Multiple Model Inference: Calibration, Selection, and Prediction with Multiple Models

This paper compares three approaches for model selection: classical least squares methods, information theoretic criteria, and Bayesian approaches. Least squares methods are not model selection methods although one can select the model that yields the smallest sum-of-squared error function. Information theoretic approaches balance overfitting with model accuracy by incorporating terms that penalize more parameters with a log-likelihood term to reflect goodness of fit. Bayesian model selection involves calculating the posterior probability that each model is correct, given experimental data and prior probabilities that each model is correct. As part of this calculation, one often calibrates the parameters of each model and this is included in the Bayesian calculations. Our approach is demonstrated on a structural dynamics example with models for energy dissipation and peak force across a bolted joint. The three approaches are compared and the influence of the log-likelihood term in all approaches is discussed.