number of draws after the burnin (@code{N}) +as well as a thinning factor that would deliver a first order chain (@code{k}). The last line of the table will also deliver the maximum over +all parameters for the respective values. + +@item raftery_lewis_qrs = [@var{DOUBLE} @var{DOUBLE} @var{DOUBLE}] +@anchor{raftery_lewis_qrs} +Sets the quantile of the CDF @code{q} that is estimated with precision @code{r} with a probability @code{s} in the +@cite{Raftery and Lewis (1992)} convergence diagnostics. Default: @code{[0.025 0.005 0.95]}. + @item consider_all_endogenous Compute the posterior moments, smoothed variables, k-step ahead filtered variables and forecasts (when requested) on all the @@ -14276,6 +14291,10 @@ Rabanal, Pau and Juan Rubio-Ramirez (2003): ``Comparing New Keynesian Models of the Business Cycle: A Bayesian Approach,'' Federal Reserve of Atlanta, @i{Working Paper Series}, 2003-30. +@item +Raftery, Adrien E. and Steven Lewis (1992): ``How many iterations in the Gibbs sampler?,'' in @i{Bayesian Statistics, Vol. 4}, +ed. J.O. Berger, J.M. Bernardo, A.P. Dawid, and A.F.M. Smith, Clarendon Press: Oxford, pp. 763-773. + @item Ratto, Marco (2008): ``Analysing DSGE models with global sensitivity analysis'', @i{Computational Economics}, 31, 115--139 diff --git a/license.txt b/license.txt index f14eaf9f6..f06d329d0 100644 --- a/license.txt +++ b/license.txt @@ -81,6 +81,11 @@ Copyright: 2010-2015 Alexander Meyer-Gohde 2015 Dynare Team License: GPL-3+ +Files: matlab/convergence_diagnostics/raftery_lewis.m +Copyright: 2016 Benjamin Born and Johannes Pfeifer + 2016 Dynare Team +License: GPL-3+ + Files: matlab/optimization/simpsa.m matlab/optimization/simpsaget.m matlab/optimization/simpsaset.m Copyright: 2005 Henning Schmidt, FCC, henning@fcc.chalmers.se 2006 Brecht Donckels, BIOMATH, brecht.donckels@ugent.be diff --git a/matlab/convergence_diagnostics/McMCDiagnostics.m b/matlab/convergence_diagnostics/McMCDiagnostics.m index cb84ff438..fb4f41262 100644 --- a/matlab/convergence_diagnostics/McMCDiagnostics.m +++ b/matlab/convergence_diagnostics/McMCDiagnostics.m @@ -123,7 +123,7 @@ LastLineNumber = record.MhDraws(end,3); NumberOfDraws = PastDraws(1); if NumberOfDraws<=2000 - warning(['estimation:: MCMC convergence diagnostics are not computed because the total number of iterations is less than 2000!']) + warning(['estimation:: MCMC convergence diagnostics are not computed because the total number of iterations is not bigger than 2000!']) return end @@ -193,6 +193,33 @@ if nblck == 1 % Brooks and Gelman tests need more than one block dyn_latex_table(M_,options_,my_title,'geweke',headers,param_name_tex,datamat,lh,12,4,additional_header); end skipline(2); + + if options_.convergence.rafterylewis.indicator + if any(options_.convergence.rafterylewis.qrs<0) || any(options_.convergence.rafterylewis.qrs>1) || length(options_.convergence.rafterylewis.qrs)~=3 ... + || (options_.convergence.rafterylewis.qrs(1)-options_.convergence.rafterylewis.qrs(2)<=0) + fprintf('\nCONVERGENCE DIAGNOSTICS: Invalid option for raftery_lewis_qrs. Using the default of [0.025 0.005 0.95].\n') + options_.convergence.rafterylewis.qrs=[0.025 0.005 0.95]; + end + Raftery_Lewis_q=options_.convergence.rafterylewis.qrs(1); + Raftery_Lewis_r=options_.convergence.rafterylewis.qrs(2); + Raftery_Lewis_s=options_.convergence.rafterylewis.qrs(3); + oo_.Raftery_Lewis = raftery_lewis(x2,Raftery_Lewis_q,Raftery_Lewis_r,Raftery_Lewis_s); + oo_.Raftery_Lewis.parameter_names=param_name; + my_title=sprintf('Raftery/Lewis (1992) Convergence Diagnostics, based on quantile q=%4.3f with precision r=%4.3f with probability s=%4.3f.',Raftery_Lewis_q,Raftery_Lewis_r,Raftery_Lewis_s); + headers = char('Variables','M (burn-in)','N (req. draws)','N+M (total draws)','k (thinning)'); + + raftery_data_mat=[oo_.Raftery_Lewis.M_burn,oo_.Raftery_Lewis.N_prec,oo_.Raftery_Lewis.N_total,oo_.Raftery_Lewis.k_thin]; + raftery_data_mat=[raftery_data_mat;max(raftery_data_mat)]; + labels_Raftery_Lewis=char(param_name,'Maximum'); + lh = size(labels_Raftery_Lewis,2)+2; + dyntable(options_,my_title,headers,labels_Raftery_Lewis,raftery_data_mat,lh,10,0); + if options_.TeX + labels_Raftery_Lewis_tex=char(param_name_tex,'Maximum'); + lh = size(labels_Raftery_Lewis_tex,2)+2; + dyn_latex_table(M_,options_,my_title,'raftery_lewis',headers,labels_Raftery_Lewis_tex,raftery_data_mat,lh,10,0); + end + end + return; end diff --git a/matlab/convergence_diagnostics/raftery_lewis.m b/matlab/convergence_diagnostics/raftery_lewis.m new file mode 100644 index 000000000..c2a162d87 --- /dev/null +++ b/matlab/convergence_diagnostics/raftery_lewis.m @@ -0,0 +1,179 @@ +function [raftery_lewis] = raftery_lewis(runs,q,r,s) +% function raftery_lewis = raftery_lewis(runs,q,r,s) +% Computes the convergence diagnostics of Raftery and Lewis (1992), i.e. the +% number of draws needed in MCMC to estimate the posterior cdf of the q-quantile +% within an accuracy r with probability s +% +% Inputs: +% - draws [n_draws by n_var] double matrix of draws from the sampler +% - q [scalar] quantile of the quantity of interest +% - r [scalar] level of desired precision +% - s [scalar] probability associated with r +% +% Output: +% raftery_lewis [structure] containing the fields: +% - M_burn [n_draws by 1] number of draws required for burn-in +% - N_prec [n_draws by 1] number of draws required to achieve desired precision r +% - k_thin [n_draws by 1] thinning required to get 1st order MC +% - k_ind [n_draws by 1] thinning required to get independence +% - I_stat [n_draws by 1] I-statistic of Raftery/Lewis (1992b) +% measures increase in required +% iterations due to dependence in chain +% - N_min [scalar] # draws if the chain is white noise +% - N_total [n_draws by 1] nburn + nprec +% + +% --------------------------------------------------------------------- +% NOTES: Example values of q, r, s: +% 0.025, 0.005, 0.95 (for a long-tailed distribution) +% 0.025, 0.0125, 0.95 (for a short-tailed distribution); +% +% - The result is quite sensitive to r, being proportional to the +% inverse of r^2. +% - For epsilon (closeness of probabilities to equilibrium values), +% Raftery/Lewis use 0.001 and argue that the results +% are quite robust to changes in this value +% +% --------------------------------------------------------------------- +% REFERENCES: +% Raftery, Adrien E./Lewis, Steven (1992a): "How many iterations in the Gibbs sampler?" +% in: Bernardo/Berger/Dawid/Smith (eds.): Bayesian Statistics, Vol. 4, Clarendon Press: Oxford, +% pp. 763-773. +% Raftery, Adrien E./Lewis, Steven (1992b): "Comment: One long run with diagnostics: +% Implementation strategies for Markov chain Monte Carlo." Statistical Science, +% 7(4), pp. 493-497. +% +% ---------------------------------------------------- + +% Copyright (C) 2016 Benjamin Born and Johannes Pfeifer +% Copyright (C) 2016 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 . + + + +[n_runs, n_vars] = size(runs); + +raftery_lewis.M_burn=NaN(n_vars,1); +raftery_lewis.N_prec=NaN(n_vars,1); +raftery_lewis.k_thin=NaN(n_vars,1); +raftery_lewis.k_ind=NaN(n_vars,1); +raftery_lewis.I_stat=NaN(n_vars,1); +raftery_lewis.N_total=NaN(n_vars,1); + + +thinned_chain = zeros(n_runs,1); +%quantities that can be precomputed as they are independent of variable +Phi = norminv((s+1)/2); %note the missing ^{-1} at the Phi in equation top page 5, see RL (1995) +raftery_lewis.N_min = fix(Phi^2*(1-q)*q/r^2+1); + +for nv = 1:n_vars % big loop over variables + if q > 0 && q < 1 + work = (runs(:,nv) <= quantile(runs(:,nv),q)); + else + error('Quantile must be between 0 and 1'); + end; + + k_thin_current_var = 1; + bic = 1; + epss = 0.001; + % Find thinning factor for which first-order Markov Chain is preferred to second-order one + while(bic > 0) + thinned_chain=work(1:k_thin_current_var:n_runs,1); + [g2, bic] = first_vs_second_order_MC_test(thinned_chain); + k_thin_current_var = k_thin_current_var+1; + end; + + k_thin_current_var = k_thin_current_var-1; %undo last step + + %compute transition probabilities + transition_matrix = zeros(2,2); + for i1 = 2:size(thinned_chain,1) + transition_matrix(thinned_chain(i1-1)+1,thinned_chain(i1)+1) = transition_matrix(thinned_chain(i1-1)+1,thinned_chain(i1)+1)+1; + end; + alpha = transition_matrix(1,2)/(transition_matrix(1,1)+transition_matrix(1,2)); %prob of going from 1 to 2 + beta = transition_matrix(2,1)/(transition_matrix(2,1)+transition_matrix(2,2)); %prob of going from 2 to 1 + + kmind=k_thin_current_var; + [g2, bic]=independence_chain_test(thinned_chain); + + while(bic > 0) + thinned_chain=work(1:kmind:n_runs,1); + [g2, bic] = independence_chain_test(thinned_chain); + kmind = kmind+1; + end; + + m_star = log((alpha + beta)*epss/max(alpha,beta))/log(abs(1 - alpha - beta)); %equation bottom page 4 + raftery_lewis.M_burn(nv) = fix((m_star+1)*k_thin_current_var); + n_star = (2 - (alpha + beta))*alpha*beta*(Phi^2)/((alpha + beta)^3 * r^2); %equation top page 5 + raftery_lewis.N_prec(nv) = fix(n_star+1)*k_thin_current_var; + raftery_lewis.I_stat(nv) = (raftery_lewis.M_burn(nv) + raftery_lewis.N_prec(nv))/raftery_lewis.N_min; + raftery_lewis.k_ind(nv) = max(fix(raftery_lewis.I_stat(nv)+1),kmind); + raftery_lewis.k_thin(nv) = k_thin_current_var; + raftery_lewis.N_total(nv)= raftery_lewis.M_burn(nv)+raftery_lewis.N_prec(nv); +end; + +end + +function [g2, bic] = first_vs_second_order_MC_test(d) +%conducts a test of first vs. second order Markov Chain via BIC criterion +n_obs=size(d,1); +g2 = 0; +tran=zeros(2,2,2); +for t_iter=3:n_obs % count state transitions + tran(d(t_iter-2,1)+1,d(t_iter-1,1)+1,d(t_iter,1)+1)=tran(d(t_iter-2,1)+1,d(t_iter-1,1)+1,d(t_iter,1)+1)+1; +end; +% Compute the log likelihood ratio statistic for second-order MC vs first-order MC. G2 statistic of Bishop, Fienberg and Holland (1975) +for ind_1 = 1:2 + for ind_2 = 1:2 + for ind_3 = 1:2 + if tran(ind_1,ind_2,ind_3) ~= 0 + fitted = (tran(ind_1,ind_2,1) + tran(ind_1,ind_2,2))*(tran(1,ind_2,ind_3) + tran(2,ind_2,ind_3))/... + (tran(1,ind_2,1) + tran(1,ind_2,2) + tran(2,ind_2,1) + tran(2,ind_2,2)); + focus = tran(ind_1,ind_2,ind_3); + g2 = g2 + log(focus/fitted)*focus; + end + end; % end of for i3 + end; % end of for i2 +end; % end of for i1 +g2 = g2*2; +bic = g2 - log(n_obs-2)*2; + +end + + +function [g2, bic] = independence_chain_test(d) +%conducts a test of independence Chain via BIC criterion +n_obs=size(d,1); +trans = zeros(2,2); +for ind_1 = 2:n_obs + trans(d(ind_1-1)+1,d(ind_1)+1)=trans(d(ind_1-1)+1,d(ind_1)+1)+1; +end; +dcm1 = n_obs - 1; +g2 = 0; +% Compute the log likelihood ratio statistic for second-order MC vs first-order MC. G2 statistic of Bishop, Fienberg and Holland (1975) +for ind_1 = 1:2 + for ind_2 = 1:2 + if trans(ind_1,ind_2) ~= 0 + fitted = ((trans(ind_1,1) + trans(ind_1,2))*(trans(1,ind_2) + trans(2,ind_2)))/dcm1; + focus = trans(ind_1,ind_2); + g2 = g2 + log(focus/fitted)*focus; + end; + end; +end; +g2 = g2*2; +bic = g2 - log(dcm1); +end diff --git a/matlab/global_initialization.m b/matlab/global_initialization.m index 12273dd17..e62b59065 100644 --- a/matlab/global_initialization.m +++ b/matlab/global_initialization.m @@ -767,6 +767,9 @@ options_.gpu = 0; %Geweke convergence diagnostics options_.convergence.geweke.taper_steps=[4 8 15]; options_.convergence.geweke.geweke_interval=[0.2 0.5]; +%Raftery/Lewis convergence diagnostics; +options_.convergence.rafterylewis.indicator=0; +options_.convergence.rafterylewis.qrs=[0.025 0.005 0.95]; % Options for lmmcp solver options_.lmmcp.status = 0; diff --git a/preprocessor/DynareBison.yy b/preprocessor/DynareBison.yy index 61230cb3e..6aaa25707 100644 --- a/preprocessor/DynareBison.yy +++ b/preprocessor/DynareBison.yy @@ -108,7 +108,7 @@ class ParsingDriver; %token LYAPUNOV_FIXED_POINT_TOL LYAPUNOV_DOUBLING_TOL LYAPUNOV_SQUARE_ROOT_SOLVER_TOL LOG_DEFLATOR LOG_TREND_VAR LOG_GROWTH_FACTOR MARKOWITZ MARGINAL_DENSITY MAX MAXIT %token MFS MH_CONF_SIG MH_DROP MH_INIT_SCALE MH_JSCALE MH_MODE MH_NBLOCKS MH_REPLIC MH_RECOVER POSTERIOR_MAX_SUBSAMPLE_DRAWS MIN MINIMAL_SOLVING_PERIODS %token MODE_CHECK MODE_CHECK_NEIGHBOURHOOD_SIZE MODE_CHECK_SYMMETRIC_PLOTS MODE_CHECK_NUMBER_OF_POINTS MODE_COMPUTE MODE_FILE MODEL MODEL_COMPARISON MODEL_INFO MSHOCKS ABS SIGN -%token MODEL_DIAGNOSTICS MODIFIEDHARMONICMEAN MOMENTS_VARENDO CONTEMPORANEOUS_CORRELATION DIFFUSE_FILTER SUB_DRAWS TAPER_STEPS GEWEKE_INTERVAL MCMC_JUMPING_COVARIANCE MOMENT_CALIBRATION +%token MODEL_DIAGNOSTICS MODIFIEDHARMONICMEAN MOMENTS_VARENDO CONTEMPORANEOUS_CORRELATION DIFFUSE_FILTER SUB_DRAWS TAPER_STEPS GEWEKE_INTERVAL RAFTERY_LEWIS_QRS RAFTERY_LEWIS_DIAGNOSTICS MCMC_JUMPING_COVARIANCE MOMENT_CALIBRATION %token NUMBER_OF_PARTICLES RESAMPLING SYSTEMATIC GENERIC RESAMPLING_THRESHOLD RESAMPLING_METHOD KITAGAWA STRATIFIED SMOOTH %token CPF_WEIGHTS AMISANOTRISTANI MURRAYJONESPARSLOW %token FILTER_ALGORITHM PROPOSAL_APPROXIMATION CUBATURE UNSCENTED MONTECARLO DISTRIBUTION_APPROXIMATION @@ -1800,6 +1800,8 @@ estimation_options : o_datafile | o_qz_zero_threshold | o_taper_steps | o_geweke_interval + | o_raftery_lewis_qrs + | o_raftery_lewis_diagnostics | o_mcmc_jumping_covariance | o_irf_plot_threshold | o_posterior_max_subsample_draws @@ -2898,6 +2900,8 @@ o_xls_range : XLS_RANGE EQUAL range { driver.option_str("xls_range", $3); }; o_filter_step_ahead : FILTER_STEP_AHEAD EQUAL vec_int { driver.option_vec_int("filter_step_ahead", $3); }; o_taper_steps : TAPER_STEPS EQUAL vec_int { driver.option_vec_int("convergence.geweke.taper_steps", $3); }; o_geweke_interval : GEWEKE_INTERVAL EQUAL vec_value { driver.option_num("convergence.geweke.geweke_interval",$3); }; +o_raftery_lewis_diagnostics : RAFTERY_LEWIS_DIAGNOSTICS { driver.option_num("convergence.rafterylewis.indicator", "1"); }; +o_raftery_lewis_qrs : RAFTERY_LEWIS_QRS EQUAL vec_value { driver.option_num("convergence.rafterylewis.qrs",$3); }; o_constant : CONSTANT { driver.option_num("noconstant", "0"); }; o_noconstant : NOCONSTANT { driver.option_num("noconstant", "1"); }; o_mh_recover : MH_RECOVER { driver.option_num("mh_recover", "1"); }; diff --git a/preprocessor/DynareFlex.ll b/preprocessor/DynareFlex.ll index 33be4c8d9..a5ca4ac04 100644 --- a/preprocessor/DynareFlex.ll +++ b/preprocessor/DynareFlex.ll @@ -272,6 +272,8 @@ DATE -?[0-9]+([YyAa]|[Mm]([1-9]|1[0-2])|[Qq][1-4]|[Ww]([1-9]{1}|[1-4][0-9]|5[0-2 lik_init {return token::LIK_INIT;} taper_steps {return token::TAPER_STEPS;} geweke_interval {return token::GEWEKE_INTERVAL;} +raftery_lewis_qrs {return token::RAFTERY_LEWIS_QRS;} +raftery_lewis_diagnostics {return token::RAFTERY_LEWIS_DIAGNOSTICS;} graph {return token::GRAPH;} nograph {return token::NOGRAPH;} nodisplay {return token::NODISPLAY;} diff --git a/tests/TeX/fs2000_corr_ME.mod b/tests/TeX/fs2000_corr_ME.mod index fe432c944..dfb933ee1 100644 --- a/tests/TeX/fs2000_corr_ME.mod +++ b/tests/TeX/fs2000_corr_ME.mod @@ -169,7 +169,7 @@ end; write_latex_prior_table; estimation(mode_compute=8,order=1,datafile='../fs2000/fsdat_simul',mode_check,smoother,filter_decomposition,mh_replic=4000, mh_nblocks=1, mh_jscale=0.8,forecast = 8,bayesian_irf,filtered_vars,filter_step_ahead=[1,3],irf=20, - moments_varendo,contemporaneous_correlation,conditional_variance_decomposition=[1 2 4],smoothed_state_uncertainty) m P c e W R k d y gy_obs; + moments_varendo,contemporaneous_correlation,conditional_variance_decomposition=[1 2 4],smoothed_state_uncertainty,raftery_lewis_diagnostics) m P c e W R k d y gy_obs; trace_plot(options_,M_,estim_params_,'PosteriorDensity',1); trace_plot(options_,M_,estim_params_,'StructuralShock',1,'e_a') diff --git a/tests/estimation/fs2000.mod b/tests/estimation/fs2000.mod index 1ef75d559..0fa67c46b 100644 --- a/tests/estimation/fs2000.mod +++ b/tests/estimation/fs2000.mod @@ -84,12 +84,19 @@ options_.solve_tolf = 1e-12; estimation(order=1,datafile=fsdat_simul,nobs=192,loglinear,mh_replic=3000,mh_nblocks=1,mh_jscale=0.8,moments_varendo,selected_variables_only,contemporaneous_correlation,smoother,forecast=8, geweke_interval = [0.19 0.49], - taper_steps = [4 7 15] + taper_steps = [4 7 15], + raftery_lewis_diagnostics, + raftery_lewis_qrs=[0.025 0.01 0.95] ) y m; + if ~isequal(options_.convergence.geweke.taper_steps,[4 7 15]') || ~isequal(options_.convergence.geweke.geweke_interval,[0.19 0.49]) error('Interface for Geweke diagnostics not working') end +if ~isequal(options_.convergence.rafterylewis.qrs,[0.025 0.01 0.95]) || ~isequal(options_.convergence.rafterylewis.indicator,1) + error('Interface for Raftery/Lewis diagnostics not working') +end + %test load_mh_file option options_.smoother=0; options_.moments_varendo=0;