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Caamaño-Carrillo, C., Bevilacqua, M., López, C., & Morales-Oñate, V. (2024). Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation. Comput. Stat. Data Anal., 191, 107887.
Abstract: A highly scalable method for (non-)Gaussian random fields estimation is proposed. In particular, a novel (a) symmetric weight function based on nearest neighbors for the method of maximum weighted composite likelihood based on pairs (WCLP) is studied. The new weight function allows estimating massive (up to millions) spatial datasets and improves the statistical efficiency of the WCLP method using symmetric weights based on distances, as shown in the numerical examples. As an application of the proposed method, the estimation of a novel non-Gaussian random field named Tukey-hh random field that has flexible marginal distributions (possibly skewed and/or heavy-tailed) is considered. In an extensive simulation study the statistical efficiency of the proposed nearest neighbors WCLP method with respect to the WCLP method using weights based on distances is explored when estimating the parameters of the Tukey-hh random field. In the Gaussian case the proposed method is compared with the Vecchia approximation from computational and statistical viewpoints. Finally, the effectiveness of the proposed methodology is illustrated by estimating a large dataset of mean temperatures in South -America. The proposed methodology has been implemented in an open-source package for the R statistical environment.
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Lagos, T., Armstrong, M., Homem-de-Mello, T., Lagos, G., & Saure, D. (2021). A framework for adaptive open-pit mining planning under geological uncertainty. Optim. Eng., 72, 102086.
Abstract: Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity-the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard-practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for large mines. Additionally, any comprehensive approach to mine planning ought to consider the underlying geostatistical uncertainty as only limited information obtained from drill hole samples of the mineral is initially available. In this regard, as blocks are extracted sequentially, information about the ore grades of blocks yet to be extracted changes based on the blocks that have already been mined. Thus, the problem lies in the class of multi-period large scale stochastic optimization problems with decision-dependent information uncertainty. Such problems are exceedingly hard to solve, so approximations are required. This paper presents an adaptive optimization scheme for multi-period production scheduling in open-pit mining under geological uncertainty that allows us to solve practical instances of the problem. Our approach is based on a rolling-horizon adaptive optimization framework that learns from new information that becomes available as blocks are mined. By considering the evolution of geostatistical uncertainty, the proposed optimization framework produces an operational policy that reduces the risk of the production schedule. Our numerical tests with mines of moderate sizes show that our rolling horizon adaptive policy gives consistently better results than a non-adaptive stochastic optimization formulation, for a range of realistic problem instances.
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