Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model

This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment

Nonparametric estimation of copulas and copula densities by orthogonal projections

In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then deduced. Its asymptotic properties are studied: we provide a large functional class for which this construction is optimal in the minimax and maxiset sense and we propose a method selection for the smoothing parameter. An intensive simulation study shows the very good performance of both copulas and copula densities estimators which we compare to a large panel of competitors. A real dataset in actuarial science illustrates this approach.Comment: 42 pages, 6 figures, 11 table

Constructing gene regulatory networks from microarray data using non-Gaussian pair-copula Bayesian networks

Many biological and biomedical research areas such as drug design require analyzing the Gene Regulatory Networks (GRNs) to provide clear insight and understanding of the cellular processes in live cells. Under normality assumption for the genes, GRNs can be constructed by assessing the nonzero elements of the inverse covariance matrix. Nevertheless, such techniques are unable to deal with non-normality, multi-modality and heavy tailedness that are commonly seen in current massive genetic data. To relax this limitative constraint, one can apply copula function which is a multivariate cumulative distribution function with uniform marginal distribution. However, since the dependency structures of different pairs of genes in a multivariate problem are very different, the regular multivariate copula will not allow for the construction of an appropriate model. The solution to this problem is using Pair-Copula Constructions (PCCs) which are decompositions of a multivariate density into a cascade of bivariate copula, and therefore, assign different bivariate copula function for each local term. In fact, in this paper, we have constructed inverse covariance matrix based on the use of PCCs when the normality assumption can be moderately or severely violated for capturing a wide range of distributional features and complex dependency structure. To learn the non-Gaussian model for the considered GRN with non-Gaussian genomic data, we apply modified version of copula-based PC algorithm in which normality assumption of marginal densities is dropped. This paper also considers the Dynamic Time Warping (DTW) algorithm to determine the existence of a time delay relation between two genes. Breast cancer is one of the most common diseases in the world where GRN analysis of its subtypes is considerably important; Since by revealing the differences in the GRNs of these subtypes, new therapies and drugs can be found. The findings of our research are used to construct GRNs with high performance, for various subtypes of breast cancer rather than simply using previous models

Optimization of Reservoir Operation for Real-Time Flood Control with Emphasis on Forecast Uncertainty: A case study of Dez Reservoir

This study presents a novel approach for real-time flood control by optimizing operation of a reservoir during the flood. However, the fundamental operational challenge of using this method is to determine optimized decisions of the reservoir management before the occurrence of flood, and optimal use of the pre-release to reduce the flood damages. In addition to this optimization challenge, since the timely forecasts are derived by employing the probabilistic methods, they would always associate with uncertainty. As a result, quantifying and considering these uncertainties in the flood control would result in reducing the risk of flood damage that can be evaluated by minimizing the expected value of the damage. Timely and continuous forecasting of inflow and reservoir operation management will be implemented before the occurrence of flood until it ends. In order to address the above challenges, a novel simulation-optimization methodology, by taking into account uncertainty, is developed; and illustrated on a case study of Dez reservoir, as a highly important reservoir system in south-west of Iran, to optimize the performance of this reservoir, during the floods. Accordingly, a new water resource management has been proposed and tested. The results derived from the proposed method, indicate a significant reduction in the peak release from the reservoir and the improved operation of the Dez reservoir in controlling the flood at real-time, which will reduce damages in the downstream area

Economic Evaluation of Mental Health Effects of Flooding using Bayesian Networks

The appraisal of appropriate levels of investment for devising flooding mitigation and to support recovery interventions is a complex and challenging task. Evaluation must account for social, political, environmental and other conditions, such as flood state expectations and local priorities. The evaluation method should be able to quickly identify evolving investment needs as the incidence and magnitude of flood events continue to grow. Quantification is essential and must consider multiple direct and indirect effects on flood related outcomes. The method proposed is this study is a Bayesian network, which may be used ex-post for evaluation, but also ex-ante for future assessment, and near real-time for the reallocation of investment into interventions. The particular case we study is the effect of flood interventions upon mental health, which is a gap in current investment analyses. Natural events such as floods expose people to negative mental health disorders including anxiety, distress and post-traumatic stress disorder. Such outcomes can be mitigated or exacerbated not only by state funded interventions, but by individual and community skills and experience. Success is also dampened when vulnerable and previously exposed victims are affected. Current measures evaluate solely the effectiveness of interventions to reduce physical damage to people and assets. This paper contributes a design for a Bayesian network that exposes causal pathways and conditional probabilities between interventions and mental health outcomes as well as providing a tool that can readily indicate the level of investment needed in alternative interventions based on desired mental health outcomes

Evaluating the bovine tuberculosis eradication mechanism and its risk factors in England’s cattle farms

Controlling bovine tuberculosis (bTB) disease in cattle farms in England is seen as a challenge for farmers, animal health, environment and policy-makers. The difficulty in diagnosis and controlling bTB comes from a variety of factors: the lack of an accurate diagnostic test which is higher in specificity than the currently available skin test; isolation periods for purchased cattle; and the density of active badgers, especially in high-risk areas. In this paper, to enable the complex evaluation of bTB disease, a dynamic Bayesian network (DBN) is designed with the help of domain experts and available historical data. A significant advantage of this approach is that it represents bTB as a dynamic process that evolves periodically, capturing the actual experience of testing and infection over time. Moreover, the model demonstrates the influence of particular risk factors upon the risk of bTB breakdown in cattle farms

Random Number Generators

The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution’s characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit