Finance plays a leading role in the context of public policy evaluation, given the close interconnection between public economics and the dynamics of financial markets. Evaluating finance, then, is prefigured as a tool to assess services and policies. Statistics is a fundamental tool for evaluating finance, financial instruments and related patterns. Financial quantities fall into two categories: those that are deterministic and those that are stochastic. In a deterministic context, one can exploit statistical variables, extrapolating the information content of the quantities under consideration. In particular, the availability of data allows the implementation of methods based on data science and data mining. One can also infer the stochastic structure of the analyzed context from its historical realizations.
Moreover, the exploration of the empirical distribution of an observed sample allows grasping global properties from disaggregated data. This makes it possible to implement extensive evaluation exercises from a particular universe. Some examples are the rank-size analysis and the assessment of the regularity properties of the data.
In a pure random context, we can refer to the statistical tools leading to the forecast and the analysis of the future (thus, non-deterministic) trajectories related to the financial quantities. This topic is of fundamental importance in the evaluation processes. Methodological statistics and inference are an integral part of the scientific macro-areas that allow for practical exploration of these contexts, enabling evaluation exercises of absolute rigour.