Non-likelihood estimation methods for spatial predictions - Heng, Chloe Yi Ning (Nanyang Technological University, 2024)
Classical geostatistical models such as those used for kriging, are typically fit using maximum likelihood estimation (MLE). While MLE is the most popular method to determine model parameters from data, there are other spatial interpolation methods like Nearest Neighbour and Inverse Distance Weighting which do not use likelihoods, and non-parametric models which cannot be estimated by MLE. This project aims to discuss the pros and cons of using non-likelihood-based methods, in making spatial predictions as compared to the traditional likelihood-based methods. For example, models which use MLE tend to be parametric which provides the advantage of having uncertainty analysis, but certain assumptions of the fitted function have to be included, resulting in the risk of suboptimal user choices that could affect its performance. On the other hand, common non-likelihood-based methods which tend to be non-parametric lack this advantage but suffers less of having strong assumptions. Hence, there exists a trade-off between obtaining uncertainty results and avoiding parameterization assumptions. Of special interest in terms of non-likelihood-based methods is a new solution which has been introduced known as Histogram via entropy reduction (HER) that is able to solve this trade-off. This is a non-parametric method that makes use of information theory and probability aggregation to provide uncertainty analysis.