Sloppy Models - predictions and parameter estimation in multiparameter nonlinear models
Joshua Waterfall, Cornell University
We investigate methods to make predictions using high dimensional nonlinear models with many poorly determined parameters. While the basin of the best fit parameters can be found, the basin has too many directions in which the cost surface is nearly flat to reliably extract a single set of “true” parameter values. Monte Carlo sampling of points in this basin then allows for both simple calculation of systematic errors in predictions of the model arising from parameter indeterminacy and the determination of which combinations of parameters most naturally describe the data. It is repeatedly observed in many different models that the significances of different parameter combinations (eigenvalues of the curvature of the basin) are linearly spaced in log values. The source of this possible universality is studied in analytically tractable models of fitting sums of exponentials or polynomials, while connections to real experiments and data are made with several models of biological signaling in cells.
Abstract Author(s): Josh Waterfall