# 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.