Inferential modelling and decision making with data
In this paper, we introduce the main concepts of a new maximum livelihood evidential reasoning (MAKER) framework for data-driven inferential modelling and decision making under different types of uncertainty. It consists of two types of model: state space model (SSM) and evidence space model (ESM), driven by the data that reflects the relationships between system inputs and output. SSM is constructed to describe different system states and changes. ESM is established by mapping data to a set of evidence that is partitioned into evidential elements each pointing to a system state set and together represents system behaviours in a probabilistic and distributed manner. The reliability of evidence and interdependence between a pair of evidence are explicitly measured. It is in the joint evidence-state space that multiple pieces of evidence with different degrees of interdependence and reliability are acquired from system inputs and combined to inference system output. A general optimal learning model is constructed, where evidence reliability can be learnt from historical data by maximising the likelihood of true state. In the MAKER framework, different types of uncertainty can be taken into account for inferential modelling, probabilistic prediction and decision making.