From 27f1858f1704d64137cc9a1f1501c3cd47613504 Mon Sep 17 00:00:00 2001 From: Johannes Pfeifer Date: Mon, 16 Sep 2013 19:16:52 +0200 Subject: [PATCH] Adds documentation of Geweke convergence diagnostics --- doc/dynare.texi | 95 ++++++++++++++++++++++++++++++++++++++++++++----- 1 file changed, 87 insertions(+), 8 deletions(-) diff --git a/doc/dynare.texi b/doc/dynare.texi index 91758669e..17495f3fa 100644 --- a/doc/dynare.texi +++ b/doc/dynare.texi @@ -4210,12 +4210,19 @@ graphs of smoothed shocks, smoothed observation errors, smoothed and historical @algorithmshead -The Monte Carlo Markov Chain (MCMC) univariate diagnostics are generated -by the estimation command if @ref{mh_nblocks} is larger than 1, if -@ref{mh_replic} is larger than 2000, and if option @ref{nodiagnostic} is -not used. As described in section 3 of @cite{Brooks and Gelman (1998)} -the convergence diagnostics are based on comparing pooled and within -MCMC moments (Dynare displays the second and third order moments, and +The Monte Carlo Markov Chain (MCMC) diagnostics are generated +by the estimation command if @ref{mh_replic} is larger than 2000 and if +option @ref{nodiagnostic} is not used. If @ref{mh_nblocks} is equal to one, +the convergence diagnostics of @cite{Geweke (1992,1999)} is computed. It uses a +chi square test to compare the means of the first and last draws specified in +@ref{geweke_interval} (@pxref{geweke_interval}) after discarding the burnin of @ref{mh_drop}. The test is +computed using variance estimates under the assumption of no serial correlation +as well as using tapering windows specified in @ref{taper_steps} (@pxref{taper_steps}). +If @ref{mh_nblocks} is larger than 1, the convergence diagnostics of +@cite{Brooks and Gelman (1998)} are used instead. +As described in section 3 of @cite{Brooks and Gelman (1998)} the univariate +convergence diagnostics are based on comparing pooled and within MCMC moments +(Dynare displays the second and third order moments, and the length of the Highest Probability Density interval covering 80% of the posterior distribution). Due to computational reasons, the multivariate convergence diagnostic does not follow @cite{Brooks and @@ -4356,8 +4363,8 @@ the total number of Metropolis draws available. Default: @code{2} @item mh_drop = @var{DOUBLE} -The fraction of initially generated parameter vectors to be dropped -before using posterior simulations. Default: @code{0.5} +@anchor{mh_drop} +The fraction of initially generated parameter vectors to be dropped as a burnin before using posterior simulations. Default: @code{0.5} @item mh_jscale = @var{DOUBLE} The scale to be used for the jumping distribution in @@ -4756,6 +4763,18 @@ Value used to test if a generalized eigenvalue is 0/0 in the generalized Schur decomposition (in which case the model does not admit a unique solution). Default: @code{1e-6}. +@item taper_steps = [@var{INTEGER1} @var{INTEGER2} @dots{}] +@anchor{taper_steps} +Percent tapering used for the spectral window in the @cite{Geweke (1992,1999)} +convergence diagnostics (requires @ref{mh_nblocks}=1). The tapering is used to +take the serial correlation of the posterior draws into account. Default: @code{[4 8 15]}. + +@item geweke_interval = [@var{double} @var{double}] +@anchor{geweke_interval} +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]}. + @end table @customhead{Note} @@ -5046,6 +5065,56 @@ Upper/lower bound of the 90\% HPD interval taking into account both parameter an @end defvr +@defvr {MATLAB/Octave variable} oo_.convergence.geweke +@anchor{convergence.geweke} +Variable set by the convergence diagnostics of the @code{estimation} command when used with @ref{mh_nblocks}=1 option (@pxref{mh_nblocks}). + +Fields are of the form: +@example +@code{oo_.convergence.geweke.@var{VARIABLE_NAME}.@var{DIAGNOSTIC_OBJECT}} +@end example +where @var{DIAGNOSTIC_OBJECT} is one of the following: + +@table @code + +@item posteriormean +Mean of the posterior parameter distribution + +@item posteriorstd +Standard deviation of the posterior parameter distribution + +@item nse_iid +Numerical standard error (NSE) under the assumption of iid draws + +@item rne_iid +Relative numerical efficiency (RNE) under the assumption of iid draws + +@item nse_x +Numerical standard error (NSE) when using an x% taper + +@item rne_x +Relative numerical efficiency (RNE) when using an x% taper + +@item pooled_mean +Mean of the parameter when pooling the beginning and end parts of the chain +specified in @ref{geweke_interval} and weighting them with their relative precision. +It is a vector containing the results under the iid assumption followed by the ones +using the @ref{taper_steps} (@pxref{taper_steps}). + +@item pooled_nse +NSE of the parameter when pooling the beginning and end parts of the chain and weighting them with their relative precision. See @code{pooled_mean} + +@item prob_chi2_test +p-value of a chi squared test for equality of means in the beginning and the end +of the MCMC chain. See @code{pooled_mean}. A value above 0.05 indicates that +the null hypothesis of equal means and thus convergence cannot be rejected +at the 5 percent level. Differing values along the @ref{taper_steps} signal +the presence of significant autocorrelation in draws. In this case, the +estimates using a higher tapering are usually more reliable. + +@end table +@end defvr + @deffn Command model_comparison @var{FILENAME}[(@var{DOUBLE})]@dots{}; @deffnx Command model_comparison (marginal_density = laplace | modifiedharmonicmean) @var{FILENAME}[(@var{DOUBLE})]@dots{}; @@ -8686,6 +8755,16 @@ Fernández-Villaverde, Jesús and Juan Rubio-Ramírez (2005): ``Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood,'' @i{Journal of Applied Econometrics}, 20, 891--910 +@item +Geweke, John (1992): ``Evaluating the accuracy of sampling-based approaches +to the calculation of posterior moments'', in J.O. Berger, J.M. Bernardo, +A.P. Dawid, and A.F.M. Smith (eds.) Proceedings of the Fourth Valencia +International Meeting on Bayesian Statistics, pp. 169--194, Oxford University Press + +@item +Geweke, John (1999): ``Using simulation methods for Bayesian econometric models: +Inference, development and communication,'' @i{Econometric Reviews}, 18(1), 1--73 + @item Ireland, Peter (2004): ``A Method for Taking Models to the Data,'' @i{Journal of Economic Dynamics and Control}, 28, 1205--26