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

Inference for exponential parameter under progressive Type-II censoring from imprecise lifetime

Progressively Type-II censored sampling is an important method ofobtaining data in lifetime studies. Statistical analysis oflifetime distributions under this censoring scheme is based onprecise lifetime data. However, in realsituations all observations and measurements of progressive Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. In this paper, we consider the estimation of exponential meanparameter under progressive Type-II censoring scheme, when thelifetime observations are fuzzy and are assumed to be related tounderlying crisp realization of a random sample. We propose a newmethod to determine the maximum likelihood estimate (MLE) of theunknown mean parameter. In addition, a new numerical method forparameter estimation based on fuzzy data is provided. Using the parametric bootstrapmethod, we then discuss the construction of confidence intervalsfor the mean parameter. Monte Carlo simulations are performed toinvestigate the performance of all the different proposedmethods. Finally, an illustrative example is also included

Exact Reliability for Consecutive k-out-of-r-from-n: F System with Equal and Unequal Components Probabilities

A consecutive k-out-of-r-from-n: F system consists of n linear ordered components such that the system fails if and only if there exist a set of r consecutive linear component that contains at least k failed components. Consecutive k-out-of-r-from-n: F system has been considered in many fields such as reliability analysis. All recent efforts in this area have been focused on acquiring band or approximation for their reliability such that less attention has been paid to their closed form and exact reliability in the literature. In the present paper, with designing an innovative algorithm the exact reliability for extensive class of consecutive k-out-of-r-from-n: F system is obtained. Specially this task for equal and unequal components probabilities is done. Finally, the numerical results for calculating the exact reliability in extensive class of this strategic systems were applied

Bayesian Inference of Pair-Copula Constriction for Multivariate Dependency Modeling of Iran’s Macroeconomic Variables

Bayesian inference of pair-copula constriction (PCC) is used for multivariate dependency modeling of Iran’s macroeconomics variables: oil revenue, economic growth, total consumption and investment. These constructions are based on bivariate t-copulas as building blocks and can model the nature of extreme events in bivariate margins individually. The model parameter was estimated based on Markov chain Monte Carlo (MCMC) methods. A MCMC algorithm reveals unconditional as well as conditional independence in Iran’s macroeconomic variables, which can simplify resulting PCC’s for these data

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

Approximating non-Gaussian Bayesian networks using minimum information vine model with applications in financial modelling

Many financial modeling applications require to jointly model multiple uncertain quantities to presentmore accurate, near future probabilistic predictions. Informed decision making would certainly benefitfrom such predictions. Bayesian networks (BNs) and copulas are widely used for modeling numerousuncertain scenarios. Copulas, in particular, have attracted more interest due to their nice property ofapproximating the probability distribution of the data with heavy tail. Heavy tail data is frequentlyobserved in financial applications. The standard multivariate copula suffer from serious limitations whichmade them unsuitable for modeling the financial data. An alternative copula model called the pair-copulaconstruction (PCC) model is more flexible and efficient for modeling the complex dependence of finan-cial data. The only restriction of PCC model is the challenge of selecting the best model structure. Thisissue can be tackled by capturing conditional independence using the Bayesian network PCC (BN-PCC).The flexible structure of this model can be derived from conditional independences statements learnedfrom data. Additionally, the difficulty of computing conditional distributions in graphical models for non-Gaussian distributions can be eased using pair-copulas. In this paper, we extend this approach furtherusing the minimum information vine model which results in a more flexible and efficient approach inunderstanding the complex dependence between multiple variables with heavy tail dependence andasymmetric features which appear widely in the financial applications