Bayesian nonparametrics for interval data. An agenda for future research

Abstract

Interval analysis (IA) and symbolic data analysis (SDA) are considered in essence nonparametric. Both fields are called to play a quite relevant role in the future of Big Data (BD) or Internet of Things (IoT). In many contexts, some of them belonging to the domain of BD andor IoT, we have some prior knowledge about the behaviour of the variables in study which can be managed using the Bayesian paradigm. As a result we are interested in how to take advantage of the information incorporated in the interval-valued dataset and our previous knowledge, both of which can be considered simultaneously in the Bayesian nonparametrics (BNP) framework. After more than 40 years of research, there is a general consensus about Nonparametric Bayesian that it is a paradigm any researcher needs to consider in order to provide alternative solutions for complex real problems. In the last 10 years several examples of these alternative solutions have been provided in Biology, Economics, Energy, Finance, Medicine, Political Sciences and so on. The most well-known approach in BNP is that of the Dirichlet process (DP). In this plenary talk I will deliver a brief primer on the DP. After that I will suggest a new and original focus on our interval dataset generated from a BNP approach based on DPs. An example of this methodology will be developed and pros and cons of this approach will be considered. As a consequence, an agenda for future research in the field of IA and SDA under a BNP framework will be outlined.