title: SENSOP: a derivative-free solver for nonlinear least squares with sensitivity scaling.
abstract: Nonlinear least squares optimization is used most often in fitting a complex model to a set of data. An ordinary nonlinear least squares optimizer assumes a constant variance for all the data points. This paper presents SENSOP, a weighted nonlinear least squares optimizer, which is designed for fitting a model to a set of data where the variance may or may not be constant. It uses a variant of the Levenberg-Marquardt method to calculate the direction and the length of the step change in the parameter vector. The method for estimating appropriate weighting functions applies generally to 1-dimensional signals and can be used for higher dimensional signals. Sets of multiple tracer outflow dilution curves present special problems because the data encompass three to four orders of magnitude; a fractional power function provides appropriate weighting giving success in parameter estimation despite the wide range.
authors.affiliation: Center for Bioengineering, University of Washington, Seattle 98195.
authors.forename: I S
authors.initials: IS
authors.lastname: Chan
authors.forename: A A
authors.initials: AA
authors.lastname: Goldstein
authors.forename: J B
authors.initials: JB
authors.lastname: Bassingthwaighte
mesh_terms: D002196:Capillaries / Q000378:metabolism; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D004058:Diffusion; D016018:Least-Squares Analysis; D008955:Models, Cardiovascular; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010539:Permeability; D012680:Sensitivity and Specificity; D012709:Serum Albumin / Q000378:metabolism; D012984:Software
chemical_list: D012709:Serum Albumin