The BCHOICE Procedure

Autocall Macros for Postprocessing

Although PROC BCHOICE provides a number of convergence diagnostic tests and posterior summary statistics, it performs the calculations only for the default tests and statistics or only if you specify the options in advance. If you want to analyze the posterior draws of unmonitored parameters or functions of the parameters that are calculated in later DATA step calls, you can use the autocall macros that are listed in Table 27.6.

Table 27.6: Postprocessing Autocall Macros

Macro	Description
%ESS	Effective sample sizes
%GEWEKE^*	Geweke diagnostic
%HEIDEL^*	Heidelberger-Welch diagnostic
%MCSE	Monte Carlo standard errors
%POSTACF	Autocorrelation
%POSTCOR	Correlation matrix
%POSTCOV	Covariance matrix
%POSTINT	Equal-tail and HPD intervals
%POSTSUM	Summary statistics
%RAFTERY	Raftery diagnostic
^*The %GEWEKE and %HEIDEL macros use a different optimization routine than that used in PROC BCHOICE. As a result, there might be numerical differences in some cases, especially when the sample size is small.

Table 27.7 lists options that are shared by all postprocessing autocall macros. For macro-specific options, see Table 27.8.

Table 27.7: Shared Options

Option	Description
DATA=SAS-data-set	Names the input data set that contains posterior samples
OUT=SAS-data-set	Specifies a name for the output SAS data set to contain the results
PRINT=YES \| NO	Displays the results (the default is YES)
VAR=variable-list	Specifies the variables on which to perform the calculation

Suppose the data set that contains posterior samples is called Post and the variables of interest are defined in the macro variable &PARMS. The following statements call the %ESS macro and calculate the effective sample sizes for each variable:

%ESS(data=Post, var=Alpha Beta U_1-U_17)

By default, the ESS estimates are displayed. You can choose not to display the result and instead use the following statement to save the output to a data set:

%ESS(data=Post, var=&parms, print=NO, out=eout)

Some of the macros can take additional options, which are listed in Table 27.8.

Table 27.8: Macro-Specific Options

Macro	Option	Description
%ESS	AUTOCORLAG=numeric	Specifies the maximum number of autocorrelation lags used in computing the ESS estimates. By default, AUTOCORLAG=MIN(500, NOBS/4), where NOBS is the sample size of the input data set.
	HIST=YES \| NO	Displays a histogram of all ESS estimates. By default, HIST=NO.
%GEWEKE	FRAC1=numeric	Specifies the earlier portion of the Markov chain used in the test. By default, FRAC1=0.1.
	FRAC2=numeric	Specifies the latter portion of the Markov chain used in the test. By default, FRAC2=0.5.
%HEIDEL	SALPHA=numeric	Specifies the $\alpha$ level for the stationarity test. By default, SALPHA=0.05.
	HALPHA=numeric	Specifies the $\alpha$ level for the halfwidth test. By default, HALPHA=0.05.
	EPS=numeric	Specifies a small positive number $\epsilon$ such that if the halfwidth is less than $\epsilon$ times the sample mean of the remaining iterations, the halfwidth test is passed. By default, EPS=0.1.
%MCSE	AUTOCORLAG=numeric	Specifies the maximum number of autocorrelation lags used in computing the Monte Carlo standard error estimates. By default, AUTOCORLAG=MIN(500, NOBS/4), where NOBS is the sample size of the input data set.
%POSTACF	LAGS=%str(numeric-list)	Specifies which autocorrelation lags to calculate. The default values are 1, 5, 10, and 50.
%POSTINT	ALPHA=value	Specifies the $\alpha$ level $(0<\alpha <1)$ for the interval estimates. By default, ALPHA=0.05.
%RAFTERY	Q=numeric	Specifies the order of the quantile of interest. By default, Q=0.025.
	R=numeric	Specifies the margin of error for measuring the accuracy of estimation of the quantile. By default, R=0.005.
	S=numeric	Specifies the probability of attaining the accuracy of the estimation of the quantile. By default, S=0.95.
	EPS=numeric	Specifies the tolerance level for the stationary test. By default, EPS=0.001.

For example, the following statement calculates and displays autocorrelation at lags 1, 6, 11, 50, and 100. Note that the lags in the numeric-list must be separated by commas.

%PostACF(data=Post, var=&parms, lags=%str(1 to 15 by 5, 50, 100))