Average Probability Research Articles

Estimating the Confidence Intervals for the Coefficients of Variation Delta-Gamma Distributions

A common application of the coefficient of variation (CV), which is the ratio of the population standard deviation to the population mean, is frequently used to assess quality control and economic processes, among others. The fiducial quantity approach, Bayesian confidence intervals (CIs) using the Jeffreys, uniform, or normal-gamma-beta (NGB) priors, and highest posterior density (HPD) intervals using the Jeffreys, uniform, or NGB priors were used to provide estimators for the CI for the ratio of CV of two delta-gamma distributions. An evaluation of their performance in terms of average length and coverage probability was carried out using Monte Carlo simulations. The results of this study indicate that the HPD using the Jeffreys prior and fiducial quantity methods are the best for estimating the CI for the ratio of the CV of two delta-gamma distributions. Rainfall data from Mae Hong Son province in Thailand was used to illustrate their practicability when analyzing real-life processes.

Medigap Guaranteed Issue Associated with Medicare Advantage Disenrollment for Beneficiaries Administered a Part B Drug

Abstract While many Medicare beneficiaries are enrolling in Medicare Advantage (MA), some beneficiaries may want to return to traditional Medicare and purchase Medigap, especially beneficiaries that have greater medical needs. Beyond minimal federal regulations, states impose additional regulations that impact Medigap affordability. Beneficiaries in some states have greater difficulty obtaining Medigap coverage because the states where they live allow Medigap insurers to experience rate the beneficiary, which can make Medigap insurance prohibitively expensive. We examined beneficiaries who received physician-administered drugs, which can be expensive and subject to high cost-sharing, to see if disenrollment from MA for these beneficiaries was greater in states with Medigap consumer protection policies levels. In 2020, we find a 1.0% average baseline average probability of MA disenrollment. For beneficiaries that received a physician-administered drug in our sample, the probability of MA disenrollment is 3.7 (95% C I: 2.6-4.8; p<0.001) percentage points higher in Medigap guaranteed issue states compared to states with no protections. We find a greater association between MA disenrollment and Medigap protection policies with higher-cost drugs. These findings suggest that beneficiaries who receive a high-volume and high-spending physician-administered drug are more likely to disenroll from MA back to traditional Medicare when Medigap is more affordable.

Bayesian inference: more than Bayes’s theorem

Bayesian inference gets its name from Bayes’s theorem, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference uses all of probability theory, not just Bayes’s theorem. Many hypotheses of scientific interest are composite hypotheses, with the strength of evidence for the hypothesis dependent on knowledge about auxiliary factors, such as the values of nuisance parameters (e.g., uncertain background rates or calibration factors). Many important capabilities of Bayesian methods arise from use of the law of total probability, which instructs analysts to compute probabilities for composite hypotheses by marginalization over auxiliary factors. This tutorial targets relative newcomers to Bayesian inference, aiming to complement tutorials that focus on Bayes’s theorem and how priors modulate likelihoods. The emphasis here is on marginalization over parameter spaces—both how it is the foundation for important capabilities, and how it may motivate caution when parameter spaces are large. Topics covered include the difference between likelihood and probability, understanding the impact of priors beyond merely shifting the maximum likelihood estimate, and the role of marginalization in accounting for uncertainty in nuisance parameters, systematic error, and model misspecification.

A semi-probabilistic Bayesian method to identify the number and location of potential sources in 3D unconfined aquifer using limited observed concentration

Source identification of a contaminant has always been challenging for accurately modeling groundwater transport. Source identification problems are classified into several parts, such as identifying the location of contamination, the strength of contamination, the time the contaminant is introduced into the groundwater, and the duration of its activity. Identifying the sources considering all the parts as variables increases the computational complexity. Reducing the number of variables in source identification problems is necessary for a swift solution through optimization approaches. The most challenging variable in source identification modeling is the location of contamination, as it is a discrete variable for almost all the numerical solutions of groundwater models. In this research study, we have created a methodology to narrow the location of contamination from a random distribution throughout the aquifer to a reasonable number of probable locations. Although methods to identify the location of contamination were devised earlier, we have attempted an approach of combining a particle tracking approach with Bayesian method of updating the probabilities as a novel approach, where the observation data is limited. We have considered the aquifer parameters and observation well data and devised a method with a Lagrangian approach to particle movement to identify the potential source locations. We have refined the source locations to a narrower probability distribution using the Bayesian method of updating the probability through new information of refined grid space. We have tested the models to identify the potential sources with different hypothetical problems and identified the sources in advective dominant transport with an average probability of 0.53, diffusion dominant transport with an average probability of 0.62, heterogenous soils with an average probability of 0.99, anisotropic aquifer with an average probability of 0.91, and aquifer with irregular boundary with an average probability of 0.96 to identify the location nearest to the actual contaminant source. The results are satisfactory in identifying the number of potential sources with an accuracy of 88 % (15 identified out of 17 sources with a probability greater than 0.4) and their locations in the aquifer with a probability of 0.223 for exact location identification. The probability of finding a source nearest to the actual location is 0.745 at an average distance of 11.6 m from the actual source location.

DẠY HỌC XÁC SUẤT - THỐNG KÊ GẮN VỚI THỰC TIỄN NGHỀ NGHIỆP CHO SINH VIÊN TRƯỜNG ĐẠI HỌC Y DƯỢC THÁI BÌNH

Based on the teaching process in the direction of developing learners’ capability and research results on the Theory of Realistic Mathematics Education, the paper proposes an educational process for using research results in Medicine and Pharmacy to design content for teaching probability and statistics at Thai Binh University of Medicine and Pharmacy, including 5 steps: (1) Finding “realistic situations” from the field of medicine and pharmacy that are suitable for students; (2) Organizing activities for learners to perform learning tasks; (3) Formalizing; (4) Applying; (5) Assessing and Self-assessing. The pedagogical experiment with the content "The law of Total probability" was conducted with the Preventive Healthcare major students at Thai Binh University of Medicine and Pharmacy in the academic year 2023 - 2024. The results showed that the proposed measure improves interest in learning and links probability and statistics knowledge with professional practice.

Performance Analysis of Free Space Optical System Over Inverse Gaussian Gamma Turbulence Channel

ABSTRACTFree space optical (FSO) communication is a proficient technology with potential applications in the next generation of wireless communication. This article evaluates the performance of the FSO system under inverse Gaussian gamma (IGG) fading. A novel closed‐form equation for the cumulative distribution function (CDF) of the received signal‐to‐noise ratio (SNR) is presented by employing an intensity modulation/direct detection (IM/DD) scheme. The analytical expressions for various performance metrics such as outage probability (OP), amount of fading (AOF), and average bit error probability (ABEP) are derived for various digital modulation schemes based on the system's probability density function (PDF) and CDF. Additionally, this article presents an upper bound on OP and asymptotic analysis for the performance metrics to gain deeper insights. It is revealed that the small‐scale eddy turbulence parameter can affect the diversity order by a factor of β/2. The results demonstrate that atmospheric turbulence considerably reduces the system's performance. Finally, Monte‐Carlo simulation is performed to ascertain the correctness of the derived mathematical expressions.

Segmentation of multi-view video speed extraction method that can cross lane dividing lines

Aiming at the problem that the existing video traffic parameter extraction methods are overly dependent on manual annotation and a single perspective cannot effectively correct the dynamic driving deviation of vehicles on site, a multi-perspective video traffic parameter extraction method that can segment and cross lane dividing lines is proposed. The method consists of an automatic annotation point generation module and a multi-perspective correction module. The automatic annotation point generation module realizes the process of automatically generating annotation points by constructing a reference block based on equal-length lane dividing lines. The multi-perspective correction module proposes multiple mapping methods between vehicles and lane dividing lines and a correction speed measurement method based on the average speed probability density function to correct the two types of deviations generated by vehicles during dynamic driving. Experimental results on public data sets and measured data sets show that the vehicle speed extraction accuracy of the proposed method is better than other speed measurement methods, and it has a certain degree of universality.

The Vasicek distribution autoregressive time-series model for aggregated data of default and delinquency rates

Abstract Is it possible to analyse time series of aggregated data of default and delinquency rates with a simple model that includes both cross-sectional and serial dependence? To address this question, this paper proposes an autoregressive time-series model for Vasicek-distributed random variables. A direct result from the proposed model is that it leads to a novel out-of-time validation test for aggregated default and delinquency rates. The motivation for the model comes from an analysis of a time series of aggregated US credit card delinquencies, for which the Poisson or binomial distribution cannot be used. The proposed model can also be employed to analyse a time series of the average default probability of a portfolio.

Decoding error probability of random parity-check matrix ensemble over the erasure channel

AbstractIn this paper we carry out an in-depth study on the average decoding error probability of the random parity-check matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random parity-check matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random parity-check matrix ensemble and the error exponent of the variance, which implies a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random linear code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.

Population Pharmacokinetic and Pharmacodynamic of Atorvastatin in Chinese Lung Transplant Recipients.

Atorvastatin is a widely prescribed cholesterol-lowering drug that inhibits 3-hydroxy-3-methylglutaryl coenzyme A reductase to reduce lipid levels. This study aimed to establish a population pharmacokinetic and pharmacodynamic model for atorvastatin in Chinese lung transplant recipients (LTRs), particularly those using voriconazole (VOR) and with different genotypes. It evaluated precise dosing regimens and analyzed the correlation between atorvastatin exposure and clinical outcomes. A nonlinear mixed-effects model was used for the population pharmacokinetic/pharmacodynamic (PK/PD) analysis. A one-compartment population PK model was developed, incorporating VOR, SLCO2A1 rs76906503, and SLC22A8 rs2187383 to assess apparent clearance and volume of distribution. LDL-C was modeled as a biomarker to evaluate atorvastatin efficacy. A Monte Carlo simulation was conducted to assess various dosing schemes and the effects of different covariates on achieving the target LDL concentration. The correlation between atorvastatin exposure and clinical outcomes was also evaluated. Results indicated that the average probability of target attainment for optimal dosing regimens across various covariate results exceeded 45.8%. Dosages of 10, 20, and 40 mg were deemed suitable for LTRs. A lower dose was recommended for LTRs taking VOR or with mutant-type genotypes to avoid overexposure and adverse reactions. The population PK/PD model offers valuable guidance for evaluating atorvastatin dosing regimens in clinical settings, particularly for LTRs using VOR and those with different genotypes.

Arithmetic Optimization Algorithm Quantization Optimized With Energy Detection Using Nonparametric Amplitude

ABSTRACTThe spectrum sensing is a major significant task in cognitive radio networks (CRNs) to avoid the unacceptable interference to primary users (PUs). Here, the threshold value determines the effectiveness of spectrum sensing and regarded as a sensing system. The fixed threshold used by the current energy detection‐based spectrum sensing (SS) techniques does not provide sufficient safety for the main users. The threshold is determined by lowering the complete probability of decision error in addition to these guidelines. Therefore, an energy detection using nonparametric amplitude quantization optimized with arithmetic optimization algorithm for enhanced spectrum sensing in CRNs (ED‐NAQ‐AOA‐SS CRN) is proposed in this paper to acquire the ideal threshold for decreasing the total error probability. The proposed method achieves greater probability of detection of 99.67%, 98.38%, 92.34%, and 97.45%, lower settling time of 98.33%, 89.34%, 83.12%, and 88.96%, and lower error rate of 93.15%, 91.25%, 79.90%, and 92.88% compared with existing techniques, like intelligent spectrum sharing and sensing in CRN with adaptive rider optimization algorithm (AROA), a novel technique for spectrum sensing in CRN utilizing fractional gray wolf optimization with the cuckoo search optimization (GWOCS), and adaptive neuro‐fuzzy inference scheme depending on cooperative spectrum sensing optimization in CRNs (ANFIS).

Classical and Bayesian inference of Cpc$\mathcal {C}_{pc}$ for Wilson–Hilferty distribution under progressively first‐failure type‐II censoring samples

AbstractThis study uses two frequentist approaches and the Bayesian method of estimation using progressively first‐failure type‐II censored data to estimate process capability index (PCI), , for the Wilson–Hilferty (WH) distribution. A competitive maximum product of spacing (MPS) method for estimation of is proposed in the frequentist method as an alternative to conventional likelihood (LK)‐based estimation. We have also taken into account the PS function in the Bayesian setup as an alternative to the conventional LK function, and both LK and PS‐based Bayesian estimates are given for . Further, the Bayes estimates are evaluated by applying Tierney–Kadane (TK) approximation method and Markov chain Monte Carlo (MCMC) method with the help of both LK and PS functions and Jeffrey's prior. Additionally, the approximate confidence intervals based on the suggested frequentist techniques as well as the Bayes highest posterior density (HPD) credible intervals are built for the index . In addition, two bootstrap confidence intervals are obtained. In the simulation exercise, the performance of the Bayes and traditional estimates of is assessed in terms of their mean squared errors, and the average width and coverage probabilities of the CIs and HPD intervals are compared. An actual data set from the electronic industries is reanalyzed in order to show the efficacy of the proposed index and estimation methodology.

A Liquid Well Barrier Element for Temporary Plug and Abandonment Operations: A Breakthrough Approach

Plug and abandonment (P&A) operations demand valuable time and resources for operational procedures and materials to establish the well barrier element. This study aims to investigate the application of a water-based fluid as a liquid well barrier element for temporary abandonment, based on estimates of its lifespan and the survival probabilities of downhole temperatures acquired through accelerated life tests. To achieve this, the water-based formulation was tested and exposed to 95, 110, 140, and 150 °C temperatures for time intervals ranging from 1 to 10 days. After the temperature exposure, the fluid properties were verified, and failure was detected by accounting for any deterioration in rheological parameters and/or a substantial increase in filtrate volume. A statistical analysis of the failure data was performed in RStudio 4.1.3 software using the Weibull Model, and the fluid average lifespans and survival probabilities were estimated for the P&A temperatures. The results obtained demonstrate that the degradation of the fluid was only observed for 140 and 150 °C temperatures. According to the results, the fluid is a promising alternative for temporary abandonment until 80 °C, with no need for monitoring once its lifetime expectation exceeds three years at this temperature. For downhole temperatures above 80 °C, the fluid is a possible alternative, however, the operation’s maximum time and monitoring requirements should consider reliability metrics for each temperature.

Universal programmable unambiguous discrimination of two unknown states with two copies

We investigate the universal programmable unambiguous discrimination of two unknown quantum states with two copies. We first present the optimal positive-operator valued measure (POVM) elements that determine the individual success probabilities. In terms of the positivity of an inconclusive operator, we derive the average success probability, which is higher than the average success probability of discriminating two unknown states with one copy given in the reference [Bergou and Hillery, Phys. Rev. Lett. 94, 160501 (2005)].

A dynamic risk assessment model for evacuation in healthcare facilities during fire scenarios

Evacuation is a critical procedure for safeguarding individuals during a fire incident within a healthcare facility. Assessing the risk associated with the evacuation process is instrumental in enhancing emergency decision-making and developing contingency strategies. Evacuation, a dynamic process, poses challenges in accurate risk evaluation using conventional static quantitative risk assessment (QRA) techniques. This study introduces a dynamic QRA approach to precisely evaluate the evacuation risk to individuals in healthcare settings during a fire. The dynamic event tree methodology is initially utilized to determine the evolving probabilities of various fire scenarios, considering the equipment failure and repair rates. Subsequently, data on fire products and the evacuation of individuals under different fire scenarios are gathered through simulations conducted with Fire Dynamics Simulator (FDS) and Pathfinder software. In addition, this research proposes a dynamic incapacitation model to calculate the consequences of fire, incorporating changes in individuals' locations and the fire products surrounding them during evacuation to accurately estimate the casualty risk. Lastly, the dynamic scenario probability was integrated with the average incapacitation probability for all individuals, introducing the concept of a fire evacuation safety time window to comprehensively assess hospital fire evacuation risk. The findings revealed that the dynamic quantitative risk analysis (DQRA) approach more effectively captures the influence of fire products on the evacuation risk compared to static methods. Specifically, the peak incapacitation probability in a hospital fire reached 0.85, with firefighting equipment, especially the sprinkler system, reducing this risk by over 97% and decreasing evacuation time by 45%. In addition, the risk of fire evacuation in hospitals reaches a critical threshold in the fourth year, enhancing the repair rate of the firefighting system postpones the risk's escalation to a critical threshold until the fourteenth year.

Breaking Water Laws in the Murray‐Darling Basin: Understanding Water Compliance Challenges and Stakeholder Perceptions

AbstractClimate change will put pressure on irrigated agriculture, increasing water scarcity and possible non‐compliance with water regulations. This is especially true in areas such as the Murray‐Darling Basin (MDB), Australia, an area where water resources have been overallocated. Understanding the expected penalties and probability of detection and prosecution of water theft faced by irrigators is important for understanding the incentives for water compliance. We analyze state‐level compliance action data and undertake a detailed case study of estimating the real penalty value of water theft in New South Wales (NSW), the largest MDB state. This analysis is supplemented with qualitative comment on compliance issues from 63 MDB stakeholder interviews. Although findings from random audits suggest that only a small percentage of irrigators commit water theft offenses, the average probabilities of audit detection and prosecution for water theft in NSW between 2018/19 and 2020/21 were low, leading to an average real expected penalty value of stealing water well below existing market prices. Stakeholder interviews confirmed that the majority did not believe there were serious water theft or water compliance challenges—whereas recent secondary survey data suggests that the general public perceives water theft and compliance as a serious and ongoing challenge in the MDB and more needs to be done to address it. Three recommendations for data and policy reform are proposed, namely: (a) improving compliance data and reporting; (b) increasing the probability of detection and prosecution; and (c) increasing penalties, regulator visibility, and reforming legislation. Results illustrate that even countries with highly advanced water governance require data improvements, along with sufficient levels of compliance activities and penalties for effective deterrence and stakeholder confidence.

Thermal Fluctuations of Matter Composition and Quark Nucleation in Compact Stars

At the extreme densities reached in the core of neutron stars, it is possible that deconfined quark matter is produced. The formation of this new phase of strongly interacting matter is likely to occur via a first-order phase transition for the typical temperatures reached in astrophysical processes. The first seeds of quark matter would then form through a process of nucleation within the metastable hadronic phase. Here, we address the role of the thermal fluctuations in the hadronic composition on the nucleation of two-flavor quark matter. At finite temperature, the thermodynamic quantities in a system fluctuate around average values. Nucleation being a local process, it is possible that it occurs in a subsystem whose composition makes the nucleation easier. We will consider the total probability of the nucleation as the product between the probability that a subsystem has a certain hadronic composition different from the average in the bulk, and the nucleation probability in that subsystem. We will show how those fluctuations of the hadronic composition can increase the efficiency of nucleation already for temperatures ∼(0.1−1) keV. However, for temperatures ≲(1−10) MeV, the needed overpressure exceeds the maximum pressure reached in compact stars. Finally, for even larger temperatures the process of nucleation can take place, even taking into account finite-size effects.

MALEXNET-EUNET: MULTI-CLASS LIVER CANCER CLASSIFICATION AND SEGMENTATION USING A HYBRID DEEP LEARNING SYSTEM

Background and objective: One of the most prevalent and significant causes of cancer-related mortality worldwide is considered to be liver cancer. Techniques for automatically segmenting and classifying liver tumors are crucial for supporting medical professionals during the tumor diagnostic process. Classifying liver tumors is challenging due to noise, nonhomogeneity, and the significant appearance diversity observed in tumor tissue. Also, in recent years, most of the research has performed binary classification, but there is still a lack of research on multi-class liver cancer classification. Therefore, we perform a multi-class liver cancer classification and segmentation in this research. Methods: We propose a hybrid deep learning-based multi-class liver cancer classification and segmentation system in this research. The collected CT images are pre-processed in four stages: contrast enhancement, noise filtering, smoothing and sharpening, and liver region segmentation. Next, the binary, texture, histogram, and rotational, scalability, and translational (RST) features are extracted from the pre-processed images. Then, the average correlation (AC) and probability of error (POE) approaches are applied to selecting relevant features and excluding less significant features. After feature selection, a modified AlexNet (MAlexNet) model is used to classify the multi-class classification of liver tumors. Finally, the identified liver tumor regions are segmented using the enhanced U-Net (EUNet) model. Results: Identified liver tumors are accurately classified into three different categories using the proposed classification model: hemangioma (HEM), hepatocellular carcinoma (HCC), and metastatic carcinoma (MET), with an average accuracy of 99.19%. We have collected the multi-class liver cancer CT images from real time patients. The results of the experiments show that proposed hybrid system provides adequate overall accuracy, is less noise-sensitive, and outperforms other state-of-the-art techniques such as SVM, Faster RCNN, Mask RCNN, and SAR-U-Net on a wide range of CT images. Conclusion: Radiologists and doctors can identify liver tumors more accurately using the suggested innovative framework.

Impressive Factors of the Victimization of Shiite Muslim Minorities in Afghanistan: A Case Study District 13 of Kabul during the Pre-Taliban Period.

Shiite Muslims are one of the most influential ethnic minorities in Afghanistan. It appears that they are more victims of violence than other population groups in Afghanistan. On the other hand, the victimization rate in society is one of the most critical issues in criminology. Being victimized can lead to property loss, psychological trauma, and even death. Sensitive ethnic minorities are particularly pronounced in these challenges, especially in traditional societies such as Afghanistan. Therefore, the victimization rate and its influential factors among Shiite Muslims in Afghanistan need to be carefully analyzed. This is a survey study whose statistical population includes all residents of District 13 of Kabul, 285 of whom were selected using a structured questionnaire designed by the researcher and a multistage cluster sampling method. In addition, a multiple-choice Likert scale was used to measure the dependent and independent variables. The study's results indicate that more than 75% of the respondents and, in the past 5 years, more than 80% of their friends and family members have been victimized. In addition, respondents reported that the overall average probability of victimization over the next 10 years is 3.41 (the probability rate ranged from a minimum of 1 to a maximum of 5). Women were more likely to be victimized than men, with average victimization rates of 1.38 and 1.24, respectively (the probability rate ranged from a minimum of 1 to a maximum of 2). There was also a significant positive correlation between victimization and other variables such as age, gender, marital status, education level, and economic status.

Quantifying maternal reproductive output of chondrichthyan fishes

For the live-bearing and egg-laying class of chondrichthyan fishes a three parameter logistic ‘maternity’ function with a variable upper asymptote, PMax, can be used to predict the average probability of a female giving birth or laying eggs in a season. Although fundamental to calculating the reproductive capacity of a population, few studies report maternity functions, with maturity functions often used as a proxy. Applying logistic models to simulated and empirical data showed that it was feasible to estimate PMax from maternal data and that accuracy, bias, and confidence interval coverage often improved compared to when a fixed value was used. However, sample sizes of 100–200 maternal females were typically required for accurate estimation of PMax. While maturity parameters could be estimated with greater accuracy, substituting them for maternity parameters overestimated lifetime reproductive output. Greater use of maternity functions has the potential to improve calculation of reproductive output in quantitative populations models. In addition to improvements in parameter estimation, this method involves fewer assumptions and enables statistical inferences to be made on frequency of reproduction.