Raman spectroscopy has been used extensively to calculate CO2 fluid density in many geological environments, based on the measurement of the Fermi diad split (Î; cm-1) in the CO2 spectrum. While recent research has allowed the calibration of several Raman CO2 densimeters, there is a limit to the inter-laboratory application of published equations. These calculate two classes of density values for the same measured Î, with a deviation of 0.09 ± 0.02 g/cm3 on average. To elucidate the influence of experimental parameters on the calibration of Raman CO2 densimeters, we propose a bottom-up approach beginning with the calibration of a new equation, to evaluate a possible instrument-dependent variability induced by experimental conditions. Then, we develop bootstrapped confidence intervals for density estimate of existing equations to move the statistical analysis from a sample-specific to a population level. We find that Raman densimeter equations calibrated based on spectra acquired with similar spectral resolution calculate CO2 density values lying within standard errors of equations and are suitable for the inter-laboratory application. The statistical analysis confirms that equations calibrated at similar spectral resolution calculate CO2 densities equivalent at 95% confidence, and that each Raman densimeter does have a limit of applicability, statistically defined by a minimum Î value, below which the error in calculated CO2 densities is too high.
This paper presents an overview of the procedures that are involved in prediction with machine learning models with special emphasis on deep learning. We study suitable objective functions for prediction in high-dimensional settings and discuss the role of regularization methods in order to alleviate the problem of overfitting. We also review other features of machine learning methods, such as the selection of hyperparameters, the role of the architecture of a deep neural network for model prediction, or the importance of using different optimization routines for model selection. The review also considers the issue of model uncertainty and presents state-of-the-art methods for constructing prediction intervals using ensemble methods, such as bootstrap and Monte Carlo dropout. These methods are illustrated in an out-of-sample empirical forecasting exercise that compares the performance of machine learning methods against conventional time series models for different financial indices. These results are confirmed in an asset allocation context.
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