This thesis presents a novel application of structural reliability concepts to assess the reliability of mining operations. “Limit-states” are defined to obtain the probability that the total productivity — measured in production time or economic gain — exceeds user-selected thresholds. Focus is on the impact of equipment downtime and other non-operating instances on the productivity and the economic costs of the operation. A comprehensive set of data gathered at a real-world mining facility is utilized to calibrate the probabilistic models. In particular, the utilization of Bayesian inference facilitates the inclusion of data — and updating of the production probabilities — as they become available. The thesis includes a detailed description of the Bayesian approach, as well as the limit-state-based reliability methodology. A comprehensive numerical example demonstrates the methodology and the usefulness of the probabilistic results. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

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Statistical analysis is used quite heavily in production operations. To use certain advanced statistical approaches such as Bayesian analysis, statistical models must be built. This thesis demonstrates the process of building the Bayesian models and addresses some of the classical limitations by presenting mathematical examples and proofs, by demonstrating the process with experimental and simulated implementations, and by completing basic analysis of the performance of the implemented models. From the analysis, it is shown that the performance of the Bayesian models is directly related to the amount of separation between the likelihood distributions that describe the behavior of the data features used to generate the multivariate Bayesian models. More specifically, the more features that had clear separation between the likelihood distributions for each possible condition, the more accurate the results were. This is shown to be true regardless of the quantity of data used to generate the model distributions during model building. In cases where distribution overlap is present, it is found that models performance become more consistent as the amount of data used to generate the models increases. In cases where distribution overlap is minimal, it is found that models performance become consistent within 4-6 data sets.

The dissertation comprises an introductory Chapter, four papers and a summary Chapter. First, a new class of Bayesian dynamic partition models for the Nelson- Siegel family of non-linear state-space Bayesian statistical models is developed. This class is applied to studying the term structure of government yields. A sequential time series of Bayes factors, which is developed from this approach, shows that term structure could act as a leading indicator of economic activity. Second, we develop a class of non-MCMC algorithms called “Direct Sampling”. This Chapter extends the basic algorithm with applications to Generalized Method of Moments and Affine Term Structure Models. Third, financial economics is characterized by long-standing problems such as the equity premium and risk free rate puzzles. In the chapter titled “Bayesian Learning, Distributional Uncertainty and Asset-Return Puzzles” solutions for equilibrium prices under a set of subjective beliefs generated by Dirichlet Process priors are developed. It is shown that the “puzzles” could disappear if a “tail thickening” effect is induced by the representative agent. A novel Bayesian methodology for retrospective calibration of the model from historical data is developed. This approach shows how predictive functionals have important welfare implications towards long-term growth. Fourth, in “Social Discounting Using a Bayesian Nonparametric model” the problem of how to better quantify the uncertainty in long-term investments is considered from a Bayesian perspective. By incorporating distribution uncertainty, we are able to provide confidence measures that are less “pessimistic” when compared to previous studies. These measures shed a new and different light when considering important cost-benefit analysis such as the valuation of environmental policies towards the resolution of global warming. Finally, the last Chapter discusses directions for future research and concludes the dissertation. / text

This thesis considers the reconstruction of subsurface models from seismic observations, a well-known high-dimensional and ill-posed problem. As a first regularization to such a problem, a reduction of the parameters' space is considered following a truncated Discrete Cosine Transform (DCT). This helps regularizing the seismic inverse problem and alleviates its computational complexity. A second regularization based on Laplace priors as a way of accounting for sparsity in the model is further proposed to enhance the reconstruction quality. More specifically, two Laplace-based penalizations are applied: one for the DCT coefficients and another one for the spatial variations of the subsurface model, which leads to an enhanced representation of cross-correlations of the DCT coefficients. The Laplace priors are represented by hierarchical forms that are suitable for deriving efficient inversion schemes. The corresponding inverse problem, which is formulated within a Bayesian framework, lies in computing the joint posteriors of the target model parameters and the hyperparameters of the introduced priors. Such a joint posterior is indeed approximated using the Variational Bayesian (VB) approach with a separable form of marginals under the minimization of Kullback-Leibler divergence criterion. The VB approach can provide an efficient means of obtaining not only point estimates but also closed forms of the posterior probability distributions of the quantities of interest, in contrast with the classical deterministic optimization methods. The case in which the observations are contaminated with outliers is further considered. For that case, a robust inversion scheme is proposed based on a Student-t prior for the observation noise. The proposed approaches are applied to successfully reconstruct the subsurface acoustic impedance model of the Volve oilfield.

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