Estimating Free Parameters in Stochastic Oscillatory Models Using a Weighted Cost Function

TL;DR

This paper introduces a new weighted cost function and an optimization method to accurately estimate parameters in stochastic oscillatory models, validated on synthetic and biophysical data.

Contribution

The paper presents a novel cost function combining spectral, analytic, and crossing features, enabling effective parameter estimation in stochastic oscillatory systems.

Findings

Successfully recovered known parameters from test data.

Applied method to a biophysical auditory model.

Validated the approach's general applicability.

Abstract

In this study, we estimate parameters in stochastic oscillatory systems by developing a novel cost function. This function incorporates power spectral density, analytic signal, and position crossings, each weighted to capture distinct oscillatory characteristics such as amplitude, frequency, and shape. By minimizing this cost via differential evolution, we estimate parameters in two stochastic systems given measured datasets. We validate this procedure by recovering known parameters from a test dataset. We then apply it to a biophysical model for auditory mechanics. Thus, we establish a general methodology for fitting stochastic oscillatory systems.