Advice - Mathematical modeling

• .  Ability characterize the observed data and to include the most important features of the data.

• .  Makes accurate and precise predictions.

• .  Increases understanding of the system.

• .  The model is actually used.

• .  The model is completed on time.

• .  Logically consistent, plausible.

• .  Validated by empirical observations.

• .  Robust to small changes in the data.

• .  Appropriate level of precision and detail.

• .  As simple as possible.

• .  Judged on what it is intended to do.

• .  Has flexibility.

• .  Is effective as a communication tool.

• .  Serves many different purposes.

• .  May allow for extrapolation outside the data range.

Clearly that’s not true, but it does make for a nice, catchy mnemonic. ‘A’ is for assume. Often there is inadequate information at the outset to solve a problem, except for the most simplest cases, so assumptions are needed right from the beginning. These assumptions may be in the form of parameter values, or model structure, or distributional assumptions, like the distribution of the model residuals. A model that has poor predictability may not be a poor model at all. Indeed, the problem may simply be that the assumptions are wrong. Next, ‘B’ is for borrow. Few models are developed in a vacuum. Most models are based on other models. Hence, knowledge is bor- rowed from the literature, from previous experience, or from colleagues and then a starting model is built to evaluate. ‘C’ is then to criticize the model and the as- sumptions the model was predicated upon. Modeling is iterative. If the model does not meet our needs then we go back to ‘A,’ modify our assumptions, and then start over again, hopefully learning from what we have just done.

(PK-PD modeling)