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In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities P (S = k) when S = ∑ i = 1 n X i and X 1 , X 2 , ... , X n are independent Bernoulli random variables that may have different success probabilities. However, their main result contained an undetermined constant, somewhat limiting its applicability. In this paper we give a nonuniform bound in the same setting but with explicit constants. Our proof uses Stein's method and, in particular, the K-function and concentration inequality approaches. We also prove a new uniform local limit theorem for Poisson binomial random variables that is used to help simplify the proof in the nonuniform case. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to use the residual strength theory to study the probability of a domino effect accident occurring following the explosion of a spherical tank. We build a novel domino effect accident probability model, using Monte Carlo methods to simulate the ejection of debris. At the same time, the velocity and velocity distribution of fragments ejecting from the upper and lower parts of the explosive spherical tank are obtained. Finally, the relationship between the volume of the exploding spherical tank and the target, the crater Angle (ψ0 and ϕ0) of debris impacting the target, the probability of target destruction and the risk of domino effect accidents are considered. The results show that the maximum speed of debris from the lower part of a spherical tank exceeds that from its upper part, and the hazard associated with the debris from the lower part cannot be ignored. With the same target volume and spacing, the probability of a domino effect accident caused by projectile debris from the upper half of an exploding spherical tank is higher than that from the lower half. As theψ0 value increases, the probability of target failure gradually decreases, and as the ϕ0 value decreases, the probability of target failure also gradually decreases. Moreover, with changes in ψ0 and ϕ0, the probabilities of destruction and the occurrence of a domino effect accident significantly change. The results of this paper can provide guidance for the risk assessment of oil and gas storage tanks. [ABSTRACT FROM AUTHOR]

The focus of this paper is impulse noise reduction in digital color images. The most popular noise reduction schemes are the vector median filter and its many variants that operate by minimizing the aggregate distance from one pixel to every other pixel in a chosen window. This minimizing operation determines the most confirmative pixel based on its similarity to the chosen window and replaces the central pixel of the window with the determined one. The peer group filters, unlike the vector median filters, determine a set of pixels that are most confirmative to the window and then perform filtering over the determined set. Using a set of pixels in the filtering process rather than one pixel is more helpful as it takes into account the full information of all the pixels that seemingly contribute to the signal. Hence, the peer group filters are found to be more robust to noise. However, the peer group for each pixel is computed deterministically using thresholding schemes. A wrong choice of the threshold will easily impair the filtering performance. In this paper, we propose a peer group filtering approach using principles of Bayesian probability theory and clustering. Here, we present a method to compute the probability that a pixel value is clean (not corrupted by impulse noise) and then apply clustering on the probability measure to determine the peer group. The key benefit of this proposal is that the need for thresholding in peer group filtering is completely avoided. Simulation results show that the proposed method performs better than the conventional vector median and peer group filtering methods in terms of noise reduction and structural similarity, thus validating the proposed approach. [ABSTRACT FROM AUTHOR]

A deep learning-based Visual Inertial SLAM technique is proposed in this paper to ensure accurate autonomous localization of mobile robots in environments with dynamic objects. Addressing the limitations of real-time performance in deep learning algorithms and the poor robustness of pure visual geometry algorithms, this paper presents a deep learning-based Visual Inertial SLAM technique. Firstly, a non-blocking model is designed to extract semantic information from images. Then, a motion probability hierarchy model is proposed to obtain prior motion probabilities of feature points. For image frames without semantic information, a motion probability propagation model is designed to determine the prior motion probabilities of feature points. Furthermore, considering that the output of inertial measurements is unaffected by dynamic objects, this paper integrates inertial measurement information to improve the estimation accuracy of feature point motion probabilities. An adaptive threshold-based motion probability estimation method is proposed, and finally, the positioning accuracy is enhanced by eliminating feature points with excessively high motion probabilities. Experimental results demonstrate that the proposed algorithm achieves accurate localization in dynamic environments while maintaining real-time performance. [ABSTRACT FROM AUTHOR]

The stochastic P-bifurcation behavior of bi-stability in a generalized van der Pol oscillator with the fractional damping under colored noise and thermal excitation is investigated. Firstly, using the principle of minimal mean square error and linearization method, the non-linear stiffness terms can be equivalent to a linear stiffness which is a function of the system amplitude, and the original system is simplified to an equivalent integer order van der Pol system. Secondly, the system amplitude stationary probability density function is obtained by the stochastic averaging, and then based on the singularity theory, the critical parametric conditions for the system amplitude stochastic P-bifurcation are found. Finally, the types of the stationary probability density function of the system amplitude are qualitatively analyzed in each area divided by the transition set curves. The consistency between the analytical results and the numerical results acquired from Monte-Carlo simulation also testifies the theoretical analysis in this paper and the method used in this paper can directly guide the design of the fractional order controller to adjust the response of the system. [ABSTRACT FROM AUTHOR]

In this paper, we propose to consider the dependence structure of the trade/no trade categorical sequence of individual illiquid stocks returns. The framework considered here is wide as constant and time-varying zero returns probability are allowed. The ability of our approach in highlighting illiquid stock's features is underlined for a variety of situations. More specifically, we show that long-run effects for the trade/no trade categorical sequence may be spuriously detected in presence of a non-constant zero returns probability. Monte Carlo experiments, and the analysis of stocks taken from the Chilean financial market, illustrate the usefulness of the tools developed in the paper. [ABSTRACT FROM AUTHOR]

Agricultural injuries remain a major concern in North America, with a fatal injury rate of 19.5 deaths per 100,000 workers in the United States. Numerous research efforts have sought to compile and analyze records of agricultural-related injuries and fatalities at a national level, utilizing resources, ranging from newspaper clippings and hospital records to Emergency Medical System (EMS) data, death certifications, surveys, and other multiple sources. Despite these extensive efforts, a comprehensive understanding of injury trends over extended time periods and across diverse types of data sources remains elusive, primarily due to the duration of data collection and the focus on specific subsets. This systematic review, following Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, consolidates and analyzes agricultural injury surveillance data from 48 eligible papers published between 1985 and 2022 to offer a holistic understanding of trends and challenges. These papers, reporting an average of 25,000 injuries each, were analyzed by database source type, injury severity, nature of injury, body part, source of injury, event/exposure, and age. One key finding is that the top source of injury or event/exposure depends on the chosen surveillance system and injury severity, underscoring the need of diverse data sources for a nuanced understanding of agricultural injuries. This study provides policymakers, researchers, and practitioners with crucial insights to bolster the development and analysis of surveillance systems in agricultural safety. The overarching aim is to address the pressing issue of agricultural injuries, contributing to a safer work environment and ultimately enhancing the overall well-being of individuals engaged in agriculture. [ABSTRACT FROM AUTHOR]

This paper introduces a novel probability distribution known as the Ejaz distribution (ED), which is characterized by two parameters. The study offers a comprehensive analysis of this distribution, including an examination of key properties such as moments, moment-generating functions, order statistics, and reliability functions. Additionally, the paper explores the graphical representation of essential functions like the probability density function, cumulative distribution function, and hazard rate function, enhancing our visual understanding of their behavior. The distribution's parameters are estimated using the widely accepted method of maximum likelihood estimation. Through real-world examples, the paper highlights the practical applicability of the Ejaz distribution, demonstrating its performance and relevance in diverse scenarios. [ABSTRACT FROM AUTHOR]

In the face of increasingly complex data forms and decision-making problems, the uncertainty of information poses a major challenge to multi-attribute decision-making methods. How to effectively organize information and serve realistic decision-making problems has attracted extensive attention in the academic circles. In view of this, based on the distribution law of random variables, we put forward the basic concept of probability numbers and construct a general framework, including the concepts of type, order, item, isomorphism and isomerism, same domain and same distribution of probability numbers. On this basis, we further define the expectation and variance formula of probability numbers, and its operation rules are defined for the same type of probability numbers. To compare the dominance and inferiority of probability numbers further accurately, we put forward the concepts of dominance degree and comparability degree of probability numbers, so that decision makers can realize the ranking of probability numbers by calculating the comprehensive dominance degree. In view of the related concepts of probability numbers, we summarize the properties and theorems of probability numbers and prove them. In addition, a probability numbers-based multi-attribute decision-making framework model is proposed to solve the multi-attribute decision-making problem. Decision makers can select appropriate sub-models to construct personalized multi-attribute decision-making methods according to actual needs. At the end of the paper, we apply the method to the multi-attribute decision case of campus express stations evaluation and verify the scientificity and rationality of the evaluation method. The concept of probability numbers and its decision model proposed in this paper extend the concept category of numbers, enrich the multi-attribute decision-making method based on probability numbers, and have certain reference significance for further research of uncertain decision theory and method. [ABSTRACT FROM AUTHOR]

When comparing two independent groups, shift functions are basically techniques that compare multiple quantiles rather than a single measure of location, the goal being to get a more detailed understanding of how the distributions differ. Various versions have been proposed and studied. This paper deals with extensions of these methods to main effects and interactions in a between-by-between, 2-by-2 design. Two approaches are studied, one that compares the deciles of the distributions, and one that has a certain connection to the Wilcoxon–Mann–Whitney method. There are many quantile estimators, but for reasons summarized in the paper, the focus is on using the Harrell–Davis quantile estimator used in conjunction with a percentile bootstrap method. Included are results comparing two methods aimed at controlling the probability of one or more Type I errors. [ABSTRACT FROM AUTHOR]

Summary: In this growing world, the field of communication is developing quickly. The research community's attention is shifting to the design of networks beyond fifth generation (5G) and the sixth generation (6G) due to the rapid spread of the 5G mobile networks. Due to that, there will be a lot of traffic in the area, which will interfere with the channels and maybe produce noise. Nonorthogonal multiple access (NOMA) contributes to streamlined communication and a decrease in the possibility of interference. The communication will be encoded and decoded from transmitter to receiver utilizing the superposition coding (SC) and successive interference cancelation (SIC) approaches, ensuring the message's secrecy. This paper considers a simultaneous wireless information and power transfer (SWIPT)‐based cooperative NOMA system, where the nearby user to the source node acts as a relay to assist the far user. To further enhance the system performance, an improved golden search optimization (IGSO) is used to determine the best power allocation and power splitting coefficients by decreasing the outage probability. The existing models are compared with the proposed model in the results section regarding outage probability and throughput, where the proposed model outperformed all other existing models. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by an adversary, and both this phenomenon and the uncertainty in the observations are modelled by two sets of Bernoulli random variables. Under the assumption that the evolution model generating the signal to be estimated is unknown and only the mean and covariance functions of the processes involved in the observation equation are available, recursive algorithms based on linear approximations of the real observations are proposed for the least-squares filtering and fixed-point smoothing problems. Finally, the feasibility and effectiveness of the developed estimation algorithms are verified by a numerical simulation example, where the impact of uncertain observation and deception attack probabilities on estimation accuracy is evaluated. [ABSTRACT FROM AUTHOR]

In this paper we generalize the transition probability matrix for a random walk on a finite network by defining the transition probabilities through a symmetric M -matrix. Usually, the walker jumps from a vertex to a neighbor according to the probabilities given by the adjacency matrix. Moreover, we can find in the literature the relation between random walks and the normalized laplacian or the combinatorial laplacian that are singular and symmetric M -matrices. Our model takes into consideration not only the probability of transitioning given by the adjacency matrix but also some added probability that depends on a node property. This also includes the probability of remaining in each node, when the M -matrix is not singular. The nodes importance is taking into account by considering the lower eigenvalue and its associated eigenfunction for the given M -matrix. We give expressions for the mean first passage time and Kemeny's constant for such a random walks in terms of 1-inverses of the considered M -matrix. [ABSTRACT FROM AUTHOR]

The classical Ellsberg experiment provides decision-makers with a choice problem in which the likelihood of winning the gambling is uncertain. In this paper, we consider a two-dimensional Ellsberg experiment in which the likelihood of winning the gambling and the income after that are both uncertain, establish a mathematical model to characterize the corresponding Ellsberg experiment and solve the choice problem based on probability theory, uncertainty theory, and chance theory. [ABSTRACT FROM AUTHOR]

This paper studies the problems of stability analysis and stabilisation synthesis for a class of impulsive switched stochastic systems. By constructing a novel impulsive switching condition, the sufficient conditions of globally asymptotic stability in probability and stochastic input-to-state stability for the considered systems are presented. Furthermore, the stabilising controller design method can be presented for the corresponding closed-loop systems. Two examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Aims: To discuss the levels of structural empowerment (SE) and psychological empowerment (PE) and the factors that influence perceptions of empowerment among newly graduated nurses (NGNs). Design: Mixed methods study. Methods: The quantitative part of the study was conducted with 220 NGNs with <1 year of job experience. The study was conducted between February and May 2023. Focus group discussions were conducted with 30 NGNs. Data were collected by using the Conditions for Work Effectiveness Questionnaire (CWEQ‐II), the Psychological Empowerment Scale (PES) and a Semi‐Structured Interview Form. Quantitative data were analysed using stepwise regression analysis. Content analysis was used to analyse qualitative data. Results: CWEQ‐II and PES were moderate. The regression analysis showed that NGNs' SE scores increased in association with the following factors, including an increase in the total score on the PES, being married/having a partner, working a day shift, having career planning, increased satisfaction with the orientation programmes of the institution and increased satisfaction with the employing institution. As a result of the descriptive analysis of the focus group interviews conducted to determine the empowerment perceptions of NGNs, we identified three contexts along with the associated themes and subthemes. These three contexts were the 'concept of power', 'professional impression' and 'empowerment process'. Conclusion: The results of this study indicate that the SE and PE levels of NGNs are moderate, and their empowerment perceptions are influenced by many factors that can be individual, organizational and work environment relevant. Impact: This study's findings will guide policymakers, educators, researchers and administrators in empowering NGNs essential to the healthcare workforce. Reporting Method: The paper adheres to the COREQ checklist. Patient or Public Contribution: No patient or public contribution. [ABSTRACT FROM AUTHOR]

In this paper, we shall discuss the extendability of probability and non-probability measures on Cayley trees to a σ -additive measure on Borel fields which has a fundamental role in the theory of Gibbs measures. [ABSTRACT FROM AUTHOR]

The local limit theorem (LLT) is one of the well-known limit theorems which can be used to estimate the probability at a particular point of a random variable. In this paper, we generalize weighted sums which are introduced by Giuliano and Weber and give the LLT with explicit error bounds. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to compute the probability Pr(G) that two elements of the group G, drawn at random with replacement, commute; that is, Pr(G) = Number of ordered pairs (x, y) ∈ G × G such that xy = yx/|G × G| = |G|² In particular, we compute Pr(G) for some groups such as the extraspecial groups of order p³, p prime, for the permutation groups G = Sn and G = An, n ≥ 5, for 10 non-abelian groups of order p4 and for simple groups of certain type. [ABSTRACT FROM AUTHOR]

The clogging phenomenon finds extensive application in both industrial processes and daily life events. While this broad spectrum of application motivated extensive research to identify the general factors underlying the clogging mechanism, it results in a fragmented and system-specific understanding of the entire clogging process. Therefore, it is essential to establish a holistic understanding of all contributing factors of clogging based on the microscopic physical mechanisms. In this paper, we experimentally investigate clogging of granular materials in a two-dimensional hopper flow and present a self-consistent physical mechanism of clogging based on precursory chain structures. These chain structures follow a specific modified restricted random walk, and clogging occurs when they are mechanically stable enough to withstand the flow fluctuations. We introduce a single-particle model that can explain the arch-forming probability. Our results provide insight into the microscopic mechanism behind clogging and a broader understanding of the dynamics of dense granular flow. The study of the general factors underlying clogging are fragmented and application-driven due to its broad spectrum of applications. The authors propose a holistic understanding of the clogging process by investigating the clogging of a granular hopper flow using high-speed imaging, finding a signature formation of precursory chain structures. [ABSTRACT FROM AUTHOR]

In this paper we consider a special kind of semicontinous distribution. We try to concern with the situation where the probability of zero observation is associated with the location and scale parameters in lognormal distribution. We first propose a goodness-of-fit test to ensure that the data can be fit by the associated delta-lognormal distribution. Then we define the updated fiducial distributions of the parameters and establish the results that the confidence interval has asymtotically correct level while the significance level of the hypothesis testing is also asymtotically correct. We propose an exact sampling method to sample from the updated fiducial distribution. It can be seen in our simulation study that the inference on the parameters is largely improved. A real data example is also used to illustrate our method. [ABSTRACT FROM AUTHOR]

Uncertainty propagation of the frequency response function is crucial for vibration problems such as model calibration, and the probability assessment is another indispensable item in structural optimization. Considering only one of them will inevitably lead to a lack of uncertain knowledge of practical engineering structures. However, it is still challenging to evaluate the system response bounds and probability characteristics simultaneously and maximally reduce the computational cost. This paper focuses on the frequency response function involving correlated uncertainties and proposes a novel uncertainty propagation and probability assessment method. First, a convex model was established to quantify the correlated uncertainty parameters, and then, the Chebyshev polynomial function was developed as the surrogate model to efficiently quantify the uncertainty propagation from uncertainty parameters to system response. Subsequently, the novel normalized and coordinated transformation combined the uncertainty propagation method, making the uncertainty system response easy to assess. Note that the response value at the interpolation point can be employed as the input of probability assessment. One can also estimate the probability characteristics at different frequency positions during the construction of the surrogate model. Finally, two numerical examples were presented to demonstrate the effectiveness and cheaper computation by a discrete system and a continuous system, respectively. Results indicate that the proposed method can be conveniently and accurately applied to assess the bounds and probability characteristics of frequency response function involving correlated uncertainties. [ABSTRACT FROM AUTHOR]

The paper studies the probability for a Galois group of a random polynomial to be An$A_n$. We focus on the so‐called large box model, where we choose the coefficients of the polynomial independently and uniformly from {−L,...,L}$\lbrace -L,\ldots , L\rbrace$. The state‐of‐the‐art upper bound is O(L−1)$O(L^{-1})$, due to Bhargava. We conjecture a much stronger upper bound L−n/2+ε$L^{-n/2 +\epsilon }$, and that this bound is essentially sharp. We prove strong lower bounds both on this probability and on the related probability of the discriminant being a square. [ABSTRACT FROM AUTHOR]

Assessing heterogeneous treatment effects (HTEs) is an essential task in epidemiology. The recent integration of machine learning into causal inference has provided a new, flexible tool for evaluating complex HTEs: causal forest. In a recent paper, Jawadekar et al (Am J Epidemiol. 2023;192(7):1155-1165) introduced this innovative approach and offered practical guidelines for applied users. Building on their work, this commentary provides additional insights and guidance to promote the understanding and application of causal forest in epidemiologic research. We start with conceptual clarifications, differentiating between honesty and cross-fitting, and exploring the interpretation of estimated conditional average treatment effects. We then delve into practical considerations not addressed by Jawadekar et al, including motivations for estimating HTEs, calibration approaches, and ways to leverage causal forest output with examples from simulated data. We conclude by outlining challenges to consider for future advancements and applications of causal forest in epidemiologic research. [ABSTRACT FROM AUTHOR]

This paper provides a new characterization of belief consistency in extensive games. We show that all consistent assessments are supported by sequences of strategy profiles with the property that all actions with vanishing probability are played according to power functions of the sequence index. The result makes it simpler to prove or disprove that a given assessment is consistent, facilitating the use of sequential equilibria. [ABSTRACT FROM AUTHOR]

This paper studies the single-index varyingcoefficient quantile model with missing covariates at random. Firstly, some estimators of index parameters and their corresponding linkage function are given by using the inverse probability weighting method for missing data in two cases including parameter estimation and non-parametric estimation for the single-index varying-coefficient quantile regression model. In particular, the latter case focuses on the study of both known and unknown probability functions. Secondly, the established estimators are proved to be asymptotic normal under some suitable regularity conditions. Finally, the simulation studies are conducted to demonstrate the finite sample performance of the proposed method. [ABSTRACT FROM AUTHOR]

Collisions involving space objects pose significant threats to space sustainability. Within these collisions, catastrophic collisions which generate a larger amount of debris are particularly harmful. The quantity and characteristics of fragments generated from a collision are usually modeled using the NASA standard breakup model (SBM). However, on several occasions, the NASA SBM has incorrectly estimated the effects of collisions, including the Yunhai 1-02 breakup event. Using outer probability measure theory and information theory, we develop a correction methodology to estimate the Yunhai 1-02 event based on NASA SBM. This methodology successfully passes a statistical test using historical data. After correction, the characteristic diameter and relative velocity distributions of fragments generated from this event exhibit greater similarity with observations. The work in this paper facilitates the analysis of the properties of the debris cloud resulting from collisions with limited information, improving the predictions of future collisions. [Display omitted] • We condense and analyze the historical collision data. • We obtain a corrected parameter to adjust the SBM result, and this adjusted result passes the statistical test. • We improve the precision of characteristic diameter and relative velocity of fragments generated from Yunhai event. • This work is important to estimate the effect of collisions with limited information. [ABSTRACT FROM AUTHOR]

We introduce a general IFS Bayesian method for getting posterior probabilities from prior probabilities, and also a generalized Bayes' rule, which will contemplate a dynamical, as well as a non-dynamical setting. Given a loss function $ {l} $ l , we detail the prior and posterior items, their consequences and exhibit several examples. Taking Θ as the set of parameters and Y as the set of data (which usually provides random samples), a general IFS is a measurable map $ \tau :\Theta \times Y \to Y $ τ : Θ × Y → Y , which can be interpreted as a family of maps $ \tau _\theta :Y\to Y,\,\theta \in \Theta $ τ θ : Y → Y , θ ∈ Θ. The main inspiration for the results we will get here comes from a paper by Zellner (with no dynamics), where Bayes' rule is related to a principle of minimization of information. We will show that our IFS Bayesian method which produces posterior probabilities (which are associated to holonomic probabilities) is related to the optimal solution of a variational principle, somehow corresponding to the pressure in Thermodynamic Formalism, and also to the principle of minimization of information in Information Theory. Among other results, we present the prior dynamical elements and we derive the corresponding posterior elements via the Ruelle operator of Thermodynamic Formalism; getting in this way a form of dynamical Bayes' rule. [ABSTRACT FROM AUTHOR]

This paper deals with the ruin problem of an insurance company investing its capital reserve in a risky asset with the price dynamics given by a conditional geometric Brownian motion whose parameters depend on a Markov process describing random variations in the economic and financial environments. We prove a sufficient condition on the distribution of jumps of the business process ensuring the smoothness of the ruin probability as a function of the initial capital and obtain for this function an integro-differential equation. [ABSTRACT FROM AUTHOR]

The reconfiguration of wireless channels with reconfigurable reflecting surface (RIS) technology offers new design options for future wireless networks. Due to its high altitude and increased probability of establishing line-of-sight linkages with ground source/destination nodes, aerial RIS (ARIS) has greater deployment flexibility than traditional terrestrial RIS. It also provides a wider-view signal reflection. To leverage the advantages of ARIS-enabled systems, this paper defines air-to-ground linkages via Nakagami-m small-scale fading and inverse-Gamma large-scale shadowing, considering realistic composite fading channels. To construct a tight approximate closed-form formula for the outage probability (OP), a new mathematical framework is proposed. Additionally, a deep-learning-based system called the BiLSTM model is deployed to evaluate OP performance in the 3D spatial movement of the ARIS system. In the offline phase, the proposed model is trained with real-value channel state estimation sets and enhances OP performance in the online phase by learning channel information in a bidirectional manner. Simulation results demonstrate that the proposed BiLSTM model outperforms all other models in analyzing OP for the ARIS system. [ABSTRACT FROM AUTHOR]

This paper presents an in‐depth analysis of the exponentiated half‐logistic Weibull (EHLW) distribution, investigating its fundamental statistical properties and exploring parameters estimation using both maximum likelihood and Bayesian approaches. Specifically, our focus centers on the analysis of stress–strength reliability, denoted as R=P(X>Y)$R=P(X>Y)$, where the strength variable X$X$ follows EHLW distribution, and the stress variable Y$Y$ follows either Weibull distribution or the EHLW distribution. The estimation of the parameter R$R$ is discussed in both scenarios, employing both Maximum Likelihood and Bayesian approaches. Furthermore, we calculate that the asymptotic confidence interval, percentile bootstrap interval, and the highest probability density credible interval are obtained for the stress–strength parameter R$R$. In order to assess the efficiency of these estimation techniques, simulation studies are conducted, providing valuable insights into the performance of each estimation approach. Finally, the proposed reliability model is applied to real datasets, highlighting its practical significance. [ABSTRACT FROM AUTHOR]

This paper takes its cue from an unpublished manuscript by the Victorian polymath William Stanley Jevons (1835–1882). I elucidate how he attempted to integrate science and religion through natural theology. I argue that Jevons's manuscript shows that he took the theory of probability to be the most appropriate tool for finding evidence of divine design in natural phenomena. Jevons thus took part in the nineteenth-century natural theology debate, specifically between William Whewell and Charles Babbage. This debate was about both how to interpret the analogy between natural and human contrivances, and about the tools which should be used in natural theology. After introducing the manuscript, I present Jevons's religious ideas about Unitarianism and the relationship between chance and design in his writings. I show Jevons's commitment to natural theology and his idea that humans, due to their finite intellect, should use the theory of probability to investigate divine providence. I then compare Jevons's position to Whewell's and Babbage's Bridgewater Treatises. I show how they had different conceptions of natural theology compared to Jevons, and different ideas about the tools that should be used to investigate natural laws. [ABSTRACT FROM AUTHOR]

Dynamic microsimulations are tools to stochastically project (synthetic) microdata into the future. In spatial microsimulations, regional discrepancies are of particular interest and must be considered accordingly. In practice, the probabilities for state changes are unknown and must be estimated, usually from survey data. However, estimating such models on the regional level is often not feasible due to limited sample size and lack of geographic information. Simply applying the model estimated at the national level to all geographies leads to biased state transitions due to regional differences in level and distribution. In this paper, we introduce a model-based alignment method to adapt predicted probabilities obtained from a nationally estimated model to subregions by integrating known marginal distributions to re-introduce regional heterogeneity and create more realistic trajectories, particularly in small areas. We show that the model-adjusted transition probabilities can capture region-specific patterns and lead to improved projections. Our findings are useful to researchers who want to harmonise model outputs with external information, in particular for the field of microsimulation. [ABSTRACT FROM AUTHOR]

Speech presence probability (SPP) and gain functions such as Wiener filter or MMSE estimators require an estimate of the a-priori signal-to-noise ratio (SNR). However, the estimation of the a-priori SNR is computationally involved and sensitive to noise variations. This paper proposes to approximate the SPP and the overall gain function of a speech enhancement system by using sigmoid functions to reduce the need of estimating the a-prior SNR. By applying an approximation via the sigmoid functions it is shown that only the a-posteriori estimate of SNR is needed, resulting in a low complexity system. The sigmoid function is designed with an optimization algorithm to optimize its parameters with respect to speech quality measures. The optimization algorithm is based on the idea that the solution obtained for a given problem should move towards the best solution and avoid the worst solution. The proposed algorithm requires minimal control parameters and does not require any algorithm specific parameters. Simulation results show that the proposed sigmoid functions achieve good results in terms of speech quality measures when compared with existing methods while providing significantly lower complexity for implementation. [ABSTRACT FROM AUTHOR]

• Novel evidence theory-based strategy is developed to characterize multi-source uncertainties. • Hybrid ellipsoid-interval model considering independence and dependence simultaneously is presented. • Data-driven approach is utilized to calculate the basic probability assignment. • Region optimal-based ensemble metamodel is constructed for belief degree calculation. For many engineering problems with epistemic uncertainty, evidence theory provides a flexible modeling framework to tackle with imprecise and conflicting information. However, the traditional model established under evidence theory framework can solely address uncorrelated or correlated evidence variables, which curtails its application in engineering practices. This paper aims to develop a unified model for evidence theory-based uncertainty analysis with consideration of parameter independence and dependence coexist scenarios. With the aid of subspace decomposition, a hybrid ellipsoid-interval model integrating evidence theory is firstly developed to quantify uncorrelated and correlated evidence variables within a unified framework. To make full use of sample information, a data-driven strategy is further proposed to determine the basic probability assignment of the above focal elements. Subsequently, the belief and plausibility measures are calculated using proposed hybrid ellipsoid-interval model integrating evidence theory. To improve the efficiency and accuracy of belief degree calculation, a region optimal-based ensemble metamodel is further introduced by applying component metamodels together. Eventually, a test example and an aeroengine blade engineering application are investigated to substantiate the effectiveness of the proposed model and method. [ABSTRACT FROM AUTHOR]

In this paper, we consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of μ-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures μ, and to adjoints of composition operators. [ABSTRACT FROM AUTHOR]

Bayesian predictive probabilities have become a ubiquitous tool for design and monitoring of clinical trials. The typical procedure is to average predictive probabilities over the prior or posterior distributions. In this paper, we highlight the limitations of relying solely on averaging, and propose the reporting of intervals or quantiles for the predictive probabilities. These intervals formalize the intuition that uncertainty decreases with more information. We present four different applications (Phase 1 dose escalation, early stopping for futility, sample size re-estimation, and assurance/probability of success) to demonstrate the practicality and generality of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper characterizes the probability of a market failure defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. The characterization employs a multivariate Cox process across the G-SIBs, which allows us to relate our work to the existing literature on intensity-based models. Various theorems related to market failure probabilities are derived, including the probability of a market failure due to two banks defaulting over the next infinitesimal interval, the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to 1. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Green measure for a class of non-Gaussian processes in R d . These measures are associated with the family of generalized grey Brownian motions B β , α , 0 < β ≤ 1 , 0 < α ≤ 2 . This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability 1 for d α > 2 and 1 < α ≤ 2 . The Green measure then generalizes those measures of all these classes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a risk model with heavy-tailed claims and Brownian perturbation. Assuming that the distribution function of claim-size is subexponential, and the arrival process of claims is a non stationary process satisfying the principle of large deviation, the asymptotic formula for the ruin probability of this risk model at random time is obtained. [ABSTRACT FROM AUTHOR]

In recent years, there has been increasing interest in the joint modelling of compound extreme events such as high temperatures and low rainfall. The increase in the frequency of occurrence of these events in many regions has necessitated the development of models for estimating the concurrent probabilities of such compound extreme events. The current study discusses an application of copula models in predicting the concurrent probabilities of compound low rainfall and high-temperature events using data from the Lowveld region of the Limpopo province in South Africa. The second stage discussed two indicators for monitoring compound high temperature and low rainfall events. Empirical results from the study show that elevations ranging from 100–350 m, 350–700 m and 700–1200 m exhibit varying probabilities of experiencing drought, with mild droughts having approximately 64%, 66%, and 65% chances, moderate droughts around 36%, 39%, and 38%, and severe droughts at approximately 16%, 19%, and 18%, respectively. Furthermore, the logistic regression models incorporating the southern oscillation index as a covariate yielded comparable results of copula-based models. The methodology discussed in this paper is robust and can be applied to similar datasets in any regional setting globally. These findings could be useful to disaster management decision makers, helping them formulate effective mitigation strategies and emergency response plans. [ABSTRACT FROM AUTHOR]

In this paper, we present an unprecedented method based on Kohonen networks that is able to automatically recognize partial discharge (PD) classes from phase-resolved partial discharge (PRPD) diagrams with features of various simultaneous PD patterns. The PRPD diagrams were obtained from the stator windings of a real-world hydro-generator rotating machine. The proposed approach integrates classification probabilities into the Kohonen method, producing self-organizing probability maps (SOPMs). For building SOPMs, a group of PRPD diagrams, each containing a single PD pattern for training the Kohonen networks and single- and multiple-class-featured samples for obtaining final SOPMs, is used to calculate the probabilities of each Kohonen neuron to be associated with the various PD classes considered. At the end of this process, a self-organizing probability map is produced. Probabilities are calculated using distances, obtained in the space of features, between neurons and samples. The so-produced SOPM enables the effective classification of PRPD samples and provides the probability that a given PD sample is associated with a PD class. In this work, amplitude histograms are the features extracted from PRPDs maps. Our results demonstrate an average classification accuracy rate of approximately 90% for test samples. [ABSTRACT FROM AUTHOR]

The selection of multiple contingency scenarios is a key task to perform resilience-oriented long-term planning analyses. However, the identification of relevant multiple contingencies may easily lead to combinatorial explosion issues, even for relatively small systems. This paper proposes an effective methodology for the identification of relevant multiple contingencies and their probabilities, suitable for the long-term resilience analysis of large power systems. The methodology is composed of two main pillars: (1) the clustering of lines that are more likely to fail together, to reduce the computational complexity of the analysis exploiting historical weather data and (2) the probability-based identification of multiple contingencies within each cluster, where the contingency probability is computed applying the copula theory. Tests performed on a portion of the Italian EHV transmission system confirm the validity of the clustering results compared against historical failure events. Moreover, the copula-based algorithm for contingency probability estimation passes the tests carried out on relatively large clusters with very low error tolerance. The method successfully pinpoints critical multiple contingency scenarios and their likelihoods, making it valuable for assessing power system resilience over long-term horizons in support of resilience-oriented planning activities. [ABSTRACT FROM AUTHOR]

The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicated will resemble the original one(s) in some important ways. At the same time, it will also be more modest insofar as meaningfulness will turn out to be relativized linguistically and probabilistically, and different choices of the linguistic and probabilistic parameters may lead to different verdicts on meaningfulness. [ABSTRACT FROM AUTHOR]

In this paper, we consider one-parameter regularly varying discrete distribution generated by Levy probability (RDLP). Some useful plots of the models are illustrated. Mathematically, to propose the RDLP model as a discrete distribution in bioinformatics, some common statistical facts such as unimodality, skewness to the right, upward/downward convexity, regular variation at infinity, and asymptotically constant slowly varying component are established for the model. Based on the Monte Carlo method and limited-memory Broyden–Fletcher–Goldfarb–Shanno for bound-constrained optimization, simulation studies are done to estimate bias, mean square error, and maximum likelihood estimation for the unknown parameter of the model. Some asymptotic properties and asymptotic expansions are given for useful functions. Moreover, we shall attempt to examine the RDLP model with a real count data set to show its application, and also compare it with two rival models. [ABSTRACT FROM AUTHOR]

Background: Shortages of mechanical ventilation have become a constant problem in Emergency Departments (EDs), thereby affecting the timely deployment of medical interventions that counteract the severe health complications experienced during respiratory disease seasons. It is then necessary to count on agile and robust methodological approaches predicting the expected demand loads to EDs while supporting the timely allocation of ventilators. In this paper, we propose an integration of Artificial Intelligence (AI) and Discrete-event Simulation (DES) to design effective interventions ensuring the high availability of ventilators for patients needing these devices. Methods: First, we applied Random Forest (RF) to estimate the mechanical ventilation probability of respiratory-affected patients entering the emergency wards. Second, we introduced the RF predictions into a DES model to diagnose the response of EDs in terms of mechanical ventilator availability. Lately, we pretested two different interventions suggested by decision-makers to address the scarcity of this resource. A case study in a European hospital group was used to validate the proposed methodology. Results: The number of patients in the training cohort was 734, while the test group comprised 315. The sensitivity of the AI model was 93.08% (95% confidence interval, [88.46 − 96.26%]), whilst the specificity was 85.45% [77.45 − 91.45%]. On the other hand, the positive and negative predictive values were 91.62% (86.75 − 95.13%) and 87.85% (80.12 − 93.36%). Also, the Receiver Operator Characteristic (ROC) curve plot was 95.00% (89.25 − 100%). Finally, the median waiting time for mechanical ventilation was decreased by 17.48% after implementing a new resource capacity strategy. Conclusions: Combining AI and DES helps healthcare decision-makers to elucidate interventions shortening the waiting times for mechanical ventilators in EDs during respiratory disease epidemics and pandemics. [ABSTRACT FROM AUTHOR]

This paper concentrates on the finite-time  H ∞  control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT)  H ∞  state feedback controller and an SFT  H ∞  observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov–Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT  H ∞  boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes. [ABSTRACT FROM AUTHOR]

Introduced in the United Kingdom in 2012, Universal Credit (UC) is a welfare benefit that replaces six working-age 'legacy' benefits for out-of-work and low-income people. Designed with the aim of simplifying benefits and incentivising paid work, UC represents a deepening of conditionality in the British welfare state. Considering these developments, this paper quantitatively investigates the effect of UC on recipients' life satisfaction. Data from the United Kingdom Household Longitudinal Study is analysed, primarily using a fixed-effects regression approach. Results reveal a significantly negative effect of UC recipience on life satisfaction. Robustness checks and alternative model specifications, including difference-in-differences and inverse probability weighting, confirm this finding. Additionally, mediation models give credence to the idea that UC also negatively affects life satisfaction indirectly by increasing psychological distress. Heterogeneity tests indicate that UC has a less negative effect on single parents' life satisfaction compared to non-parents. Meanwhile, UC has a significantly more negative effect on the life satisfaction of people not in paid work (for reasons other than unemployment) than those in paid work. Discussion focuses on the potential effect of welfare conditionality specifically, and implications for future research and policy are explored. [ABSTRACT FROM AUTHOR]

The Lomax distribution is one of the well-known distributions that is used to fit heavy-tailed data. In this paper, we investigate the estimation of Shannon entropy of the Lomax distribution using noninformative priors. Some important priors including Jeffreys prior, reference priors and probability matching priors are presented. We demonstrate that the reference and matching priors for the Lomax entropy do not match the reference and probability matching priors of the Lomax parameters, regardless of which parameter of interest is considered. The propriety and the existence of the expectation of the posterior under each prior are validated, respectively. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian estimates in terms of the mean squared error and coverage probability. Finally, the approach is applied to three real data sets for illustrative purposes. [ABSTRACT FROM AUTHOR]

Entanglement purification is an important and useful tool in quantum communications that allows parties to enhance the entanglement of a set of less-entangled particles using local operations and classical communication. Utilizing photon polarization parity checks implemented through the coupling system between a single-sided cavity and a charged quantum dot, an entanglement purification scheme is proposed in this paper. The fidelity and the success probability of the scheme are calculated under bit-flip error channel and depolarizing channel, respectively. Furthermore, the impact of imperfect quantum-dot-cavity coupling system is investigated, and the feasibility is discussed. In the strong coupling and weak cavity side leakage regime, our scheme can approach the maximal fidelities and success probabilities in theory. So the scheme has potential applications in long-distance quantum communication with the development of relevant technologies. [ABSTRACT FROM AUTHOR]