## Info

Reinforcer *

FIGURE 1.2 Relationship between procedure and model. The output of the procedure (stimulus and reinforcement) is the input to the model; the output of the model (responses) is the input to the procedure.

FIGURE 1.2 Relationship between procedure and model. The output of the procedure (stimulus and reinforcement) is the input to the model; the output of the model (responses) is the input to the procedure.

rapidly. There are, however, disadvantages. The explicit solutions have been restricted to specific procedures, so it is difficult to ascertain whether the same model is being used in the explicit solutions for different procedures. They have used some additional simplifying approximations that may not be correct. Although symbolic programs such as Mathematica and Maple provide considerable help, many of the explicit solutions require substantial mathematical knowledge and effort to create, check, or even to understand.

Simulations of the model may also be used to estimate values of the parameters from the data, and the fit of the model to the data. Although the simulations will contain some sampling error, this error can be reduced to any amount by increasing the sample size. No additional simplifying approximations are needed, and the simulations require little mathematical knowledge to create, to avoid error, or to understand. They simply require the ability to follow the logic of following explicit rules to transform the output of the procedure (stimuli and reinforcers) to the output of the model (responses).

With a standard modern computer and a good programming style, the simulations can be done rapidly. Most importantly, the model to be simulated may be kept completely independent of the procedure, as shown in Figure 1.2. The model receives stimuli and reinforcers from the procedure and outputs responses to the procedure. No change in the model is required when a different procedure is used. Thus, one can be sure that the same model is being used in the simulations for different procedures.

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