Brett Matzuka

Biology and Noise: how the moon mission figured it out

Abstract: In biological systems, we are trying to construct simple 
models to describe the underlying biological processes without becoming 
intractable or incomprehensible to clinicians and biologists.  
Mathematicians deal with complex processes, with potentially sparse and 
noisy data, and construct quantitative models to help provide insight 
into the system.  Whether using simplified models (logistic model, 
Lotka-Volterra, etc) or more complex systems (PBPK, molecular dynamics, 
genetics, etc), our goal is to fit our model to the data to obtain 
information on important features of the model (parameters, hidden 
states, etc).  Using the information from these fits, usually 
conditioned on a smaller cost than when we started, we conclude our 
study and give our results.  However, a 'good' fit is not enough.  
Relegating noises appropriately, obtaining confidence for a given 
estimate, and other post-hoc metrics can be utilized better to help 
provide further insight into a model than originally intended.  Using 
the Kalman filter, originally developed and used on the Apollo missions, 
on a cardiovascular model, we provide results and use metrics to 
understand the role noise plays in models.  The overall goal is to 
promote more thought on noise in models and estimation.