Mathematical Models, Parameter Identification, and Uncertainty
Many mathematical models, such as those commonly used to quantitatively describe various biological processes, contain a large number of rate constants. The components of the state vector usually are not directly observable, and first-principles estimates of the rate constants rarely are available. Instead, one relies on time series that are functions of the state vector to validate the model. This talk will discuss the following question: if values of model parameters can be found that fit the observed data, then what confidence can we place in predictions from the model? The predictions depend on the model parameters, for which there may or may not be unique estimates that correspond to a given set of observations; this is the identifiability problem. I will give examples from simple SIR models to more complicated models of prostate cancer.