This chapter considers statistical data-driven analysis methods, and focuses on parametric as well as more recent information theoretic and nonparametric statistical approaches to biophysical data analysis with an emphasis on single-molecule applications. It then reviews simpler parametric approaches starting from an assumed model with unknown parameters. Model selection criteria are widely used in biophysical data analysis from image deconvolution to single-molecule step detection and continue to be developed by statisticians. The goal of successful model selection criteria is to pick models whose complexity is penalized, in a principled fashion, to avoid overfitting and that convincingly fit the data provided (the training set). The chapter summarizes both information theoretic as well as Bayesian model selection criteria. Finally, the chapter discusses efforts to use information theory in experimental design and ends with some considerations on the broader applicability of information theory.