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Adds documentation of Geweke convergence diagnostics

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Johannes Pfeifer 2013-09-16 19:16:52 +02:00
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@ -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