Uncertain hypothesis test for uncertain differential equations

Uncertain hypothesis test is a statistical tool that uses uncertainty theory to determine whether some hypotheses are correct or not based on observed data. As an application of uncertain hypothesis test, this paper proposes a method to test whether an uncertain differential equation fits the observed data or not. In order to demonstrate the test method, some numerical examples are provided. Finally, both uncertain currency model and stochastic currency model are used to model US Dollar to Chinese Yuan (USD–CNY) exchange rates. As a result, it is shown that the uncertain currency model fits the exchange rates well, but the stochastic currency model does not.

Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach

Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probability-generating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.

Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference

When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to show symptoms of COVID-19 after being exposed to an infected environment or the surrounding air. It was proven that the proposed stochastic COVID-19 model is biologically well-justifiable by showing the existence, uniqueness, and positivity of the solution. We also explored the model for a unique global solution and derived the necessary conditions for the persistence and extinction of the COVID-19 epidemic. For the persistence of the disease, we observed that Rs0>1, and it was noticed that, for Rs<1, the COVID-19 infection will tend to eliminate itself from the population. Supplementary graphs representing the solutions of the model were produced to justify the obtained results based on the analysis. This study has the potential to establish a strong theoretical basis for the understanding of infectious diseases that re-emerge frequently. Our work was also intended to provide general techniques for developing the Lyapunov functions that will help the readers explore the stationary distribution of stochastic models having perturbations of the nonlinear type in particular.

Scalar Measures of Volatility and Dependence for the Multivariate Models with Applications to Asian Financial Markets

The variance–covariance matrix is a multi-dimensional array of numbers, containing information about the individual variabilities and the pairwise linear dependence of a set of variables. However, the matrix itself is difficult to represent in a concise way, particularly in the context of multivariate autoregressive conditional heteroskedastic models. The common practice is to report the plots of k(k−1)/2 time-varying pairwise conditional covariances, where k is the number of markets (or assets) considered;thus, when k=10, there will be 45 graphs. We suggest a scalar measure of overall variabilities (and dependences) by summarizing all the elements in a variance–covariance matrix into a single quantity. The determinant of the covariance matrix Σ, called the generalized variance, can be used as a measure of overall spread of the multivariate distribution. Similarly, the positive square root of the determinant ;R;of the correlation matrix, called the scatter coefficient, will be a measure of linear independence among the random variables, while collective correlation+(1−;R;)1/2 will be an overall measure of linear dependence. In an empirical application to the six Asian market returns, these statistics perform the intended roles successfully. In addition, these are shown to be able to reveal and explain the empirical facts that cannot be uncovered by the traditional methods. In particular, we show that both the contagion and interdependence (among the national equity markets) are present and could be quantitatively measured in contrast to previous studies, which revealed only market interdependence.

The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model

In this article, a multivariate extension of the unit-sinh-normal (USHN) distribution is presented. The new distribution, which is obtained from the conditionally specified distributions methodology, is absolutely continuous, and its marginal distributions are univariate USHN. The properties of the multivariate USHN distribution are studied in detail, and statistical inference is carried out from a classical approach using the maximum likelihood method. The new multivariate USHN distribution is suitable for modeling bounded data, especially in the (0,1)p region. In addition, the proposed distribution is extended to the case of the regression model and, for the latter, the Fisher information matrix is derived. The numerical results of a small simulation study and two applications with real data sets allow us to conclude that the proposed distribution, as well as its extension to regression models, are potentially useful to analyze the data of proportions, rates, or indices when modeling them jointly considering different degrees of correlation that may exist in the study variables is of interest.

UNIFORM INFERENCE IN A GENERALIZED INTERVAL ARITHMETIC CENTER AND RANGE LINEAR MODEL

Via generalized interval arithmetic, we propose a Generalized Interval Arithmetic Center and Range (GIA-CR) model for random intervals, where parameters in the model satisfy linear inequality constraints. We construct a constrained estimator of the parameter vector and develop asymptotically uniformly valid tests for linear equality constraints on the parameters in the model. We conduct a simulation study to examine the finite sample performance of our estimator and tests. Furthermore, we propose a coefficient of determination for the GIA-CR model. As a separate contribution, we establish the asymptotic distribution of the constrained estimator in Blanco-Fernández (2015, Multiple Set Arithmetic-Based Linear Regression Models for Interval-Valued Variables) in which the parameters satisfy an increasing number of random inequality constraints.

TTRISK: Tensor train decomposition algorithm for risk averse optimization

This article develops a new algorithm named TTRISK to solve high‐dimensional risk‐averse optimization problems governed by differential equations (ODEs and/or partial differential equations [PDEs]) under uncertainty. As an example, we focus on the so‐called Conditional Value at Risk (CVaR), but the approach is equally applicable to other coherent risk measures. Both the full and reduced space formulations are considered. The algorithm is based on low rank tensor approximations of random fields discretized using stochastic collocation. To avoid nonsmoothness of the objective function underpinning the CVaR, we propose an adaptive strategy to select the width parameter of the smoothed CVaR to balance the smoothing and tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can be computed by using the smoothed CVaR as a control variate. To accelerate the computations, we introduce an efficient preconditioner for the Karush–Kuhn–Tucker (KKT) system in the full space formulation.The numerical experiments demonstrate that the proposed method enables accurate CVaR optimization constrained by large‐scale discretized systems. In particular, the first example consists of an elliptic PDE with random coefficients as constraints. The second example is motivated by a realistic application to devise a lockdown plan for United Kingdom under COVID‐19. The results indicate that the risk‐averse framework is feasible with the tensor approximations under tens of random variables.

Inventory planning under supplier uncertainty in a two-level supply chain

PurposeDue to uncertainty in supply chains caused by the coronavirus disease 2019 (COVID-19), organizations are adjusting their supply chain design to address challenges faced during the pandemic. To safeguard their operations against disruption in order quantities, supply chain members have been looking for alternate suppliers. This paper considers a two-level supply chain consisting of a manufacturer and two suppliers of a certain type of components required for the production of a finished product. The primary supplier (supplier A) is unreliable, in the sense that the quantity delivered is usually less than the ordered quantity. The proportion of the ordered quantity delivered by supplier A is a random variable with a known probability distribution. The secondary supplier (supplier B) always delivers the order in its entirety at a higher cost and can respond instantaneously. In order for supplier B to respond instantaneously, the manufacturer is required to reserve a certain quantity at an additional cost. Once the quantity received from the main supplier is observed, the manufacturer may place an order not exceeding the reserved quantity.Design/methodology/approachA mathematical model describing the production/inventory situation of the supply chain is formulated. The model allows the determination of the manufacturer's optimal ordering policy.FindingsAn expression for the expected total cost per unit time function is derived. The optimal solution is determined by solving a system of nonlinear equations obtained by minimizing the expected total cost function.Practical implicationsThe proposed model can be used by supply chain managers aiming at identifying various ways of handling the uncertainty in the flow of supplies across the chain.Originality/valueThis proposed model addresses a gap in the production/inventory literature.

Solving Optimization Problems Using an Extended Gradient-Based Optimizer

This paper proposes an improved method for solving diverse optimization problems called EGBO. The EGBO stands for the extended gradient-based optimizer, which improves the local search of the standard version of the gradient-based optimizer (GBO) using expanded and narrowed exploration behaviors. This improvement aims to increase the ability of the GBO to explore a wide area in the search domain for the giving problems. In this regard, the local escaping operator of the GBO is modified to apply the expanded and narrowed exploration behaviors. The effectiveness of the EGBO is evaluated using global optimization functions, namely CEC2019 and twelve benchmark feature selection datasets. The results are analyzed and compared to a set of well-known optimization methods using six performance measures, such as the fitness function's average, minimum, maximum, and standard deviations, and the computation time. The EGBO shows promising results in terms of performance measures, solving global optimization problems, recording highlight accuracies when selecting significant features, and outperforming the compared methods and the standard version of the GBO.

Dimensions Analysis to Excess Investment in Fuzzy Portfolio Model from the Threshold of Guaranteed Return Rates

Portfolio selection is a major topic for investors to allocate their assets and maximize their profit under constrained risk. For uncertain investment behavior in a vagueness environment, some researchers have devoted themselves to this field of fuzzy portfolio models for portfolio selection. Especially, Tsaur, Chiu and Huang in 2021 defined guaranteed return rates to excess investment for securities whose return rates are bigger than the guaranteed return rates in the fuzzy portfolio selection. However, an independent investor has original ideas in investment, and thus we need to consider more types of risk attitudes for an investor's portfolio selection when the guaranteed return rates are used to excess investment. To manage the excess investment by the risk preference, a new concept of s dimensions of excess investment is introduced to perceive the risk attitude of an investor for portfolio selection. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model. This example shows that the higher dimensions of excess investment derive lower expected return rates with lower constrained risk than that of dimension s = 1;and we suggest lower risk preference should select a higher dimension of excess investment. Then, the dimension of excess investment s = 2 can be applied for portfolio selection when the risk preference is lower.

Relaxation of the parameter independence assumption in the bootComb R package

BackgroundThe bootComb R package allows researchers to derive confidence intervals with correct target coverage for arbitrary combinations of arbitrary numbers of independently estimated parameters. Previous versions (<1.1.0) of bootComb used independent bootstrap sampling and required that the parameters themselves are independent—an unrealistic assumption in some real-world applications.FindingsUsing Gaussian copulas to define the dependence between parameters, the bootComb package has been extended to allow for dependent parameters.ImplicationsThe updated bootComb package can now handle cases of dependent parameters, with users specifying a correlation matrix defining the dependence structure. While in practice it may be difficult to know the exact dependence structure between parameters, bootComb allows running sensitivity analyses to assess the impact of parameter dependence on the resulting confidence interval for the combined parameter.AvailabilitybootComb is available from the Comprehensive R Archive Network (https://CRAN.R-project.org/package=bootComb).

A general framework for quantifying uncertainty at scale

In many fields of science, comprehensive and realistic computational models are available nowadays. Often, the respective numerical calculations call for the use of powerful supercomputers, and therefore only a limited number of cases can be investigated explicitly. This prevents straightforward approaches to important tasks like uncertainty quantification and sensitivity analysis. This challenge can be overcome via our recently developed sensitivity-driven dimension-adaptive sparse grid interpolation strategy. The method exploits, via adaptivity, the structure of the underlying model (such as lower intrinsic dimensionality and anisotropic coupling of the uncertain inputs) to enable efficient and accurate uncertainty quantification and sensitivity analysis at scale. Here, we demonstrate the efficiency of this adaptive approach in the context of fusion research, in a realistic, computationally expensive scenario of turbulent transport in a magnetic confinement tokamak device with eight uncertain parameters, reducing the effort by at least two orders of magnitude. In addition, we show that this refinement method intrinsically provides an accurate surrogate model that is nine orders of magnitude cheaper than the high-fidelity model.Ionuţ-Gabriel Farcaş, Gabriele Merlo and colleagues developed a framework for uncertainty quantification and sensitivity analysis at scale by focusing on important input parameters. The framework was demonstrated to reduce computational effort and cost compared to standard methods in a turbulent transport simulation in the context of fusion research.

Effects of Supply Reliability, Risk Aversion, and Wealth on Retailer’s Optimal Order Strategy

This study examines the effects of supply reliability, risk aversion, and wealth on the optimal order strategy of retailers in the case of uncertain demand by measuring the degree of risk aversion. A more practical model of optimal ordering strategy is proposed, considering supply reliability, demand uncertainty, risk aversion, and retailer wealth, in which two random variables, supply reliability factors and demand, are introduced into the retailer’s function of expected utility. To avoid nonconvergence at both ends, the demand follows a triangular rather than a normal distribution. It is found that the optimal order quantity will increase with the improvement of supply reliability when the risk-averse degree is fixed. The results also show that the optimal order quantity of risk-averse retailers is smaller than that of risk-neutral retailers. Additionally, the optimal order quantity for the risk-averse retailer decreases as the degree of risk aversion increases, when supply reliability is fixed. Further research shows that the retailer is a constant absolute risk aversion (CARA). That means retailer’s wealth has nothing to do with the risk aversion and changes in the retailer’s wealth will not affect the retailer’s optimal order quantity. This study provides valuable insights for sustainable supply chain management and marketing.

Ratio of Two Independent Lindley Random Variables.

The distribution of the ratio of two independently distributed Lindley random variables X and Y , with different parameters, is derived. The associated distributional properties are provided. Furthermore, the proposed ratio distribution is fitted to two applications data (COVID-19 and Bladder Cancer Data), and compared it with some well-known right-skewed variations of Lindley distribution, namely; Lindley distribution, new generalized Lindley distribution, new quasi Lindley distribution and a three parameter Lindley distribution. The numerical result of the study reveals that the proposed distribution of two independent Lindley random variables fits better to the above said data sets than the compared distribution.

Information Approach for Change Point Analysis of EGGAPE Distribution and Application to COVID-19 Data

The exponentiated generalized Gull alpha power exponential distribution is an extension of the exponential distribution that can model data characterized by various shapes of the hazard function. However, change point problem has not been studied for this distribution. In this study, the change point detection of the parameters of the exponentiated generalized Gull alpha power exponential distribution is studied using the modified information criterion. In addition, the binary segmentation procedure is used to identify multiple change point locations. The assumption is that all the parameters of the EGGAPE distributions are considered changeable. Simulation study is conducted to illustrate the power of the modified information criterion in detecting change point in the parameters with different sample sizes. Three applications related to COVID-19 data are used to demonstrate the applicability of the MIC in detecting change point in real life scenario.

Survival Models By Non-Parametric And Semi-Parametric Methods For Patients Infected With Coronavirus In Al-Kindi Teaching Hospital

A study of the non-parametric survival model (Kaplan-Meier) and the semi-parametric Cox Regression model. From the practical side, it was found that the effect of the change of age by (3.483) when the patient's age was transferred from one age group to another on the estimation of the survival function by semi-parametric method using the (Cox Regression) model. From the comparison between the models of survival (nonparametric, semi-parametric) from the mean squares of relative error (RMSE) statistics, it was found that the best model for estimating the survival function is the nonparametric model (Kaplan-Meier). The study came out with several results, the most important of which is that by estimating the survival function by the nonparametric method (Kaplan-Meier), it is possible to obtain the lowest cumulative risk rate for each survival time. This means that the probability of the patient staying in the time period (t) increases and that the risk rate is affected by the change in the patient's age and duration of stay when estimating the survival and cumulative risks by the semi-parametric method (Cox Regerssion).

Statistical Inference to the Parameter of the Inverse Power Ishita Distribution under Progressive Type-II Censored Data with Application to COVID-19 Data

The goal of the article is the inference about the parameters of the inverse power ishita distribution (IPID) using progressively type-II censored (Prog–II–C) samples. For IPID parameters, maximum likelihood and Bayesian estimates were obtained. Two bootstrap “confidence intervals” (CIs) are also proposed in addition to “approximate confidence intervals” (ACIs). In addition, Bayesian estimates for “squared error loss” (SEL) and LINEX loss functions are provided. The Gibbs within Metropolis–Hasting samplers process is used to provide Bayes estimators of unknown parameters also “credible intervals” (CRIs) of them by using the “Markov Chain Monte Carlo” (MCMC) technique. Then, an application of the suggested approaches is considered a set of real-life data this data set COVID-19 data from France of 51 days recorded from 1 January to 20 February 2021 formed of mortality rate. To evaluate the quality of the proposed estimators, a simulation study is conducted.

Fuzzy confidence interval construction and its application in recovery time for COVID-19 patients

An approach is proposed to construct fuzzy confidence intervals for unknown parameters in statistical models. In this approach, a family of confidence intervals of the unknown crisp parameters is considered. Such confidence intervals are used to obtain a fuzzy confidence interval for the parameter of interest. The proposed approach enjoys a wide range of confidence intervals to obtain a trapezoidal shaped fuzzy set of the parameter space as the fuzzy confidence interval for the parameter of interest. By using the resolution identity, it is shown that the constructed fuzzy confidence intervals are really fuzzy sets of the parameter space. Some numerical examples are provided to explain the functionality of the approach at one-sided and two-sided fuzzy confidence intervals. Moreover, the application of this proposed approach in health sciences is provided for the case of the recovery time of olfactory and gustatory dysfunctions for COVID-19 patients.

A stochastic algorithm for solving the posterior inference problem in topic models

Latent Dirichlet allocation (LDA) is an important probabilistic generative model and has usually used in many domains such as text mining, retrieving information, or natural language processing domains. The posterior inference is the important problem in deciding the quality of the LDA model, but it is usually non-deterministic polynomial (NP)-hard and often intractable, especially in the worst case. For individual texts, some proposed methods such as variational Bayesian (VB), collapsed variational Bayesian (CVB), collapsed Gibb's sampling (CGS), and online maximum a posteriori estimation (OPE) to avoid solving this problem directly, but they usually do not have any guarantee of convergence rate or quality of learned models excepting variants of OPE. Based on OPE and using the Bernoulli distribution combined, we design an algorithm namely general online maximum a posteriori estimation using two stochastic bounds (GOPE2) for solving the posterior inference problem in LDA model. It also is the NP-hard non-convex optimization problem. Via proof of theory and experimental results on the large datasets, we realize that GOPE2 is performed to develop the efficient method for learning topic models from big text collections especially massive/streaming texts, and more efficient than previous methods.

Optimal Purchasing Decisions with Supplier Default in Portfolio Procurement

As global public health events and regional conflicts have greater influence on supply chains nowadays, supplier default in procurement becomes more and more common in practice. However, there is less research on portfolio procurement purchasing decisions in the case of fixed-term contract supplier default. This paper focuses on the optimal purchasing decision of buyers by using a combination of fixed-term contracts and spot transactions, which is a beneficial extension of the classical newsvendor model. When supplier default is not considered, the optimal purchase quantity in the fixed-term contract is first obtained, which maximizes the buyer’s expected profits. Research shows that supplier default has an important impact on the optimal purchasing decision making in portfolio procurement. The optimal purchase quantity of the buyer in the fixed-term contract decreases with the increase in the default rate of the contract supplier, which implies that the default from the contract supplier inhibits a larger purchase quantity in the fixed-term contract. In addition, it is proved that the buyer’s expected profits from portfolio procurement increases with the decrease in the contract supplier’s default rate. Finally, numerical experiments and sensitivity analysis are conducted to prove the result, and some management opinions on the optimal decision-making in portfolio procurement with fixed-term contracts and spot transactions are put forward.