Comparison of Alternative Markov Models for Sea Floor Grain Size Interpolation and Estimation

In this work, we have aimed to compare both a Markov Tree statistical modeling and estimation method and Markov Random Field modeling and estimation methods with each other and with ordinary kriging, an estimation technique commonly used in geostatistical modeling and data interpolation. Our goal has been to identify robust statistical estimation methods that offer novel capabilities including: straightforward interpolated estimation of entire spatial statistic fields from a sparse, non-uniform collection; ability to model and estimate from data of varying measurement qualities; robust handling of fields with a mixture of locally homogeneous and inhomogeneous (non-stationary) behavior over the field; and efficient estimation both from large quantities of data and for large numbers of parameters.