Abstract: The theory of financial markets is well developed, but before any of it can be applied there are statistical questions to be answered: Are the hypotheses of proposed models reasonably consistent with what data show? If so, how should we infer parameter values from data? How do we quantify the error in our conclusions? This paper examines these questions in the context of the two main areas of quantitative finance, portfolio selection and derivative pricing. By looking at these two contexts, we get a very clear understanding of the viability of the two main statistical paradigms, classical (frequentist) statistics and Bayesian statistics.