Adds documentation of Geweke convergence diagnostics
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@ -4210,12 +4210,19 @@ graphs of smoothed shocks, smoothed observation errors, smoothed and historical
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@algorithmshead
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The Monte Carlo Markov Chain (MCMC) univariate diagnostics are generated
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by the estimation command if @ref{mh_nblocks} is larger than 1, if
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@ref{mh_replic} is larger than 2000, and if option @ref{nodiagnostic} is
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not used. As described in section 3 of @cite{Brooks and Gelman (1998)}
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the convergence diagnostics are based on comparing pooled and within
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MCMC moments (Dynare displays the second and third order moments, and
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The Monte Carlo Markov Chain (MCMC) diagnostics are generated
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by the estimation command if @ref{mh_replic} is larger than 2000 and if
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option @ref{nodiagnostic} is not used. If @ref{mh_nblocks} is equal to one,
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the convergence diagnostics of @cite{Geweke (1992,1999)} is computed. It uses a
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chi square test to compare the means of the first and last draws specified in
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@ref{geweke_interval} (@pxref{geweke_interval}) after discarding the burnin of @ref{mh_drop}. The test is
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computed using variance estimates under the assumption of no serial correlation
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as well as using tapering windows specified in @ref{taper_steps} (@pxref{taper_steps}).
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If @ref{mh_nblocks} is larger than 1, the convergence diagnostics of
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@cite{Brooks and Gelman (1998)} are used instead.
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As described in section 3 of @cite{Brooks and Gelman (1998)} the univariate
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convergence diagnostics are based on comparing pooled and within MCMC moments
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(Dynare displays the second and third order moments, and
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the length of the Highest Probability Density interval covering 80% of
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the posterior distribution). Due to computational reasons, the
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multivariate convergence diagnostic does not follow @cite{Brooks and
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@ -4356,8 +4363,8 @@ the total number of Metropolis draws available. Default:
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@code{2}
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@item mh_drop = @var{DOUBLE}
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The fraction of initially generated parameter vectors to be dropped
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before using posterior simulations. Default: @code{0.5}
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@anchor{mh_drop}
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The fraction of initially generated parameter vectors to be dropped as a burnin before using posterior simulations. Default: @code{0.5}
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@item mh_jscale = @var{DOUBLE}
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The scale to be used for the jumping distribution in
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@ -4756,6 +4763,18 @@ Value used to test if a generalized eigenvalue is 0/0 in the generalized
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Schur decomposition (in which case the model does not admit a unique
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solution). Default: @code{1e-6}.
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@item taper_steps = [@var{INTEGER1} @var{INTEGER2} @dots{}]
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@anchor{taper_steps}
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Percent tapering used for the spectral window in the @cite{Geweke (1992,1999)}
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convergence diagnostics (requires @ref{mh_nblocks}=1). The tapering is used to
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take the serial correlation of the posterior draws into account. Default: @code{[4 8 15]}.
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@item geweke_interval = [@var{double} @var{double}]
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@anchor{geweke_interval}
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Percentage of MCMC draws at the beginning and end of the MCMC chain taken
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to compute the @cite{Geweke (1992,1999)} convergence diagnostics (requires @ref{mh_nblocks}=1)
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after discarding the first @ref{mh_drop} percent of draws as a burnin. Default: @code{[0.2 0.5]}.
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@end table
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@customhead{Note}
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@ -5046,6 +5065,56 @@ Upper/lower bound of the 90\% HPD interval taking into account both parameter an
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@end defvr
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@defvr {MATLAB/Octave variable} oo_.convergence.geweke
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@anchor{convergence.geweke}
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Variable set by the convergence diagnostics of the @code{estimation} command when used with @ref{mh_nblocks}=1 option (@pxref{mh_nblocks}).
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Fields are of the form:
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@example
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@code{oo_.convergence.geweke.@var{VARIABLE_NAME}.@var{DIAGNOSTIC_OBJECT}}
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@end example
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where @var{DIAGNOSTIC_OBJECT} is one of the following:
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@table @code
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@item posteriormean
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Mean of the posterior parameter distribution
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@item posteriorstd
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Standard deviation of the posterior parameter distribution
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@item nse_iid
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Numerical standard error (NSE) under the assumption of iid draws
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@item rne_iid
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Relative numerical efficiency (RNE) under the assumption of iid draws
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@item nse_x
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Numerical standard error (NSE) when using an x% taper
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@item rne_x
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Relative numerical efficiency (RNE) when using an x% taper
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@item pooled_mean
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Mean of the parameter when pooling the beginning and end parts of the chain
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specified in @ref{geweke_interval} and weighting them with their relative precision.
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It is a vector containing the results under the iid assumption followed by the ones
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using the @ref{taper_steps} (@pxref{taper_steps}).
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@item pooled_nse
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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}
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@item prob_chi2_test
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p-value of a chi squared test for equality of means in the beginning and the end
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of the MCMC chain. See @code{pooled_mean}. A value above 0.05 indicates that
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the null hypothesis of equal means and thus convergence cannot be rejected
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at the 5 percent level. Differing values along the @ref{taper_steps} signal
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the presence of significant autocorrelation in draws. In this case, the
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estimates using a higher tapering are usually more reliable.
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@end table
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@end defvr
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@deffn Command model_comparison @var{FILENAME}[(@var{DOUBLE})]@dots{};
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@deffnx Command model_comparison (marginal_density = laplace | modifiedharmonicmean) @var{FILENAME}[(@var{DOUBLE})]@dots{};
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@ -8686,6 +8755,16 @@ Fernández-Villaverde, Jesús and Juan Rubio-Ramírez (2005): ``Estimating
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Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood,''
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@i{Journal of Applied Econometrics}, 20, 891--910
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@item
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Geweke, John (1992): ``Evaluating the accuracy of sampling-based approaches
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to the calculation of posterior moments'', in J.O. Berger, J.M. Bernardo,
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A.P. Dawid, and A.F.M. Smith (eds.) Proceedings of the Fourth Valencia
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International Meeting on Bayesian Statistics, pp. 169--194, Oxford University Press
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@item
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Geweke, John (1999): ``Using simulation methods for Bayesian econometric models:
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Inference, development and communication,'' @i{Econometric Reviews}, 18(1), 1--73
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@item
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Ireland, Peter (2004): ``A Method for Taking Models to the Data,''
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@i{Journal of Economic Dynamics and Control}, 28, 1205--26
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