# Applied Math Colloquium

### Mathematical Models, Parameter Identification, and Uncertainty

### Abstract

: 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.