CALLING GREGPLUS

The code GREGPLUS is normally called via Athena, by clicking on the desired options under PARAMETER ESTIMATION. For very detailed control of the available options, GREGPLUS may be called as follows from a user-provided MAIN program for the given problem  

CALL GREGPLUS(NEVT,JWT,LEVEL,NRESP,NBLK,IBLK,IOBS,YTOL, 

A NMOD,NPARV,NPHIV,OBS,SQRW,PAR.BNDLW,BNDUP,CHMAX, 

NWRITE, 

C ADTOL,RPTOL,RSTOL,MODEL,IPROB,UMAX,LISTS,IDIF,IRES2, 

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If VAR(NRESP,NRESP) and NUEB(NBLK) have been inferred, as in Example C.3, from a very detailed model parameterized to the point of minimum residual variance, then this minimum point provides estimates of VAR and NUEB. If replicates are not available, we may proceed as in that example declare and insert VAR and NUEB in the MAIN program, declare KVAR(0 0) to show the absence of replicates, and declare KVAR(0)= —1 before calling GREGPLUS. GREGPLUS then proceeds as for KVAR(0)=1, except for the different source of VAR and NUEB. 

NWRITE needed information, such as conditions and inputs for the next execution of an implicit algorithm. To use these files, the user must insert conditions and initial guesses into NREAD before calling GREGPLUS. In execution, MODEL must read from NREAD and write the updated values into NWRITE for each event. GREGPLUS does the needed manipulations of these files and their labels during each iteration to save the latest confirmed values in NREAD until an updated file NWRITE is ready to serve asNREAD for the next iteration. 

Uniform weighting (known as simple least squares) is appropriate wJien the expected variances of the observations are equal and is commonly used when these values are unknown. GREGPLUS uses this w eighting when called with JWT = 0 the values MwijJ = 1 are then provided automatically. 

The derivatives F r are called the first-order parametric sensitivities of the model. Their direct computation via Newton s method is implemented in Subroutines DDAPLUS (Appendix B) and PDAPLUS. Finite-difference approximations are also provided as options in GREGPLUS to produce the matrix A in either the Gauss-Newton or the full Newton form these approximations are treated in Problems 6.B and 6.C. 

GREGPLUS uses this objective function when called via Athena or by a user-provided code at Level 10, with the observations (preferably adjusted to remove systematic errors such as mass-balance departures) provided in the array OBS. Each weight u , = the user-assigned ratio... 

The right-hand value Uf, is used when GREGPLUS is called with LEVEL = 20, whereas (n + mb + 1) is used when LEVEL = 22. LEVEL 20 requires fuller data and gives a fuller covariance analysis it gives expectation estimates of the covariance elements for each data block. LEVEL 22 gives maximum-density (most probable) covariance estimates these are smaller than the expectation values, which are averages over the posterior probability distribution. 

The estimates in Item 1 are then computed along with any of Items 2, 3. and 4 that the user requests. Thus, NPHIV(JMOD).GT.O is used in the call of GREGPLUS to request auxiliary function computations for model JMOD KVAR(0).NE.0 to request calculations of goodness of fit and posterior probability share for each model considered and JNEXT, NMOD. and IDSIGN control selection of the next event condition. These calculations are described below, and their statistical foundations are presented in Chapters 6 and 7. 

At Level 10 when called with IDIF = 2, GREGPLUS starts with... 

When called with IDIF = 1 at any level, GREGPLUS sets IDIF to zero at the first indication of line search difficulty. 

If there is no such information, declare KVAR(0 0) and set KVAR(0)=0 in the MAIN program, and declare NUEB(l) and VAR(1,1) as zeros for the call to GREGPLUS. 

If VAR and NUEB are provided from other information or belief, specify them before the call of GREGPLUS. Also declare KVAR(0 0) and set KVAR(0)=2, to indicate that the variance information is from another source. 

If VAR is exactly known (as in some computer simulations), specify it before the call of GREGPLUS. Declare KVAR(0 0) and set KVAR(0)=3, to indicate an exact specification of VAR. NUEB then becomes a dummy zero array of order NRESP, VAR is an asymptote for infinitely many degrees of freedom, and the F-test is replaced by a test. 

If any DEL(i).NE.0. GREGPLUS will complete DPHIDP with central-difFerencevalues if needed, using f values from calls of MODEL with IDER = -1,... 

DW.Double precision work array in the call of GREGPLUS. 

MODEL must not write in DW, but may read saved values that were stored before the call of GREGPLUS see JGDW. 

This example uses parametric sensitivity analysis to estimate the analytic formulas for all the derivatives dYi(tu 6)/d6j. Therefore, the array DEL is set to zero before GREGPLUS is called, and the IDIF value is read by GREGPLUS but not used. The settings of lOBS, NBLK, YTOL, and LISTS are the same as in Example C.4. 

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