Nonparametric Estimates of Biological Transducer Functions

Using bootstrap local fitting to overcome parameteric regression problems. A common task in applying signal-processing methods to biological systems is estimating a transducer function. The particular system being analyzed may range from the very small, such as a retinal photoreceptor producing a voltage response on being stimulated with a flash of light, to the large and complex, such as a human patient pressing a switch on hearing a test tone through headphones. Achieving a good estimate of the transducer function from a set of data may be an important first step in understanding the underlying biological processes as well as in helping to describe the system more generally in terms of its critical components. In some applications, the form of the transducer function is already known, and estimating it may involve the optimization of just a few parameters to achieve a fit of a model curve to the experimental data. In many other applications, however, there is no standard model. This may be because the underlying process is poorly understood or the function itself represents several simpler processes interacting with each other in a complicated way. The problem of estimating a transducer function when its form is unknown can be addressed in several ways. To help set the context of the bootstrap nonparametric approach to this problem, it is useful to review two classical parametric approaches, one based on linear regression and the other on a certain class of nonlinear functions.