Scientists -- unlike philosophers and literary critics -- are contractually obliged to evaluate our theories in the harsh light of experimental data. Despite Ernest Rutherford's famously acerbic comment, "If your experiment needs statistics, you ought to have done a better experiment," experiments have progressed a bit since 1908. Statistical inference has become mandatory in quantum information science. And at the heart of statistical inference lies the likelihood function -- a mathematical representation of "the harsh light of experimental data", encapsulating everything that the data has to say about the theory. I'll discuss how to go beyond maximum- likelihood estimation (MLE) and use the likelihood function more effectively to characterize quantum systems, with three specific examples:
(1) Hedged MLE,http://arxiv.org/abs/1001.2029
(2) Entanglement verification via likelihood ratios, http://arxiv.org/abs/1005.0003
(3) Interval estimates for quantum states (work in progress).