Adding Support for Theory in Open Science Big Data

Open Science Big Data is emerging as an important area of research and software development. Although there are several high quality frameworks for Big Data, additional capabilities are needed for Open Science Big Data. These include data provenance, citable reusable data, data sources providing links to research literature, relationships to other data and theories, transparent analysis/reproducibility, data privacy, new optimizations/advanced algorithms, data curation, data storage and transfer. An important part of science is explanation of results, ideally leading to theory formation. In this paper, we examine means for supporting the use of theory in big data analytics as well as using big data to assist in theory formation. One approach is to fit data in a way that is compatible with some theory, existing or new. Functional Data Analysis allows precise fitting of data as well as penalties for lack of smoothness or even departure from theoretical expectations. This paper discusses principal differential analysis and related techniques for fitting data where, for example, a time-based process is governed by an ordinary differential equation. Automation in theory formation is also considered. Case studies in the fields of computational economics and finance are considered.