Conditional Probability Research Articles

Probabilistic literacy and reasoning of prospective secondary school teachers when interpreting media news

AbstractEducating students to apply probability literacy and reasoning in out-of-school contexts requires the previous preparation of teachers, which should include the assessment of their mathematical and didactic knowledge. Consequently, we investigated three research questions concerning the probabilistic reasoning and literacy of 66 prospective secondary school teachers when solving probability questions related to a report taken from the media news, their ability to identify the fundamental stochastic ideas needed to solve the task, and their capacity to predict their students’ potential difficulties. The participants needed to compute the probability of a complementary event, several conditional probabilities, and perform critical reading of the information in the report. Despite the participants’ good mathematical knowledge, a high percentage showed reasoning biases, such as the fallacy of the transposed conditional, confusion between conditioning and causation, and few identified the information missing to solve a question. There was a poor capacity to determine the stochastic ideas needed to solve the questions, beyond probability, sample space, conditional probability, and sampling. The participants quoted a few potential errors of their students, mainly conceptual mistakes with scarce recognition of interpretation errors. These results reveal the need to reinforce teachers’ probabilistic literacy, reasoning, and related didactic knowledge.

Improvements on Phase Classification Using Atmospheric Melting and Refreezing Energy Based on Soundings

AbstractDetermining precipitation as solid (snow) or liquid (rain) phase is crucial for remote sensing of precipitation. Most phase classification methods rely on near‐surface temperatures. Further attempts to incorporate atmospheric information aloft only achieved mixed level of success, particularly for precipitation with temperature inversion. In our study, we developed a phase classification scheme based on the upper‐level melting energy (ME) and refreezing energy (RE), which is proportional to the area enclosed by the temperature profile and the 0°C isotherm. We performed least squares fitting and linear discriminant analysis to derive phase separation functions using observed surface and sounding data in North America. We provided separation functions for snow conditional probabilities ranging from 30% to 80% for various applications. Compared to a previously published (Probsnow) method, our energy method achieved comparable performance for Type 1 soundings with one near‐surface melting layer, and significantly improves the phase classification scores for Type 2 soundings with an aloft melting layer and a near‐surface refreezing layer. We innovatively combined surface ice‐bulb temperature with the ratio between the ME and RE to represent Type 2 profiles. For Type 2 soundings, our energy method improves the Heidke skill score (HSS) from 0.25 to 0.47 and reduces false alarm rate (FAR) by 0.47 compared to the Probsnow method for 50% threshold. By applying the physically based method, we improved accuracy and HSS, and reduced FAR for more than two thirds of the evaluation stations across the North America. Finally, we tested the application of the new method in satellite snowfall retrievals.

Conditional survival nomogram for patients with colon mucinous adenocarcinoma to predict prognosis: a dynamic survival analysis.

The aim was to assess conditional survival for colon mucinous adenocarcinoma (MAC) patients, and to construct nomograms to predict conditional survival probability. Survival analysis was done using conditional survival, which was defined as the probability of surviving additional y years for patients who have survived for x years. The mathematical definition was express as: CS (y|x) = S (x + y)/S (x). Cox regression analyses were used to identify prognostic factors. A nomogram is constructed to predict conditional disease-free survival (DFS) and overall survival (OS) probability according to years that already survive. A total of 179 colon MAC patients were included. The 5-year DFS was 67% after surgery, and the 5-year survival probability of patients, who already survived 1, 2, 3, and 4 years were 75%, 87%, 95%, and 98%, respectively. The 5-year OS was 73% after surgery and increased to 76%, 82%, 88%, and 92% at 1, 2, 3, and 4 years, respectively. Subgroup analyses demonstrated the superiority of conditional survival was more pronounced in advanced stages than in stage I. And pT stage, pN stage, and lymphovascular invasion were significantly associated with DFS and OS. Conditional survival nomograms were constructed to predict the 5-year conditional DFS and OS probability given survival for 1, 2, 3, 4 years after surgery. Conditional survival can provide dynamic survival probability according to years that already survive, especially for patients with advanced stages. Taking into account the years already survived accounted for, novel nomograms contributed to effectively predicting conditional survival.

Optimization of a wind farm layout to mitigate the wind power intermittency

A multi-objective optimization method utilizing genetic algorithms is developed to optimize wind farm layout design with the dual objectives of enhancing the production of wind power and reducing hour-level intermittency in the generated power. This method introduces a novel metric for annual wind power intermittency based on the transition probability of wind conditions (i.e., speed and direction). The present multi-objective optimization method ensures that Pareto optimal layouts are evenly distributed according to multiple cost function values. To mitigate wind power intermittency, the spatial distribution of wake fields is strategically manipulated to counteract hourly fluctuations in wind conditions. In wind conditions favoring high power generation, it is found that increasing the overlap between wakes and turbines helps to minimize disparities in generated power compared to other wind conditions.

Advanced Bayesian study on inland navigational risk of remotely controlled autonomous ship

The arise of autonomous ships has necessitated the development of new risk assessment techniques and methods. This study proposes a new framework for navigational risk assessment of remotely controlled Maritime Autonomous Surface Ships (MASS). This framework establishes a set of risk influencing factors affecting safety of navigation of a remotely-controlled MASS. Next, model parameters are defined based on the risk factors, and the model structure is developed using Bayesian Networks. To this end, an extensive literature survey is conducted, enhanced with the domain knowledge elicited from the experts and improved by the experimental data obtained during representative MASS model trials carried out in an inland river. Conditional Probability Tables are generated using a new function employing expert feedback regarding Interval Type 2 Fuzzy Sets. The developed Bayesian model yields the expected utilities results representing an accident’s probability and consequence, with the results visualized on a dedicated diagram. Finally, the developed risk assessment model is validated by conducting three axiom tests, extreme scenarios analysis, and sensitivity analysis. Navigational environment, natural environment, traffic complexity, and shore-ship collaboration performance are critical from the probability and consequence perspective for inland navigational accidents to a remotely controlled MASS. Lastly, important nodes to Shore-Ship collaboration performance include autonomy of target ships, cyber risk, and transition from other remote control centers.

Single-pixel imaging based on self-supervised conditional mask classifier-free guidance

Reconstructing high-quality images at a low measurement rate is a pivotal objective of Single-Pixel Imaging (SPI). Currently, deep learning methods achieve this by optimizing the loss between the target image and the original image, thereby constraining the potential of low measurement values. We employ conditional probability to ameliorate this, introducing the classifier-free guidance model (CFG) for enhanced reconstruction. We propose a self-supervised conditional masked classifier-free guidance (SCM-CFG) for single-pixel reconstruction. At a 10% measurement rate, SCM-CFG efficiently completed the training task, achieving an average peak signal-to-noise ratio (PSNR) of 26.17 dB on the MNIST dataset. This surpasses other methods of photon imaging and computational ghost imaging. It demonstrates remarkable generalization performance. Moreover, thanks to the outstanding design of the conditional mask in this paper, it can significantly enhance the accuracy of reconstructed images through overlay. SCM-CFG achieved a notable improvement of an average of 7.3 dB in overlay processing, in contrast to only a 1 dB improvement in computational ghost imaging. Subsequent physical experiments validated the effectiveness of SCM-CFG.

Bank tail risk in China

AbstractIn this study, we investigate the tail dependency between bank stocks in China and 35 common risk factors. We measure univariate and multivariate conditional tail risk probabilities. The evidence indicates that tail events from risk factors in the banking, security trading, real estate, and energy industries have the largest effects on the realization of extreme returns from Chinese bank stocks. The univariate conditional tail risk is considerably higher than the unconditional tail risk. The impact of multiple tail events from several risk factors occurring simultaneously is much stronger than tail events from one single risk factor. In general, there is a stronger cross‐market tail linkage between emerging market risk factors and bank stocks in China when compared with developed market risk factors. However, the cross‐market tail linkage between developed market risk factors and bank stocks in China rose sharply during the 2008 financial crisis.

Some New Interpretations of the Connectives in Classical Logic

In this paper, the connectives: conditional, conjunction and disjunction of the classical logic are given new interpretations without violating the laws of contradiction and excluded middle unlike fuzzy logic. It is shown that these connectives are equivalent to those of conditional probability, intersection and union of sets/events.

On the extreme wall shear stress events in a turbulent pipe flow

This study investigates the extreme wall shear stress events in a turbulent pipe flow by direct numerical simulation at a frictional Reynolds number Reτ≈500. A two-step conditional averaging scheme is implemented to identify the locations of extreme events and construct their spatial structures. Combined with the joint probability density functions of shear stresses, further evidence is provided for the argument that extreme positive events occur below an intense sweep event (Q4), and the formation of the backflow events is predominantly aided by an identifiable oblique vortex. Moreover, the conditional probability distribution of shear stress for varying thresholds used to define extreme events reveals that, when the threshold is above or below the mean, the probability distributions of the extreme positive events or the backflow events generally follow an exponential relationship, suggesting the extreme wall shear stress events are a threshold-independent process. Finally, the conditional space–time proper orthogonal decomposition is performed to extract the dominant modes and characterize the evolution of the extreme events from inception to dissipation, which exhibits morphological features of real flow structures. It is found that the observation of uθ modes can provide a basic representation of the entire variation process and the extreme values return to normal levels in a very short time.

Optimization of Abnormal Hydraulic Fracturing Conditions of Unconventional Natural Gas Reservoirs Based on a Surrogate Model

Abnormal conditions greatly reduce the efficiency of hydraulic fracturing of unconventional gas reservoirs. Optimizing the fracturing scheme is crucial to minimize the likelihood of abnormal operational conditions, such as pressure channeling, casing deformation, and proppant plugging. This paper proposes a novel machine learning-based method for optimizing abnormal conditions during hydraulic fracturing of unconventional natural gas reservoirs. Firstly, the main controlling factors of abnormal conditions are selected through a hybrid controlling analysis, upon which a surrogate model is established for predicting the occurrence probability of abnormal conditions, rather than whether abnormal conditions happen or not. Subsequently, a machine learning-based optimization algorithm is developed to minimize the occurrence probability of abnormal conditions, acknowledging their inevitability during the fracturing process. The optimal results demonstrate the proposed method outperforms traditional methods, on average. The proposed methodology is more in line with the needs of practical operation in an environment full of uncertainty.

Determining the functioning efficiency of a fire safety subsystem when operating the hydrogen storage and supply system

The object of research is the fire safety subsystem of hydrogen storage and supply systems. The subject of the study is the efficiency index of the fire safety subsystem of hydrogen storage and supply systems for different modes of its operation. As such an efficiency indicator, the conditional probability that the fire safety subsystem correctly recognizes the actual state of the hydrogen storage and supply system is used. The fire safety subsystem functions under the control mode and under the test mode. Mathematical models of the operation of the fire safety subsystem were built for such modes, based on the use of graph theory. The weight matrices of these graphs include the completeness of control or testing and the intensity of transition of the fire safety subsystem from one state to another. Determination of the effectiveness of such a subsystem – reliability of functioning – is carried out using Kolmogorov’s equations. It is shown that during the testing of hydrogen storage and supply system, the probability of its being in a fire-safe state has a maximum. It is shown that with values of completeness of control (testing) that do not differ from 1.0, the effectiveness of the functioning of the fire safety subsystem is invariant with respect to the mode of its functioning. With values of completeness of control (testing), which are significantly different from 1.0, the functioning of the fire safety subsystem under the testing mode is more effective. The identified features of the functioning of the fire safety subsystem make it possible in practice to implement an optimal or adaptive algorithm for the functioning of such subsystems. For example, with the appropriate selection of testing parameters, the fire safety subsystem provides determination of the location of the hydrogen storage and supply system with maximum probability

Improving a method for detecting stealth aerial vehicles by using a network of two small-sized radars with decentralized information processing

The object of this study is the process of detecting stealth aerial vehicles by a network of two small-sized radars with decentralized signal processing. The main hypothesis of the study assumed that combining two small-sized radars into a network could improve the quality of detection of stealth aerial vehicles with decentralized signal processing. The improved method for detecting a stealth aerial vehicle by a network of two small-sized radars with decentralized processing, unlike the known ones, provides for the following: – each radar emits its own probing signal; – each radar receives only its own signal; – coordinated filtering in the reception system of each radar of its signal; – quadratic detection of its signal in each radar; – finding the sum of detected signals in each radar at the output of its matched filter; – preliminary detection of the signal is carried out by each radar separately; – in each range element, the signal is compared with the threshold level; – when the threshold level in the range element is exceeded, such range element is assigned a value of one, otherwise – zero; – the sequence of zeros and ones obtained in this way in each radar of the network is transmitted to the central processing point; – at the central processing point, a decision is made about the presence or absence of a stealth aerial vehicle in the range element. Such a decision is made based on the results of the combined processing of binary sequences coming from the radars according to the "k out of m" criterion. It was established that when detecting a stealth aerial vehicle by a network of two small-sized radars, decentralized information processing provides a higher value of the conditional probability of correct detection, by (19–26) % on average

Human Reliability Analysis for Fishing Vessels in Korea Using Cognitive Reliability and Error Analysis Method (CREAM)

In this paper, we introduce a model designed to predict human error probability (HEP) in the context of fishing boat operations utilizing the cognitive reliability and error analysis method (CREAM). We conducted an analysis of potential accidents on fishing boats and calculated the cognitive failure probability (CFP) for each identified accident. The common performance conditions (CPCs) from the original CREAM were adapted to better reflect the conditions on fishing boats, with the adapted CPCs’ validity confirmed through expert consultations. To apply CREAM, data were gathered via a survey of fishermen, with the uncertainty in the collected data addressed through the application of fuzzy set theory (FST). We then established a Bayesian network (BN) model to elucidate the relationship between the fuzzy data and HEP, utilizing a weighted sum algorithm to determine conditional probabilities within the BN. Both basic and extended versions of CREAM were applied to analyze the most common accidents among fishermen, calculating the CFP for each type of accident. According to our analysis, the poorer the dynamic CPC, the higher the probability that a fall accident will occur inside the boat due to human error, necessitating a countermeasure. The paper proposes safety enhancements for small fishing boats and illustrates the increased precision of human reliability analysis (HRA) models in forecasting human error by incorporating quantitative methods. It calls for further data collection and refinement of the model for more accurate operational risk assessments.

What can hospital emergency admissions prior to cancer diagnosis tell us about socio-economic inequalities in cancer diagnosis? Evidence from population-based data in England.

More deprived cancer patients are at higher risk of Emergency Presentation (EP) with most studies pointing to lower symptom awareness and increased comorbidities to explain those patterns. With the example of colon cancer, we examine patterns of hospital emergency admissions (HEAs) history in the most and least deprived patients as a potential precursor of EP. We analysed the rates of hospital admissions and their admission codes (retrieved from Hospital Episode Statistics) in the two years preceding cancer diagnosis by sex, deprivation and route to diagnosis (EP, non-EP). To select the conditions (grouped admission codes) that best predict emergency admission, we adapted the purposeful variable selection to mixed-effects logistic regression. Colon cancer patients diagnosed through EP had the highest number of HEAs than all the other routes to diagnosis, especially in the last 7 months before diagnosis. Most deprived patients had an overall higher rate and higher probability of HEA but fewer conditions associated with it. Our findings point to higher use of emergency services for non-specific symptoms and conditions in the most deprived patients, preceding colon cancer diagnosis. Health system barriers may be a shared factor of socio-economic inequalities in EP and HEAs.

An Efficient Methodology to Identify Relevant Multiple Contingencies and Their Probability for Long-Term Resilience Studies

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.

Maximum Likelihood Deconvolution of Beamforming Images with Signal-Dependent Speckle Fluctuations

Ocean Acoustic Waveguide Remote Sensing (OAWRS) typically utilizes large-aperture linear arrays combined with coherent beamforming to estimate the spatial distribution of acoustic scattering echoes. The conventional maximum likelihood deconvolution (DCV) method uses a likelihood model that is inaccurate in the presence of multiple adjacent targets with significant intensity differences. In this study, we propose a deconvolution algorithm based on a modified likelihood model of beamformed intensities (M-DCV) for estimation of the spatial intensity distribution. The simulated annealing iterative scheme is used to obtain the maximum likelihood estimation. An approximate expression based on the generalized negative binomial (GNB) distribution is introduced to calculate the conditional probability distribution of the beamformed intensity. The deconvolution algorithm is further simplified with an approximate likelihood model (AM-DCV) that can reduce the computational complexity for each iteration. We employ a direct deconvolution method based on the Fourier transform to enhance the initial solution, thereby reducing the number of iterations required for convergence. The M-DCV and AM-DCV algorithms are validated using synthetic and experimental data, demonstrating a maximum improvement of 73% in angular resolution and a sidelobe suppression of 15 dB. Experimental examples demonstrate that the imaging performance of the deconvolution algorithm based on a linear small-aperture array consisting of 16 array elements is comparable to that obtained through conventional beamforming using a linear large-aperture array consisting of 96 array elements. The proposed algorithm is applicable for Ocean Acoustic Waveguide Remote Sensing (OAWRS) and other sensing applications using linear arrays.

A novel multi-source TWD model based on multi-granularity ball for multiple decision makers

Three-way incomplete multi-attribute decision-making model (TWIMADM) for multiple decision makers is an important topic in data science, which is an effective tool for decision making. However, calculation results of neighborhood blocks are still affected by neighborhood radius. In addition, most of the existing models without considering the information from the evaluations of multiple decision makers separately is difficult to obtain a comprehensive assessment. To address these problems, this paper builds a novel multi-source TWD model based on multi-granularity ball. First, the well-established granular ball is extended to multi-granularity, by which a weighted conditional probability is generated to divide the concerned region into three parts: positive, negative and boundary region. The calculation of the multi-granularity ball is independence of the neighborhood radius parameter. Subsequently, the joint entropy is developed by using the defined multi-granularity to obtain the optimal decision. Furthermore, the relative utility function is utilized to capture the preferences of decision makers, the classification and ranking of each object are determined by calculating the threshold value and expected utility value. Evaluation information from all decision makers are combined and fused. Finally, a novel TWD model is developed to address the challenges of incomplete multi-attribute decision-making problems involving multiple decision makers. The comparative case analyses and experimental evaluations have demonstrated the stability, validity, and feasibility of our model.

Towards evaluating the conditional probability of waterborne microbial risks associated with critical rainfall events following land application of animal waste — A focus on Irish pastures

ABSTRACT Modelling surface runoff and infiltration in an agricultural watershed is essential for understanding the nutrient cycle and water quality management. This research evaluates the critical rainfall events causing maximum surface runoff and infiltration. Empirical models such as Soil Conservation Service (SCS) curve number and Explicit Green-Ampt (EGA) were analysed for different soil hydraulic conditions and storm events with specific return periods. The present study forecasted the maximum daily rainfall and intensity as 113.6 mm and 19.9 cm h–1, respectively, considering a 100-year return period storm. The deterministic part of the model calculates the daily maximum surface runoff as 5.51 cm (from the SCS model). The EGA model revealed that the rainfall intensity of 0.143, 0.163, 0.175, 0.179, 0.181, 0.182, and 0.182 cm h−1 (duration of 24 h) was found critical for 1, 2, 5, 10, 25, 50, 100 year return period of the storm, respectively in different soil texture classes (sand, loamy sand, sandy loam, loam, silt loam, sandy clay loam, clay loam, silty clay soils). Exceptions imply for three occasions where the intensity of 0.407 cm h−1 and duration of 18 h produced maximum infiltration for silty clay loam, and intensity of 0.352 and 0.354 cm h−1 with 9 h rainfall (each) produced maximum infiltration for clay. The probabilistic model revealed that a daily storm event probability of 2.74 × 10–5 is associated with a simulated mean runoff depth of 0.69 cm and infiltration of 20.7 cm. Critical rainfall probabilities calculated in this study can be multiplied with the overall microbial/pollutant human health risk assessment framework to calculate conditional probability and better estimate microbial risk through the drinking water pathway. This study is very relevant for the wet climatic condition of Ireland, where most land use is pastures.

Exploring the co-occurrence of depression, anxiety and insomnia symptoms, diagnoses and treatments in primary care: observational study using UK primary care data.

Depression, anxiety and insomnia often co-occur. However, there is a lack of research regarding how they cluster and how this is related to medication used to treat them. To describe the frequencies and associations between depression, anxiety and insomnia, and treatment for these conditions in primary care. A retrospective cohort study using UK electronic primary care records. We included individuals aged between 18 and 99 years old with one or more records suggesting they had a diagnosis, symptom or drug treatment for anxiety, depression or insomnia between 2015 and 2017. We report the conditional probabilities of having different combinations of diagnoses, symptoms and treatments recorded. There were 1 325 960 records indicative of depression, anxiety or insomnia, for 739 834 individuals. Depression was the most common condition (n = 106 117 records), and SSRIs were the most commonly prescribed medication (n = 347 751 records). Overall, individuals with a record of anxiety were most likely to have co-occurring symptoms and diagnoses of other mental health conditions. For example, of the individuals with a record of generalised anxiety disorder (GAD), 24% also had a diagnosis of depression. In contrast, only 0.6% of those who had a diagnosis of depression had a diagnosis or symptom of GAD. Prescribing of more than one psychotropic medication within the same year was common. For example, of those who were prescribed an SNRI (serotonin-norepinephrine reuptake inhibitor), 40% were also prescribed an SSRI (selective serotonin reuptake inhibitor). The conditional probabilities of co-occurring anxiety, depression and insomnia symptoms, diagnoses and treatments are high.

Structural Safety Assessment of the Transmission Tower Using Bayesian Network

To clarify the disaster-causing factors and preventive measure for the transmission tower, a structural safety assessment method based on Bayesian network is proposed in this study. Firstly, various disaster-causing factors triggering structural damage of transmission towers are systematically analyzed, and three layers network model is constructed based on Bayesian causality. And then, the a priori probability and conditional probability of the network model are quantitatively calculated by combining expert scoring and fuzzy theory. A connectivity tree is formed by building a doxastic map and eliminating elements of the Build Constructive Tree (BuildCT) algorithm. Finally, forward and backward reasoning algorithm using the monitoring data is implemented to capture probabilities of disaster-causing and resulting factors for maintenance. Results shows that the possibility of wind bias tripping is the most feasible factor to be triggered under specific meteorological conditions condition, which is in line with expectation of experts. And strong winds and Serious icing are the key causative factors for tower disconnection and excessive deformation.