Q: When and how should I use Bayesian fitting?

A: The SAAM II Bayesian feature allows the incorporation of prior knowledge of the model parameters into the modeling of the kinetic data. The additional information is entered as a mean and standard deviation for one or more of the parameters in the model. The values can come from previous individual experiments, analysis of a population, or from published results. The prior knowledge must be justifiable independently of the model.

In both the SAAM II Compartmental and Numerical applications, the use of Bayesian estimation results in an additional factor being included in the objective function during optimization (fitting).  The final fitted value of any Bayesian parameter is thus influenced by the population mean and standard deviation used.

For example, suppose a model contains parameters k(1,2), k(2,1)and k(0,1), but the data is not rich enough to allow reliable estimation of fitted values. If examples could be found in literature where k(0,1) had been measured before, and values for  k(0,1) and a measure of its variability were provided, this information, expressed in terms of the mean and standard deviation, could be entered into the Compartmental model as the Bayesian mean and SD for parameter k(0,1). The final fit will combine the information from the kinetic data and the prior knowledge on k(0,1). In all cases, the influence of the prior knowledge on the final estimates and the results must be carefully assessed.

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