An accessible introduction to the principles of computational and mathematical modeling in psychology and cognitive science
This practical and readable work provides students and researchers, who are new to cognitive modeling, with the background and core knowledge they need to interpret published reports, and develop and apply models of their own. The book is structured to help readers understand the logic of individual component techniques and their relationships to each other.
Chapter 5: Parameter Uncertainty and Model Comparison
Parameter Uncertainty and Model Comparison
Chapter 4 dealt with full specification of a model, including a probability distribution, and estimating the parameters of the model using maximum likelihood estimation (MLE). If we had run an experiment and collected some data, fitting the model to those data using MLE would produce two end products: a vector of ML parameter estimates, and the value of the maximized log-likelihood. Although the obtained estimates are in most respects the best estimates, and the globally maximized log-likelihood is by definition the best (in that it is the highest possible log-likelihood for that model), we haven't really given attention to how these estimates are affected by variability.
As we've discussed in Chapter 4, variability creeps into our model ...