This volume presents a selection of papers from the Fourth International Workshop on Artificial Intelligence and Statistics. This biennial workshop brings together researchers from both fields to discuss problems of mutual interest and to compare approaches to their solution. The fourth workshop focused on the topic of selecting models from data. As the papers in this volume attest, the empirical approaches from the two separate fields have much in common yet still depart enough from one another to stimulate active interdisciplinary work. The papers cover a wide spectrum of problems in empirical modelling including model selection in general, graphical models, causal models, regression and other statistical models, and general algorithms and software tools. This timely volume will benefit all researchers with an active interest in model selection, empirical model building, or more generally the interaction between Statistics and Artificial Intelligence.