Likelihood For Regression Models Research Articles

3-D geochemical interpolation guided by geophysical inversion models

3-D geochemical subsurface models, as constructed by spatial interpolation of drill-core assays, are valuable assets across multiple stages of the mineral industry's workflow. However, the accuracy of such models is limited by the spatial sparsity of the underlying drill-core, which samples only a small fraction of the subsurface. This limitation can be alleviated by integrating collocated 3-D models into the interpolation process, such as the 3-D rock property models produced by modern geophysical inversion procedures, provided that they are sufficiently resolved and correlated with the interpolation target. While standard machine learning algorithms are capable of predicting the target property given these data, incorporating spatial autocorrelation and anisotropy in these models is often not possible. We propose a Gaussian process regression model for 3-D geochemical interpolation, where custom kernels are introduced to integrate collocated 3-D rock property models while addressing the trade-off between the spatial proximity of drill-cores and the similarities in their collocated rock properties, as well as the relative degree to which each supporting 3-D model contributes to interpolation. The proposed model was evaluated for 3-D modelling of Mg content in the Kevitsa Ni-Cu-PGE deposit based on drill-core analyses and four 3-D geophysical inversion models. Incorporating the inversion models improved the regression model's likelihood (relative to a purely spatial Gaussian process regression model) when evaluated at held-out test holes, but only for moderate spatial scales (100 m).

A fusion of least squares and empirical likelihood for regression models with a missing binary covariate

Multiply robust inference has attracted much attention recently in the context of missing response data. An estimation procedure is multiply robust, if it can incorporate information from multiple candidate models, and meanwhile the resulting estimator is consistent as long as one of the candidate models is correctly specified. This property is appealing, since it provides the user a flexible modeling strategy with better protection against model misspecification. We explore this attractive property for the regression models with a binary covariate that is missing at random. We start from a reformulation of the celebrated augmented inverse probability weighted estimating equation, and based on this reformulation, we propose a novel combination of the least squares and empirical likelihood to separately handling each of the two types of multiple candidate models, one for the missing variable regression and the other for the missingness mechanism. Due to the separation, all the working models are fused concisely and effectively. The asymptotic normality of our estimator is established through the theory of estimating function with plugged-in nuisance parameter estimates. The finite-sample performance of our procedure is illustrated both through the simulation studies and the analysis of a dementia data collected by the national Alzheimer’s coordinating center.