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Bayesian Estimation
The likely distance between the posterior mean and the unknown true parameter is
reported in the third column, labeled S.D., and that number is analogous to the standard
error in maximum likelihood estimation. Additional columns contain the convergence
statistic (C.S.), the median value of each parameter, the lower and upper 50%
boundaries of the distribution of each parameter, and the skewness, kurtosis, minimum
value, and maximum value of each parameter. The lower and upper 50% boundaries
are the endpoints of a 50% Bayesian credible set, which is the Bayesian analogue of a
50% confidence interval. Most of us are accustomed to using a confidence level of
95%, so we will soon show you how to change to 95%.
When you choose
Analyze →Bayesian Estimation, the MCMC algorithm begins
sampling immediately, and it continues until you click the
Pause Sampling button to
halt the process. In the figure on p. 391, sampling was halted after
completed samples. Amos generated and discarded 500 burn-in samples prior to
drawing the first sample that was retained for the analysis. Amos draws burn-in
samples to allow the MCMC procedure to converge to the true joint posterior
distribution. After Amos draws and discards the burn-in samples, it draws additional
samples to give us a clear picture of what this joint posterior distribution looks like. In
the example shown on p. 391, Amos has drawn 5,831 of these analysis samples, and it
is upon these analysis samples that the results in the summary table are based. Actually,
the displayed results are for 500 burn-in and 5,500 analysis samples. Because the
sampling algorithm Amos uses is very fast, updating the summary table after each
sample would lead to a rapid, incomprehensible blur of changing results in the
Bayesian SEM window. It would also slow the analysis down. To avoid both problems,
Amos refreshes the results after every 1,000 samples.
Changing the Refresh Options
To change the refresh interval:
E From the menus, choose View > Options.
E Click the Refresh tab in the Options dialog box to show the refresh options.
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