Consider a random vector y = Σ ^1/2 x, where the p elements of the vector x are i.i.d. real-valued random variables with zero mean and finite fourth moment, and Σ ^1/2 is a deterministic p × p matrix such that the eigenvalues of the population correlation matrix R of y are uniformly bounded away from zero and infinity. In this paper, we find that the log determinant of the sample correlation matrix R based on a sample of size n from the distribution of y satisfies a CLT (central limit theorem) for p/n → γ ∈ (0, 1] and p ≤ n. Explicit formulas for the asymptotic mean and variance are provided. In case the mean of y is unknown, we show that after re-centering by the empirical mean the obtained CLT holds with a shift in the asymptotic mean. This result is of independent interest in both large dimensional random matrix theory and high-dimensional statistical literature of large sample correlation matrices for non-normal data. Finally, the obtained findings are applied for testing of uncorrelatedness of p random variables. Surprisingly, in the null case R = I, the test statistic becomes distribution-free and the extensive simulations show that the obtained CLT also holds if the moments of order four do not exist at all, which conjectures a promising and robust test statistic for heavy-tailed high-dimensional data.

Multivariate statistical models can be simplified by assuming that a pattern of conditional independence is presented in the given data. A popular way of capturing the (conditional) independence is to use probabilistic graphical models. The relationship between strongly chordal graphs and m-saturated vines is proved. Moreover, an algorithm to construct an m-saturated vine structure corresponding to strongly chordal graph is provided. This allows the reduction of regular vine copula models complexity. When the underlying data is sparse our approach leads to model estimation improvement when compared with current heuristic methods. Furthermore, due to reduction of model complexity it is possible to evaluate all vine structures as well as to fit non-simplified vines. These advantages have been shown in the simulated and real data examples.¹

Technology forecasting is an essential starting point for conceptual design of any complex engineering system. In fact, many research projects are focused on developing a small set of promising technologies to a suitable readiness level. However, selecting a set of technologies from a larger pool is a nontrivial task, opposed by uncertainty and subjective tradeoffs. This paper proposes a probabilistic method to represent technologies and quantify their effects, while accounting for uncertainty. Using probabilistic inversion, technologies can be selected from a larger set to meet a certain combination of requirements. Several test cases illustrate the method and how it may be used in conceptual design projects. It is concluded that probabilistic inversion enables answering technology development and selection queries, which would be challenging to answer with traditional deterministic approaches, or purely forward uncertainty propagation approaches.

An extension of the D-vine based forward regression procedure to a R-vine forward regression is proposed. In this extension any R-vine structure can be taken into account. Moreover, a new heuristic is proposed to determine which R-vine structure is the most appropriate to model the conditional distribution of the response variable given the covariates. It is shown in the simulation that the performance of the heuristic is comparable to the D-vine based approach. Furthermore, it is explained how to extend the heuristic into a situation when more than one response variable are of interest. Finally, the proposed R-vine regression is applied to perform a stress analysis on the manufacturing sector which shows its impact on the whole economy.

The selection of vine structure to represent dependencies in a data set with a regular vine copula model is still an open question. Up to date, the most popular heuristic to choose the vine structure is to construct consecutive trees by capturing largest correlations in lower trees. However, this might not lead to the optimal vine structure. A new heuristic based on sampling orders implied by regular vines is investigated. The idea is to start with an initial vine structure, that can be chosen with any existing procedure and search for a regular vine copula representing the data better within vines having 2 common sampling orders with this structure. Several algorithms are proposed to support the new heuristic. Both in the simulation study and real data analysis, the potential of the new heuristic to find a structure fitting the data better than the initial vine copula model, is shown.

The availability of resources is crucial for the socio-economic stability of our society. For more than two decades, there was a debate on how to structure this issue within the context of life-Cycle assessment (LCA). The classical approach with LCA is to describe "scarcity" for future generations (100-1000 years) in terms of absolute depletion. The problem, however, is that the long-term availability is simply not known (within a factor of 100-1000). Outside the LCA community, the short-term supply risks (10-30 years) were predicted, resulting in the list of critical raw materials (CRM) of the European Union (EU), and the British risk list. The methodology used, however, cannot easily be transposed and applied into LCA calculations. This paper presents a new approach to the issue of short-term material supply shortages, based on subsequent sudden price jumps, which can lead to socio-economic instability. The basic approach is that each resource is characterized by its own specific supply chain with its specific price volatility. The eco-costs of material scarcity are derived from the so-called value at risk (VAR), a well-known statistical risk indicator in the financial world. This paper provides a list of indicators for 42 metals. An advantage of the system is that it is directly related to business risks, and is relatively easy to understand. A disadvantage is that "statistics of the past" might not be replicated in the future (e.g., when changing from structural oversupply to overdemand, or vice versa, which appeared an issue for two companion metals over the last 30 years). Further research is recommended to improve the statistics.

This paper describes a novel sensitivity analysis method, able to handle dependency relationships between model parameters. The starting point is the popular Morris (1991) algorithm, which was initially devised under the assumption of parameter independence. This important limitation is tackled by allowing the user to incorporate dependency information through a copula. The set of model runs obtained using latin hypercube sampling, are then used for deriving appropriate sensitivity measures. Delft3D-WAQ (Deltares, 2010) is a sediment transport model with strong correlations between input parameters. Despite this, the parameter ranking obtained with the newly proposed method is in accordance with the knowledge obtained from expert judgment. However, under the same conditions, the classic Morris method elicits its results from model runs which break the assumptions of the underlying physical processes. This leads to the conclusion that the proposed extension is superior to the classic Morris algorithm and can accommodate a wide range of use cases.

The use of different copula-based models to represent the joint distribution of an eight-dimensional mixed discrete and continuous problem consisting of five discrete and three continuous variables is investigated. The discussion starts with the theoretical properties of the copula-based models. Four different models are constructed for the data collected for the purpose of predicting the length of disruption caused by problems with the train detection system in the Dutch railway network and their performance is tested. The more complex models turn out to represent the data better. Nevertheless, it is shown that the simpler eight dimensional Normal copula still constitutes a statistically sound model for the data.