Predictive Statistical Modelling Approaches for Events in Discrete Space and Time

Abstract

This thesis investigates the use of predictive modelling to improve decision-making for events that are distributed over discrete space and occur in discrete time. We explore three main statistical methods: Kernel Density Estimation (KDE), Bayesian methods, and Maximum Likelihood Estimation (MLE) known for their effectiveness in analyzing data and applicability to continuous and discrete time scenarios. A key contribution is developing an advanced KDE model that features adaptive bandwidth and weighted approaches for more accurate density estimates. We focus our modelling approaches on coal production data from various mines; we demonstrate how these predictive models can address uncertainties and periodic trends in mine output. Accurately forecasting mine production can enhance resource allocation and inventory management. The thesis further extends to prescriptive analytics by incorporating mathematical optimization to allocate coal optimally from mines to power plants. This involves formulating and solving a mathematical model with real-world constraints to find the best allocation solution. By combining predictive and prescriptive analytics, these research findings have the potential to significantly impact the sectors where future events can occur only in discrete space and time, leading to more informed and data-driven decisions.