Goodness-of-fit Tests for Time Dependent Ensemble Averages

Sammanfattning: Fitting a model to a time-dependent ensemble average is a process repeated frequently throughout biophysics. A selected ensemble-averaged observable (⟨y(t)⟩) for a given system can be predicted through the use of an estimated ensemble average, where the estimated ensemble average is created via simulated or experimental data sets. Fitting a model to this estimated ensemble average allows for estimations of ⟨y(t)⟩. Often, one tests the quality of a fitted model through the use of a ’goodness-of-fit’ (GOF) procedure. The quality of the model is determined by the placement of a test statistic (S) on its associated probability distribution (φ(S)). Traditional choices of S, such as the normalised residual sum of squares (RSS), neglect correlations in fluctuations of the ensemble average around the fitted model. Under this assumption, the normalised RSS is distributed according to the χ2-distribution (φχ2(S)), with mean (μ) and variance (σ2) proportional to the degree of freedom (υ) of the fitted model. The inability of the traditional χ2-GOF procedure to account for these correlations can lead to less reliable evaluations of the quality of a fitted model. The thesis covers the derivation and validation of the correct form of φ(S) when correla- tions are considered, for use in a new GOF procedure. The new GOF procedure was tested under varying parameters, correlation types and ensemble make-ups. Testing environments included three ensemble generating prototype models, and three movies of noisified sim- ulations of vesicle movement. It is demonstrated that the new GOF procedure correctly accepts and rejects well and poor fitting models respectively, and is a valid indicator of model quality. Furthermore, it is shown that compared to the traditional χ2-GOF proce- dure, the new GOF procedure is a more accurate measure of model quality under a variety of correlation types, is reliable in a greater region of parameter space, and performs better in all tested scenarios.