Optimizer

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The way in which the Optimizer "fits" the model to the data is determined in the Optimizer pane of the Computational Settings window.  The user can limit the number of iterations that the optimizer can use in "fitting" the model to the data. 

The variance model can be based upon  model or data. Data weighting is used when a measurement of confidence in each particular datum is provided. Weights for each datum are calculated from the standard deviations assigned to the data.  Model weighting expresses the confidence in each of the calculated Sample values rather than in the data.

Weights in SAAM II can be absolute or relative. Absolute weighting assumes that the overall weighting of each data element (variable) is the same, while in relative weighting each data element is given an additional weight that indicates how well that element fits the resulting model sample curve.

SAAM II uses approximate derivatives of the model function "s(p, ti,j)" during the "fitting" process, and when computing statistics. The optimizer computes a step size for each parameter equal to "d(pU - pL)", where "pU" and "pL" are the upper and lower limits for "p", and "d" is the convergence criterion (see below). The step size is used to form either a forward or central difference approximation to the derivative of "s(p, ti,j)" with respect to "p".  Central difference approximations have a smaller truncation error, resulting in a smaller total error, but usually require twice the execution time.

Two different convergence tests are used to terminate the "fitting" process: parameter convergence and objective convergence. The user can specify the value for the convergence criterion "d" in this field or accept the default value of "0.0001".

Bayesian estimation incorporates prior knowledge of an adjustable parameter's value into the fitting process. Check Include Bayesian Term to allow Bayesian information to be provided for any adjustable parameters, and Bayesian inference to be used during a fit.

In Bayesian estimation, a mean value and a standard deviation are specified for one or more adjustable parameters. If the mean value of a parameter is specified but the standard deviation is not specified, lambda is used to assign a default standard deviation to that parameter. If "pU" and "pL" are the upper and lower limits for the parameter, the default standard deviation is "s = lambda(pU - pL)".

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