DYNAMICLINEAR Procedure

INITIALDISTRIBUTION Statement

INITIALDISTRIBUTION <options>;

The INITIALDISTRIBUTION statement defines the initial parameters of the posterior normal-gamma distribution, which sets the starting point for the filtering process in the model. This involves specifying the mean vector, variance-covariance matrix, and other hyperparameters that are associated with the normal-gamma distribution to establish the prior beliefs about the state vector before any data are processed.

You can use one of the following methods to specify the parameters for the initial gamma distribution:

Default value: If you do not specify a value, a system-defined default value is applied to all variables.
Position-value number-list pair: You can provide a list in which each pair consists of a variable’s position in the variables, followed by the desired gamma distribution parameter.
INGAMMA= option: You can assign parameters directly through an input data table that you specify in the INGAMMA= option.

When you use multiple methods to specify the gamma distribution parameters, they are applied in the preceding sequence: first, the default value is applied; then, any specified position-value number-list pairs override the default; and finally, any values that are provided in the input table supersede previous specifications.

You can specify the following options:

INCOVARIANCE=libref.data-table INCOV=libref.data-table

specifies the covariance matrices for the state variables by inputting full matrices. Note: For the covariance matrices, you need to provide only the lower-triangular part of each full matrix. libref.data-table is a two-level name, where libref refers to the library, and data-table specifies the name of the input data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.

You can find an example input table for the INCOVARIANCE= option in the section Simultaneous Graphical Dynamic Linear Models and the format requirements in the section INCOVARIANCE= Data Table in the INITIALDISTRIBUTION Statement.

INCOVARIANCE(DIAGONAL)=libref.data-table INCOVARIANCE(DIAG)=libref.data-table

specifies the diagonal elements of the covariance matrices, following the same structural guidelines as those for the INMEAN= option (see the section INMEAN= Data Table in the INITIALDISTRIBUTION Statement). libref.data-table is a two-level name, where libref refers to the library, and data-table specifies the name of the input data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.

It is crucial to ensure that the inputs for the diagonal elements in the table are nonzero values. This is because zero values on the diagonal of a covariance matrix imply no variance, which is invalid in the context of defining a distribution. Variance must be greater than zero to reflect the inherent uncertainty and variability of the state variables.

You can find example inputs in the section INCOVARIANCE(DIAGONAL)= Data Table in the INITIALDISTRIBUTION Statement.

INGAMMA=libref.data-table

specifies initial values for the shape and rate parameters of the normal-gamma distribution. libref.data-table is a two-level name, where libref refers to the library, and data-table specifies the name of the input data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.

The input data table must adhere to specific format requirements. These are provided in the section INGAMMA= Data Table in the INITIALDISTRIBUTION Statement.

INMEAN=libref.data-table

specifies initial values for means by using a column-oriented table. You can find an example input table for this option in the section Simultaneous Graphical Dynamic Linear Models. The inclusion of varname and parmname in the table is optional, because they primarily serve to clarify the table. There are certain requirements for specifying the INMEAN= option. The requirements are provided in the section INMEAN= Data Table in the INITIALDISTRIBUTION Statement. libref.data-table is a two-level name, where libref refers to the library, and data-table specifies the name of the input data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.

MEAN=number

specifies the default initial value for all means within the normal-gamma distribution framework. By default, MEAN=0.

OUTVERIFICATION=(suboptions) OUTVERIFY=(suboptions)

outputs the initial distribution to tables for validation.

You can specify the following suboptions:

COVARIANCE=libref.data-table COV=libref.data-table: specifies the output table for the covariances of the initial distribution. libref.data-table is a two-level name, where libref refers to the library, and data-table specifies the name of the output data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.
GAMMA=libref.data-table: specifies the output table for the shape and rate parameters of the initial distribution. libref.data-table is a two-level name, where libref refers to the library, and data-table specifies the name of the output data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.
MEAN=libref.data-table: specifies the output table for the means of the initial distribution. libref.data-table is a two-level name, where libref refers to the library, and data-table specifies the name of the output data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.

RATE=(suboptions)

specifies the initial values for the rate parameters of gamma priors that are associated with all variables (series) in the MODEL statement. For the rate parameters, you must specify positive numbers greater than 0.

You can specify the following suboptions:

DEFAULT=number DEF=number: specifies the default rate parameter for all variables. By default, DEFAULT=5.
POSITIONS=(number-list) POS=(number-list): designates the positions of the variables for which values differ from the default. Every number in the number-list must be a positive integer.
VALUES=(number-list) VAL=(number-list): specifies values that correspond to the POSITIONS= option list values. Every number in the number-list must be greater than 0.

SHAPE=(suboptions)

specifies the initial values for the shape parameters of gamma priors that are associated with all variables (series) in the MODEL statement. For the rate parameters, specified values must be positive numbers greater than 1. These parameters are crucial, because they influence the skewness and variability of the prior distribution, thereby affecting the posterior estimates in Bayesian analysis.

You can specify the following suboptions:

DEFAULT=number DEF=number: specifies the default shape parameter for all variables. By default, DEFAULT=10.
POSITIONS=(number-list) POS=(number-list): designates the positions of the variables for which values differ from the default. Every number in the number-list must be a positive integer.
VALUES=(number-list) VAL=(number-list): specifies values that correspond to the POSITIONS= option list values. Every number in the number-list must be greater than 1.

Last updated: July 09, 2026