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This article aims to introduce the inverse new XLindley distribution, a further extension of the new XLindley distribution. The article explores various properties of the proposed model, such as the quantile function, stochastic orders, entropies, fuzzy reliability, moments, and stress–strength estimation. The paper also compares different methods of estimating the parameters of the proposed model and evaluates their performance using a simulation study. Moreover, the paper demonstrates the usefulness of the proposed model by applying it to two real datasets. The article shows that the proposed model fits the data better than seven existing models based on model selection criteria, goodness-of-fit test statistics, and graphical visualizations. The paper concludes that the new model can be a valuable tool for modeling and analyzing hazard functions or survival data in various fields and contributing to probability theory and statistical inferences. [ABSTRACT FROM AUTHOR]

Simple Summary: This paper provides a review of statistical methods for tumor-agnostic clinical trials. In particular, the review focuses on basket trials and provides methodological insights into various Bayesian approaches. The key concept of borrowing information through Bayesian hierarchical models is emphasized, and some novel trial designs are introduced. The review is expected to provide oncology and biostatistics researchers with more exposure to powerful Bayesian methods for the design and analysis of tumor-agnostic clinical trials. Basket trials allow simultaneous evaluation of a single therapy across multiple cancer types or subtypes of the same cancer. Since the same treatment is tested across all baskets, it may be desirable to borrow information across them to improve the statistical precision and power in estimating and detecting the treatment effects in different baskets. We review recent developments in Bayesian methods for the design and analysis of basket trials, focusing on the mechanism of information borrowing. We explain the common components of these methods, such as a prior model for the treatment effects that embodies an assumption of exchangeability. We also discuss the distinct features of these methods that lead to different degrees of borrowing. Through simulation studies, we demonstrate the impact of information borrowing on the operating characteristics of these methods and discuss its broader implications for drug development. Examples of basket trials are presented in both phase I and phase II settings. [ABSTRACT FROM AUTHOR]

Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a class of weighted Support Vector Machines (wSVMs) has been developed to estimate class probabilities through ensemble learning for K-class problems (Wu et al., 2010; Wang et al., 2019), where K is the number of classes. The estimators are robust and achieve high accuracy for probability estimation, but their learning is implemented through pairwise coupling, which demands polynomial time in K. In this paper, we propose two new learning schemes, the baseline learning and the One-vs-All (OVA) learning, to further improve wSVMs in terms of computational efficiency and estimation accuracy. In particular, the baseline learning has optimal computational complexity in the sense that it is linear in K. Though not the most efficient in computation, the OVA is found to have the best estimation accuracy among all the procedures under comparison. The resulting estimators are distribution-free and shown to be consistent. We further conduct extensive numerical experiments to demonstrate their finite sample performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic analysis of sojourn times of random fields with continuous sample paths. Under a very general framework we show that there is an interesting relationship between tail asymptotics of sojourn times and that of supremum. Moreover, we establish the uniform double-sum method to derive the tail asymptotics of sojourn times. In the literature, based on the pioneering research of S. Berman the sojourn times have been utilised to derive the tail asymptotics of supremum of Gaussian processes. In this paper we show that the opposite direction is even more fruitful, namely knowing the asymptotics of supremum of random processes and fields (in particular Gaussian) it is possible to establish the asymptotics of their sojourn times. We illustrate our findings considering i) two dimensional Gaussian random fields, ii) chi-process generated by stationary Gaussian processes and iii) stationary Gaussian queueing processes. [ABSTRACT FROM AUTHOR]

Owing to probabilistic uncertainties associated with seasonal forecasts, especially over areas such as southern Africa where forecast skill is limited, non-climatologists and users of such forecasts frequently prefer them to be presented or distributed in terms of the likelihood (expressed as a probability) of certain categories occurring or thresholds being exceeded. Probabilistic forecast verification is needed to verify such forecasts. Whilst the resulting verification statistics can provide clear insights into forecast attributes, they are often difficult to understand, which might hinder forecast uptake and use. This problem can be addressed by issuing forecasts with some understandable evidence of skill, with the purpose of reflecting how similar forecasts may have performed in the past. In this paper, we present a range of different probabilistic forecast verification scores, and determine if these statistics can be readily compared to more commonly known and understood ‘ordinary’ correlations between forecasts and their associated observations – assuming that ordinary correlations are more intuitively understood and informative to seasonal forecast users. Of the range of scores considered, the relative operating characteristics (ROC) was found to be the most intrinsically similar to correlation. [ABSTRACT FROM AUTHOR]

Recurrent events—outcomes that an individual can experience repeatedly over the course of follow-up—are common in epidemiologic and health services research. Studies involving recurrent events often focus on time to first occurrence or on event rates, which assume constant hazards over time. In this paper, we contextualize recurrent event parameters of interest using counterfactual theory in a causal inference framework and describe an approach for estimating a target parameter referred to as the mean cumulative count. This approach leverages inverse probability weights to control measured confounding with an existing (and underutilized) nonparametric estimator of recurrent event burden first proposed by Dong et al. in 2015. We use simulations to demonstrate the unbiased estimation of the mean cumulative count using the weighted Dong-Yasui estimator in a variety of scenarios. The weighted Dong-Yasui estimator for the mean cumulative count allows researchers to use observational data to flexibly estimate and contrast the expected number of cumulative events experienced per individual by a given time point under different exposure regimens. We provide code to ease application of this method. [ABSTRACT FROM AUTHOR]

The use of technology in teaching and learning the topic of probability and statistics in the educational system in our country, Albania, has the potential to be encouraged in different level of classes in the educational system. Lee and Hollebrands (2011) have done better characterization of teaching probability and statistics with the help of technology, through the integration of Statistical Knowledge, Technological Statistical Knowledge, and Technological Pedagogical Statistical Knowledge. Also, we have integrated this framework with Pedagogical Knowledge as a very important factor. In this paper is given as a case study, the process of mastering the concepts of probability and statistics, with students of a lower secondary school in our country to understand the role of technology in the process of teaching and learning, realized concretely during the lessons, specifically throughout a project-based learning by demonstrating the results of the project by the students themselves. Our students recognize and analyze the data, then collect and represent it, to provide graphical presentation Thus, we focus on the potential advantages of using technology in teaching and learning the topics of probability and statistics in school mathematics during different levels of educational process in our country and beyond. [ABSTRACT FROM AUTHOR]

Given a probability distribution p := {pk}k=1∞ on the positive integers, there are two natural ways to construct a random permutation in Sn or a random permutation of N from IID samples from p. One is called the p-biased construction and the other the p-shifted construction. In the first part of the paper we consider the case that the distribution p is the geometric distribution with parameter 1 - q ∈ (0, 1). In this case, the p-shifted random permutation has the Mallows distribution with parameter q. Let Pnb;Geo(1-q) and Pns;Geo(1-q) denote the biased and the shifted distributions on Sn. The expected number of inversions of a permutation under Pns;Geo(1-q) is greater than under Pnb;Geo(1-q), and under either of these distributions, a permutation tends to have many fewer inversions than it would have under the uniform distribution. For fixed n, both Pnb;Geo(1-q) and Pns;Geo(1-q) converge weakly as q → 1 to the uniform distribution on Sn. We compare the biased and the shifted distributions by studying the inversion statistic under ... and ... for various rates of convergence of qn to 1. In the second part of the paper we consider p-biased and p-shifted permutations for the case that the distribution p is itself random and distributed as a GEM(θ)-distribution. In particular, in both the GEM(θ)-biased and the GEM(θ)-shifted cases, the expected number of inversions behaves asymptotically as it does under the Geo(1 - q)-shifted distribution with θ = q / 1-q . This allows one to consider the GEM(θ)-shifted case as the random counterpart of the Geo(q)-shifted case. We also consider another p-biased distribution with random p for which the expected number of inversions behaves asymptotically as it does under the Geo(1 - q)-biased case with θ and q as above, and with θ → ∞ and q → 1 [ABSTRACT FROM AUTHOR]

Simple Summary: In the modern era, characterized by parenchymal-sparing procedures, in some cases pneumonectomy remains the only therapeutic approach to achieving oncological radicality. One of the most feared complications is undoubtedly respiratory failure and ARDS. Its cause after pneumonectomy is still unclear, and the study of risk factors is a subject of debate. In this paper, we evaluate the main risk factors for ARDS of a large cohort of patients and we classify them in four classes of growing risk in order to quantify their postoperative risk of ARDS and facilitate their global management. (1) Background: The cause of ARDS after pneumonectomy is still unclear, and the study of risk factors is a subject of debate. (2) Methods: We reviewed a large panel of pre-, peri- and postoperative data of 211 patients who underwent pneumonectomy during the period 2014–2021. Univariable and multivariable logistic regression was used to quantify the association between preoperative parameters and the risk of developing ARDS, in addition to odds ratios and their respective 95% confidence intervals. A backward stepwise selection approach was used to limit the number of variables in the final multivariable model to significant independent predictors of ARDS. A nomogram was constructed based on the results of the final multivariable model, making it possible to estimate the probability of developing ARDS. Statistical significance was defined by a two-tailed p-value < 0.05. (3) Results: Out of 211 patients (13.3%), 28 developed ARDS. In the univariate analysis, increasing age, Charlson Comorbidity Index and ASA scores, DLCO < 75% predicted, preoperative C-reactive protein (CRP), lung perfusion and duration of surgery were associated with ARDS; a significant increase in ARDS was also observed with decreasing VO2max level. Multivariable analysis confirmed the role of ASA score, DLCO < 75% predicted, preoperative C-reactive protein and lung perfusion. Using the nomogram, we classified patients into four classes with rates of ARDS ranking from 2.0% to 34.0%. (4) Conclusions: Classification in four classes of growing risk allows a correct preoperative stratification of these patients in order to quantify the postoperative risk of ARDS and facilitate their global management. [ABSTRACT FROM AUTHOR]

Simple Summary: Prostate cancer (PCa) is the most common cancer and the second leading cause of cancer-related mortality among males in the US. Definitive radiation therapy (RT) plays an important role in curative-intent treatment for localized PCa and can be delivered with several different techniques, depending on the availability of resources and patient-specific criteria. With an analysis of the extensive National Cancer Database, this paper investigates trends in utilization, survival probability, and factors associated with overall survival of six common RT modalities utilized for the treatment of PCa patients—stratified by the three risk groups. Background: In this study, the utilization rates and survival outcomes of different radiotherapy techniques are compared in prostate cancer (PCa) patients stratified by risk group. Methods: We analyzed an extensive data set of N0, M0, non-surgical PCa patients diagnosed between 2004 and 2015 from the National Cancer Database (NCDB). Patients were grouped into six categories based on RT modality: an intensity-modulated radiation therapy (IMRT) group with brachytherapy (BT) boost, IMRT with/without IMRT boost, proton therapy, stereotactic body radiation therapy (SBRT), low-dose-rate brachytherapy (BT LDR), and high-dose-rate brachytherapy (BT HDR). Patients were also stratified by the National Comprehensive Cancer Network (NCCN) guidelines: low-risk (clinical stage T1–T2a, Gleason Score (GS) ≤ 6, and Prostate-Specific Antigen (PSA) < 10), intermediate-risk (clinical stage T2b or T2c, GS of 7, or PSA of 10–20), and high-risk (clinical stage T3–T4, or GS of 8–10, or PSA > 20). Overall survival (OS) probability was determined using a Kaplan–Meier estimator. Univariate and multivariate analyses were performed by risk group for the six treatment modalities. Results: The most utilized treatment modality for all PCa patients was IMRT (53.1%). Over the years, a steady increase in SBRT utilization was observed, whereas BT HDR usage declined. IMRT-treated patient groups exhibited relatively lower survival probability in all risk categories. A slightly better survival probability was observed for the proton therapy group. Hormonal therapy was used for a large number of patients in all risk groups. Conclusion: This study revealed that IMRT was the most common treatment modality for PCa patients. Brachytherapy, SBRT, and IMRT+BT exhibited similar survival rates, whereas proton showed slightly better overall survival across the three risk groups. However, analysis of the demographics indicates that these differences are at least in part due to selection bias. [ABSTRACT FROM AUTHOR]

A central issue in assessing the airborne risk of COVID-19 infections in indoor spaces pertains to linking the viral load in infected subjects to the lung deposition probability in exposed individuals through comprehensive aerosol dynamics modelling. In this paper, we achieve this by combining aerosol processes (evaporation, dispersion, settling, lung deposition) with a novel double Poisson model to estimate the probability that at least one carrier particle containing at least one virion will be deposited in the lungs and infect a susceptible individual. Multiple emission scenarios are considered. Unlike the hitherto used single Poisson models, the double Poisson model accounts for fluctuations in the number of carrier particles deposited in the lung in addition to the fluctuations in the virion number per carrier particle. The model demonstrates that the risk of infection for 10-min indoor exposure increases from 1 to 50% as the viral load in the droplets ejected from the infected subject increases from 2 × 108 to 2 × 1010 RNA copies/mL. Being based on well-established aerosol science and statistical principles, the present approach puts airborne risk assessment methodology on a sound formalistic footing, thereby reducing avoidable epistemic uncertainties in estimating relative transmissibilities of different coronavirus variants quantified by different viral loads. [ABSTRACT FROM AUTHOR]

This paper presents two data-driven virtual sensors to estimate the time-series of the probability of high-concentration occurrence of naturally occurring radioactive materials (NORMs; 238U and 222Rn) in groundwater based on the in-situ groundwater quality monitoring data and geological information. The random forest was applied to estimate the NORM concentration based on the actual in-situ groundwater quality data, rock type, and the aquifer depth. Additionally, this study proposes three data sampling techniques (i.e., under-sampling, synthetic minority over-sampling, and a complex sampling) to improve the model applicability and accuracy. The developed models were validated using the actual data acquired from 201 locations in South Korea. The models for 238U and 222Rn showed estimation accuracies of 85% and 80%, respectively; the models with over-sampling showed better performance. All the results verified the usefulness of the developed models as virtual sensors for providing immediate information on the in-situ presence of NORMs in groundwater. [Display omitted] • Naturally occurring radioactive material (NORMs) in groundwater can be problematic. • Virtual sensor for in-situ estimating the probability of high-concentration of NORMs. • Major geochemical factors for NORMs were evaluated using statistical analyses. • Methods for solving data imbalance problem in training virtual sensor were proposed. • Major factors for the estimation were consistent with the statistical analysis result. [ABSTRACT FROM AUTHOR]

In this paper we exemplify the types of Plithogenic Probability and respectively Plithogenic Statistics. Several applications are given. The Plithogenic Probability of an event to occur is composed from the chances that the event occurs with respect to all random variables (parameters) that determine it. Each such a variable is described by a Probability Distribution (Density) Function, which may be a classical, (T,I,F)-neutrosophic, I-neutrosophic, (T,F)-intuitionistic fuzzy, (T,N,F)-picture fuzzy, (T,N,F)-spherical fuzzy, or (other fuzzy extension) distribution function. The Plithogenic Probability is a generalization of the classical MultiVariate Probability. The analysis of the events described by the plithogenic probability is the Plithogenic Statistics. [ABSTRACT FROM AUTHOR]

In these cases getting accurate confidence intervals is of first order importance, and the methods Ignatiadis and Wager develop are likely to be useful. I want to congratulate Nikolaos Ignatiadis and Stefan Wager on a very stimulating paper on a timely and important topic. [Extracted from the article]

Focusing on the global integrity monitoring performance of the BDS-3, the integrity failure model and effect analysis (IFMEA) of the system space segment and the ground control segment were carried out, and the system integrity risk tree model was established according to the IFMEA results. To evaluate the system's integrity risk probability more reasonably, this paper establishes an abnormal event prediction model with a Bayesian method, based on actual operation data, under a situation in which the BDS-3 just opened service. With statistical analysis results of system anomalies since 27 December 2018—which is the date the BDS-3 began providing basic service—according to the anomaly prediction model, the system's integrity risk probability under the 95% confidence limit was calculated to be approximately 0.9e-7/h, meeting the design index requirements of 1e-7/h. The analysis results also show that the main risk factors affecting the integrity of BDS-3 are 'pseudorange measurement anomaly' and 'miss-detection of satellite autonomous integrity monitoring'. The results are important references with practical engineering significance for improving the integrity performance of BDS-3. [ABSTRACT FROM AUTHOR]

As an excellent discriminant classifier based on generating prior knowledge, the minimax probability machine (MPM) has been widely used and deeply researched in many fields. The core idea of minimax probability machine is to directly estimate probability accuracy bound by minimizing the maximum probability of misclassification. However, minimax probability machine does not include a regularization term for the construction of the separating hyperplane, and it needs to solve a large-scale second-order cone programming problem in the solution process, which greatly limits it development and application. In this paper, to improve the performance of minimax probability machine, we propose a novel binary classification method called regularized twin minimax probability machine classification (TMPMC). The TMPMC constructs two non-parallel hyperplanes for final classification by solving two smaller second-order cone programming problems to improve the performance of the MPM. For each hyperplane, our method is theoretically well grounded on the idea of minimizing the worst case (maximum) probability of misclassification of a class of samples while the distance to the other class is as large as possible. Our approach was first derived as linear methods, and subsequently extended as kernel-based strategies for nonlinear classification. Additionally, we extend TMPMC to the regression problem and propose a new regularized twin minimax probability machine regression (TMPMR). Experimental results on several datasets show that our methods are competitive in terms of generalization performance compared to other algorithms. • The regularized twin minimax probability machine classification (TMPMC) is proposed. • The regularized twin minimax probability machine regression (TMPMR) is presented. • Both TMPMC and TMPMR utilizes the geometric information and the statistical information of the data. • Both TMPMC and TMPMR avoid the assumption of distribution of conditional density. • Experimental results on multiple datasets demonstrate the effectiveness of TMPMC and TMPMR. [ABSTRACT FROM AUTHOR]

Background: Previous research pointed to a close relationship between the incidence of tuberculosis (TB) in aging populations and socio-economic conditions, however there has been lack of studies focused on a region of unbalanced socio-economic development. The aim of this paper is to explore the spatio-temporal variation in TB incidence and examine risk determinants of the disease among aging populations in a typical region.Methods: Data on TB-registered cases between 2009 and 2014, in addition to social-economic factors, were collected for each district/county in Beijing, Tianjin and Hebei, a region characterized by an aging population and disparities in social-economic development. A Bayesian space-time hierarchy model (BSTHM) was used to reveal spatio-temporal variation in the incidence of TB among the elderly in this region between 2009 to 2014. GeoDetector was applied to measure the determinant power (q statistic) of risk factors for TB among the elderly.Results: The incidence of TB among the elderly exhibited geographical spatial heterogeneity, with a higher incidence in underdeveloped rural areas compared with that in urban areas. Hotspots of TB incidence risk among the elderly were mostly located in north-eastern and southern areas in the study region, far from metropolitan areas. Areas with low risk were distributed mainly in the Beijing-Tianjin metropolitan areas. Social-economic factors had a non-linear influence on elderly TB incidence, with the dominant factors among rural populations being income (q = 0.20) and medical conditions (q = 0.17). These factors had a non-linear interactive effect on the incidence of TB among the elderly, with medical conditions and the level of economic development having the strongest effect (q = 0.54).Conclusions: The findings explain spatio-temporal variation in TB incidence and risk determinants of elderly TB in the presence of disparities in social-economic development. High-risk zones were located mainly in rural areas, far from metropolitan centres. Medical conditions and the economic development level were significantly associated with elderly TB incidence, and these factors had a non-linear interactive effect on elderly TB incidence. The findings can help to optimize the allocation of health resources and to control TB transmission in the aging population in this region. [ABSTRACT FROM AUTHOR]