Positive Probability Research Articles

New method for stability of probabilistic Boolean networks with inequality constraints

This paper studies the stability of probabilistic Boolean networks (PBNs) with state inequality constraints by establishing a new algebraic representation. On one hand, combining with the semi-tensor product (STP) of matrices and the law of total expectation, the algebraic representation of PBNs is established. On the other hand, based on the STP of matrices, an algorithm is proposed to determine the solution set of the state inequality constraints. Then, based on the algebraic representation and the inequality constrained solution set, a new form of transition probability matrix is constructed for PBNs. Finally, by the proposed transition probability matrix, new criteria are proposed for the finite-time stability with positive probability of PBNs. Several simulation examples are used to illustrate the effectiveness of the obtained results.

A spatially explicit assessment of factors shaping attitudes toward African elephant conservation.

Conservation plans that explicitly account for the social landscape where people and wildlife co-occur can yield more effective and equitable conservation practices and outcomes. Yet, social data remain underutilized, often because social data are treated as aspatial or are analyzed with approaches that do not quantify uncertainty or address bias in self-reported data. We conducted a survey (questionnaires) of 177 households in a multiuse landscape in the Kenya-Tanzania borderlands. In a mixed-methods approach, we used Bayesian hierarchical models to quantify and map local attitudes toward African elephant (Loxodonta africana) conservation while accounting for response bias and then combined inference from attitude models with thematic analysis of open-ended responses and cointerpretation of results with local communities to gain deeper understanding of what explains attitudes of people living with wildlife. Model estimates showed that believing elephants have sociocultural value increased the probability of respondents holding positive attitudes toward elephant conservation in general (mean increase=0.31 [95% credible interval, CrI, 0.02-0.67]), but experiencing negative impacts from any wildlife species lowered the probability of respondents holding a positive attitude toward local elephant conservation (mean decrease=-0.20 [95% CrI -0.42 to 0.03]). Qualitative data revealed that safety and well-being concerns related to the perceived threats that elephants pose to human lives and livelihoods, and limited incentives to support conservation on community and private lands lowered positive local attitude probabilities and contributed to negative perceptions of human-elephant coexistence. Our spatially explicit modeling approach revealed fine-scale variation in drivers of conservation attitudes that can inform targeted conservation planning. Our results suggest that approaches focused on sustaining existing sociocultural values and relationships with wildlife, investing in well-being, and implementing species-agnostic approaches to wildlife impact mitigation could improve conservation outcomes in shared landscapes.

Development and assessment of algorithms for predicting brain amyloid positivity in a population without dementia

BackgroundThe accumulation of amyloid-β (Aβ) peptide in the brain is a hallmark of Alzheimer’s disease (AD), occurring years before symptom onset. Current methods for quantifying in vivo amyloid load involve invasive or costly procedures, limiting accessibility. Early detection of amyloid positivity in non-demented individuals is crucial for aiding early AD diagnosis and for initiating anti-amyloid immunotherapies at early stages. This study aimed to develop and validate predictive models to identify brain amyloid positivity in non-demented patients, using routinely collected clinical data.MethodsPredictive models for amyloid positivity were developed using data from 853 non-demented participants in the MEMENTO cohort. Amyloid levels were measured potentially repeatedly during study course through Positron Emision Tomography or CerebroSpinal Fluid analysis.The probability of amyloid positivity was modelled using mixed-effects logistic regression. Predictors included demographic information, cognitive assessments, visual brain MRI evaluations of hippocampal atrophy and lobar microbleeds, AD-related blood biomarkers (Aβ42/40 and P-tau181), and ApoE4 status. Models were subjected to internal cross-validation and external validation using data from the Amsterdam Dementia Cohort. Performance also was evaluated in a subsample that met the main criteria of the Appropriate Use Recommendations (AUR) for lecanemab.ResultsThe most effective model incorporated demographic data, cognitive assessments, ApoE status, and AD-related blood biomarkers, achieving AUCs of 0.82 [95%CI 0.81-0.82] in MEMENTO sample and 0.90 [95%CI 0.86-0.94] in the external validation sample. This model significantly outperformed a reference model based solely on demographic and cognitive data, with an AUC difference in MEMENTO of 0.10 [95%CI 0.10-0.11]. A similar model without ApoE genotype achieved comparable discriminatory performance. MRI markers did not improve model performance. Performances in AUR of lecanemab subsample were comparable.ConclusionA predictive model integrating demographic, cognitive, and blood biomarker data offers a promising method to help identify amyloid status in non-demented patients. ApoE genotype and brain MRI data were not necessary for strong discriminatory ability, suggesting that ApoE genotyping may be deferred when assessing the risk-benefit ratio of immunotherapies in amyloid-positive patients who desire treatment. The integration of this model into clinical practice could reduce the need for lumbar puncture or PET examinations to confirm amyloid status.

An Ensemble Method for the Fraud Detection in Transactions

In today's world, bank fraud has become one of the significant threats to the financial stability and security of clients of financial institutions. The development of technologies, in particular in the field of machine learning, opens up wide opportunities for building effective systems for detecting and preventing fraud in the banking sector [1, 2]. Detecting fraudulent transactions is an important task that requires thoughtful and technological solutions. One of these methods is the use of machine learning approaches and methods. This paper proposes the use of an ensemble method that combines several machine learning models at once. This approach will reduce the probability of false positives and increase classification accuracy. In addition, for the optimal operation of the model, preprocessing of the data will be carried out, in particular, their normalization, balancing of classes, as well as the selection of features. During the research, it is important not only to achieve high accuracy, but also to reduce as much as possible the number of fraudulent transactions that will be mistakenly classified as normal [3]. This is related to the business requirements of the banking sector, as each such transaction causes losses to the system's reputation, as well as direct financial losses. Within the framework of the study, it is substantiated that the use of this approach gives better classification results than single models due to the compensation of the shortcomings of each of them. The choice of this approach is also due to high practicality, compatibility with financial systems, as well as ease of integration. This paper analyzes the proposed model, its advantages and disadvantages in comparison with analogues. The ensemble method helps to combine the advantages of simple models and reduce the impact of their shortcomings on the final result. In general, the choice of software should depend on the technical requirements of the project and to obtain better results, different models and approaches should be analyzed.

The Predictive Role of Mammography, Dynamic Contrast-Enhanced Breast Magnetic Resonance Imaging and Diffusion-Weighted Imaging in Hormone Receptor Status of Pure Ductal Carcinoma In Situ Lesions.

The aim of this retrospective study was to analyze the predictive capabilities of preoperative mammography, dynamic contrast-enhanced-magnetic resonance imaging (DCE-MRI), and diffusion-weighted imaging (DWI) in determining hormone receptor (HRc) status for pure ductal carcinoma in situ (DCIS) lesions. The study included a total of 79 patients who underwent preoperative mammography (MG) and MRI between December 2018 and December 2023 and were subsequently diagnosed with pure DCIS after surgery. The correlation between MG, DCE-MRI, and DWI features and estrogen receptor (ER) and progesterone receptor (PR) status was examined. Among the lesions, 44 were double HRc-positive (ER and PR-positive), 13 were single HRc-positive (ER-positive and PR-negative or ER-negative and PR-positive) and 22 were double HRc-negative (ER and PR-negative). The presence of symptom (p = 0.029), the presence of comedo necrosis (p = 0.005) and high histological grade (p<0.001) were found to be associated with ER and PR negativity. Amorphous microcalcifications were more commonly observed in the double HRc-negative group, while linear calcifications were more prevalent in both double and single HRc-positive groups (p = 0.020). Non-mass enhancement (NME) with a linear distribution was significantly more common in double HRc-negative lesions (38%), and NME with a segmental distribution in both double (43%) and single (50%) receptor-positive lesions (p = 0.042). Evaluation of DWI findings revealed that a higher lesion-to-normal breast parenchyma apparent diffusion coefficient (ADC) ratio statistically increased the probability of HRc positivity (p = 0.033). Certain clinicopathological, mammography, and MRI features, along with the lesion-to-normal breast parenchyma ADC ratio, can serve as predictors for HRc status in DCIS lesions.

Termination and Universal Termination Problems for Nondeterministic Quantum Programs

Verifying quantum programs has attracted a lot of interest in recent years. In this paper, we consider the following two categories of termination problems of quantum programs with nondeterminism, namely: (1) (termination) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the nontermination? (2) (universal termination) Are all inputs terminating with probability one under their respective schedulers? If yes, a further question asks whether there is a scheduler that forces all inputs to be terminating with probability one together with how to synthesize it; otherwise, how can an input be provided to refute the universal termination? For the effective verification of the first category, we over-approximate the reachable set of quantum program states by the reachable subspace, whose algebraic structure is a linear space. On the other hand, we study the set of divergent states from which the program terminates with probability zero under some scheduler. The divergent set also has an explicit algebraic structure. Exploiting these explicit algebraic structures, we address the decision problem by a necessary and sufficient condition, i. e. the disjointness of the reachable subspace and the divergent set. Furthermore, the scheduler synthesis is completed in exponential time, whose bottleneck lies in computing the divergent set, reported for the first time. For the second category, we reduce the decision problem to the existence of invariant subspace, from which the program terminates with probability zero under all schedulers. The invariant subspace is characterized by linear equations and thus can be efficiently computed. The states on that invariant subspace are evidence of the nontermination. Furthermore, the scheduler synthesis is completed by seeking a pattern of finite schedulers that forces all inputs to be terminating with positive probability. The repetition of that pattern yields the desired universal scheduler that forces all inputs to be terminating with probability one. All the problems in the second category are shown, also for the first time, to be solved in polynomial time. Finally, we demonstrate the aforementioned methods via a running example — the quantum Bernoulli factory protocol.

Non-parametric Bayesian approach to multiple treatment comparisons in network meta-analysis with application to comparisons of anti-depressants

Abstract Network meta-analysis is a powerful tool to synthesize evidence from independent studies and compare multiple treatments simultaneously. A critical task of performing a network meta-analysis is to offer ranks of all available treatment options for a specific disease outcome. Frequently, the estimated treatment rankings are accompanied by a large amount of uncertainty, suffer from multiplicity issues, and rarely permit possible ties of treatments with similar performance. These issues make interpreting rankings problematic as they are often treated as absolute metrics. To address these shortcomings, we formulate a ranking strategy that adapts to scenarios with high-order uncertainty by producing more conservative results. This improves the interpretability while simultaneously accounting for multiple comparisons. To admit ties between treatment effects in cases where differences between treatment effects are negligible, we also develop a Bayesian non-parametric approach for network meta-analysis. The approach capitalizes on the induced clustering mechanism of Bayesian non-parametric methods, producing a positive probability that two treatment effects are equal. We demonstrate the utility of the procedure through numerical experiments and a network meta-analysis designed to study antidepressant treatments.

Evidence disclosure with heterogeneous priors

We investigate an interesting type of equilibrium of a game where a collective decision is reached by aggregating the preferred alternatives of a group of Receivers. A Sender that cares about the collective decision must make efforts (not below a normative-minimum) to gather evidence relevant for the Receivers to gauge their preferred alternatives. Research efforts may be unsuccessful, which allows for strategic concealment. Each Receiver cares only about her preferred alternative so that the goal of the Sender is achieved by affecting the beliefs of a single representative Receiver (e.g., pivotal voter). Disagreement between the players about the best alternative is based solely on heterogeneous priors. The type of equilibrium that we study arises when the Sender and the representative Receiver agree based on their priors but disagree based on some evidence. In such situations, while unfavorable evidence is concealed always, both disclosure and concealment of favorable evidence may happen with positive probability. Interestingly, for sufficiently low normative-minimum efforts, there arises a continuum of equilibria in which the Sender discloses favorable evidence with higher probability.

Diagnostic Value of Neutrophil-Lymphocyte Ratio in Predicting Post-Operative Infection after Orthopedic Surgery: A Systematic Review and Meta-Analysis.

Objective: This study aims to evaluate the predictive value of neutrophil-lymphocyte ratio (NLR) in determining infection after orthopedic surgery. Methods: A comprehensive search was conducted in PubMed, EBASE, CNKI, and Wanfang databases to identify relevant studies. The quality of the included studies was assessed using QUADAS-2. Data extraction was performed to calculate sensitivity, specificity, and other indicators. Bivariate mixed-effects meta-analysis was conducted using Stata software. The sources of heterogeneity were evaluated, and a summary receiver operating characteristic curve was generated. Results: A total of 16 literatures comprising 18 studies involving 3737 patients were included in this analysis. NLR demonstrated moderate sensitivity (0.77) and specificity (0.69) in diagnosing orthopedic post-operative infection, with an area under the curve of 0.80 and diagnostic odds ratio of 7.76. Significant heterogeneity was observed among the studies, primarily due to variations in surgical type, infection type, blood test timing, and NLR cutoff value. Fagan nomogram indicated that NLR could increase the positive posterior probability to 72% and decrease the negative posterior probability to 25%. The pooled effect of the likelihood ratio dot plot for diagnosis fell in the lower right quadrant. Deek funnel plot suggested no publication bias in this study. Conclusion: NLR holds certain value in diagnosing infection after orthopedic surgery and can provide additional information to assess the risk of infection. However, its predictive performance is influenced by various factors, and it cannot be used as a sole criterion for confirming the diagnosis. Prospective studies should be conducted in the future to optimize the diagnostic threshold and explore its combination with other indicators.

Application of artificial intelligence in lung cancer screening: A real-world study in a Chinese physical examination population.

With the rapid increase of chest computed tomography (CT) images, the workload faced by radiologists has increased dramatically. It is undeniable that the use of artificial intelligence (AI) image-assisted diagnosis system in clinical treatment is a major trend in medical development. Therefore, in order to explore the value and diagnostic accuracy of the current AI system in clinical application, we aim to compare the detection and differentiation of benign and malignant pulmonary nodules between AI system and physicians, so as to provide a theoretical basis for clinical application. Our study encompassed a cohort of 23 336 patients who underwent chest low-dose spiral CT screening for lung cancer at the Health Management Center of West China Hospital. We conducted a comparative analysis between AI-assisted reading and manual interpretation, focusing on the detection and differentiation of benign and malignant pulmonary nodules. The AI-assisted reading exhibited a significantly higher screening positive rate and probability of diagnosing malignant pulmonary nodules compared with manual interpretation (p < 0.001). Moreover, AI scanning demonstrated a markedly superior detection rate of malignant pulmonary nodules compared with manual scanning (97.2% vs. 86.4%, p < 0.001). Additionally, the lung cancer detection rate was substantially higher in the AI reading group compared with the manual reading group (98.9% vs. 90.3%, p < 0.001). Our findings underscore the superior screening positive rate and lung cancer detection rate achieved through AI-assisted reading compared with manual interpretation. Thus, AI exhibits considerable potential as an adjunctive tool in lung cancer screening within clinical practice settings.

Exact interval estimation for three parameters subject to false positive misclassification

SummaryBinary data subject to one type of misclassification exist in various fields. It is collected in a double‐sampling scheme that includes a gold standard test and a fallible test. The main parameter of interest for this type of data is the positive probability of the gold standard test. Existing intervals are unreliable because the given nominal level is not achieved. In this paper, we construct an exact interval by inverting the E+M score tests and improve it by the general ‐function method. We find that the total length of the improved interval is shorter than the exact intervals that are also the improved intervals when we apply the ‐function to several existing approximate intervals, including the score and Bayesian intervals. Therefore, it is recommended for practice. We are also interested in two other parameters: —the difference between the two positive rates for the fallible and gold standard tests—and —the false positive rate for the fallible test. To the best of our knowledge, the research on these two parameters is limited. For , we find that any interval for can be converted to an interval for . So, the interval converted from the aforementioned recommended interval for is recommended for inferring . For , the improved interval by the ‐function method over the E+M score interval is derived. We use an example to illustrate how the intervals are computed and provide a real data analysis.

A Random Copositive Matrix Is Completely Positive with Positive Probability

A Random Copositive Matrix Is Completely Positive with Positive Probability

Some further results on random OBIC rules

We study the structure of probabilistic voting rules that are ordinal Bayesian incentive compatible (OBIC) with respect to independently distributed prior beliefs that can be considered generic (Majumdar and Sen (2004)). We first identify a class of priors, such that for each prior in that class there exists a probabilistic voting rule that puts a positive probability weight on “compromise” candidates. The class of priors include generic priors. Next, we consider a class of randomized voting rules that have a “finite range”. For this class of rules, we identify an appropriate generic condition on priors such that, any rule in this class is OBIC with respect to a prior satisfying the generic condition if and only if the rule is a random dictatorship.

Combining reproductive endocrinology and ROC analysis to identify changes with sex, age, and pregnancy status in botos Inia geoffrensis

Reproductive hormone profiles were described against physical characteristics during growth and development in male and female botos (Amazon River dolphins Inia geoffrensis) and during pregnancy. We determined hormone concentrations in 226 wild botos located in Mamirauá Reserve, Amazonas State, Brazil, as a part of the long-term population monitoring program known as Projeto Boto. Additionally, we applied receiver operator characteristic (ROC) analysis to compare diagnostic probabilities of using ultrasound, hormones, or combinations of these to detect pregnancy. Based on single-point analysis of serum testosterone (T), males with &lt;2.5 ng ml-1 T and a mean 163 cm total body length were classified as immature, 2.5 to &lt;4.9 ng ml-1 T and 183 cm as pubescent, and &gt;5 ng ml-1 T and 227 cm as adult botos. For females, only progesterone (P4), T, relaxin (Rlx), and the combination of P4 × T2 were significantly different between non-pregnant and pregnant females, but androstenedione (A4) and the P4:T ratio were not. ROC analysis indicated that ultrasound and P4 × T2 were considered excellent as pregnancy diagnostic tests, and P4, T, and Rlx were classified as good predictors. Results indicated that negative and positive predictive probabilities from each diagnostic test could be used to accurately predict a pregnancy and calf loss rate of 13% for this population. Application of these methods for evaluating wild population reproductive success from a single serum sample can now be used for health evaluations of wild populations of boto and provide timely information for the development or evaluation of any conservation initiatives.

Research on SDP-BF Method with Low False Positive Face to Passive Detection System

With the rapid development of 5G, UAV, and military communications, the data volume obtained by the non-cooperative perception system has increased exponentially, and the distributed system has become the development trend of the non-cooperative perception system. The data distribution service (DDS) produces a significant effect on the performance of distributed non-cooperative perception systems. However, the traditional DDS discovery protocol has problems such as false positive misjudgment and high flow overhead, so it can hardly adapt to a large multi-node distributed system. Therefore, the design of a DDS discovery protocol for large distributed system is technically challenging. In this paper, we proposed SDP-DCBF-SFF, a discovery protocol based on the Dynamic Counter Bloom Filter (DCBF) and Second Feedback Filter (SFF). The proposed discovery protocol coarsely filters the interested endpoints through DCBF and then accurately screens the uninterested endpoints through SFF to eliminate the connection requests of false positive endpoints and avoid extra flow overhead. The experimental results indicate that the proposed discovery protocol could effectively reduce the network overhead, and eliminate the false positive probability of endpoints in small, medium, large, and super large systems. In addition, it adopts the self-adaptive extension mechanism of BF to reduce the reconfiguration delay of BF and achieve the smallest system transmission delay. Therefore, the proposed discovery protocol has optimal comprehensive performance and system adaptability.

A cost-sensitive decision model for efficient pooled testing in mass surveillance of infectious diseases like COVID-19

The COVID-19 pandemic has imposed significant challenges on global health, emphasizing the persistent threat of large-scale infectious diseases in the future. This study addresses the need to enhance pooled testing efficiency for large populations. The common approach in pooled testing involves consolidating multiple test samples into a single tube to efficiently detect positivity at a lower cost. However, what is the optimal number of samples to be grouped together in order to minimize costs? i.e. allocating ten individuals per group may not be the most cost-effective strategy. In response, this paper introduces the hierarchical quotient space, an extension of fuzzy equivalence relations, as a method to optimize group allocations. In this study, we propose a cost-sensitive multi-granularity intelligent decision model to further minimize testing costs. This model considers both testing and collection costs, aiming to achieve the lowest total cost through optimal grouping at a single layer. Building upon this foundation, two multi-granularity models are proposed, exploring hierarchical group optimization. The experimental simulations were conducted using MATLAB R2022a on a desktop with Intel i5-10500 CPU and 8G RAM, considering scenarios with a fixed number of individuals and fixed positive probability. The main findings from our simulations demonstrate that the proposed models significantly enhance the efficiency and reduce the overall costs associated with pooled testing. For example, testing costs were reduced by nearly half when the optimal grouping strategy was applied, compared to the traditional method of grouping ten individuals. Additionally, the multi-granularity approach further optimized the hierarchical groupings, leading to substantial cost savings and improved testing efficiency.

Characteristics and Source Analysis of VOCs Pollution During Emergency Response in Tianjin

To elucidate the characteristics of VOCs chemical components during heavy pollution episodes, hourly online VOCs data derived from 11 heavy pollution events in Tianjin from 2019 to 2020 were employed. The positive matrix factorization （PMF） and conditional bivariate probability function （CBPF） were employed to analyze the sources of VOCs during heavy pollution episodes. The results indicated that the average VOCs volume fraction during these episodes was recorded at 35.7×10-9. Furthermore, it was observed that during the winter emergency response period, there was a discernible increase in the volume fraction of VOCs when compared to that during the autumn season. Specifically, there was a notable upswing of 48% in the olefins category, whereas alkanes registered a 4% increase. Additionally, the VOCs component structure changed significantly during the heavy pollution episodes. During the orange warning period, the proportion of alkanes increased by 36%, and the proportion of acetylene decreased by 32%. During the yellow warning period, the proportion of alkanes increased by 14%, and the proportion of acetylene decreased by 5%. During the emergency response period, motor vehicle emission sources, natural gas evaporative sources, and solvent use sources were the main contributors of VOCs in environmental receptors, contributing 17.5%, 15.4%, and 15.2%, respectively. Compared with that during the period antecedent to the emergency response, the contribution of vehicle emission sources and diesel volatile sources to VOCs in environmental receptors decreased by 2.0% to 5.5% and 2.1% to 6.6%, respectively, and the contribution of solvent use sources decreased by 0.2% to 2.4% during the yellow warning period. During the orange warning period, the contribution of motor vehicle emission sources was reduced by 0.1% to 8.3%, and the contribution of solvent use sources was reduced by 0.5% to 6.2%.

Interpretation of results of PCR and B-D-glucan for the diagnosis of Pneumocystis Jirovecii Pneumonia in immunocompromised adults with acute respiratory failure

BackgroundThe accuracy of a diagnostic test depends on its intrinsic characteristics and the disease incidence. This study aims to depict post-test probability of Pneumocystis pneumonia (PJP), according to results of PCR and Beta-D-Glucan (BDG) tests in patients with acute respiratory failure (ARF).Materials and methodsDiagnostic performance of PCR and BDG was extracted from literature. Incidence of Pneumocystis pneumonia was assessed in a dataset of 2243 non-HIV immunocompromised patients with ARF. Incidence of Pneumocystis pneumonia was simulated assuming a normal distribution in 5000 random incidence samples. Post-test probability was assessed using Bayes theorem.ResultsIncidence of PJP in non-HIV ARF patients was 4.1% (95%CI 3.3-5). Supervised classification identified 4 subgroups of interest with incidence ranging from 2.0% (No ground glass opacities; 95%CI 1.4–2.8) to 20.2% (hematopoietic cell transplantation, ground glass opacities and no PJP prophylaxis; 95%CI 14.1–27.7). In the overall population, positive post-test probability was 32.9% (95%CI 31.1–34.8) and 22.8% (95%CI 21.5–24.3) for PCR and BDG, respectively. Negative post-test probability of being infected was 0.10% (95%CI 0.09–0.11) and 0.23% (95%CI 0.21–0.25) for PCR and BDG, respectively. In the highest risk subgroup, positive predictive value was 74.5% (95%CI 72.0-76.7) and 63.8% (95%CI 60.8–65.8) for PCR and BDG, respectively.ConclusionAlthough both tests yield a high intrinsic performance, the low incidence of PJP in this cohort resulted in a low positive post-test probability. We propose a method to illustrate pre and post-test probability relationship that may improve clinician perception of diagnostic test performance according to disease incidence in predefined clinical settings.

Relation coarsest partition method to observability of probabilistic Boolean networks

Using the relational coarsest partition (RCP) method, this article aims to study the observability problem of probabilistic Boolean networks (PBNs). The key step to solving this problem is to find the parallel cycle and the coarsest refinement partition of the given initial partition. Firstly, several definitions of observability for PBNs are proposed, and the connections between finite-time observability with positive probability (FTOPP), asymptotical observability (AO), and finite-time observability with probability one (FTOPO) are revealed. Secondly, by defining the appropriate transition relation, the RCP method is introduced into PBNs. In addition, based on the output signal mapping set, the initial partition is constructed. Thirdly, the concept of a parallel cycle for PBNs is proposed, and two algorithms are presented for computing the cycle and parallel cycle of PBNs. Moreover, with the help of the RCP method, a series of criteria are derived to solve the observability problem of PBNs, which works more efficiently. Fourth, when PBN is unobservable, an algorithm is proposed to design the state-flipping set with the smallest number of states, which can make the unobservable PBN observable. To show the validity and effectiveness of the obtained results, examples are finally given.

Dependent censoring with simultaneous death times based on the Generalized Marshall–Olkin model

In this paper, we consider the problem of dependent censoring models with a positive probability that the times of failure are equal. In this context, we propose to consider the Marshall–Olkin type model and studied some properties of the associated survival copula in its application to censored data. We also introduce estimators for the marginal distributions and the joint survival probabilities under different schemes and show their asymptotic normality under appropriate conditions. Finally, we evaluate the finite-sample performance of our approach relying on a small simulation study with synthetic data real data applications.