Conditional Probability Research Articles

Attribution of aerosol particle number size distributions to main sources using an 11-year urban dataset

Abstract. Source apportionment was performed using size-segregated atmospheric particle number concentrations (PNCs) in 27 size channels over a diameter range of 6–1000 nm augmented by air pollutants with a time resolution of 1 h in Budapest for 11 full years. The input dataset was treated for the effect of the local meteorology using dispersion correction. Both the uncorrected dataset and corrected dataset were evaluated using positive matrix factorization for separate seasons. Six source types including nucleation, two road vehicle emission sources separated into a semi-volatile fraction and a solid-core fraction, a diffuse urban source, a secondary inorganic aerosol (SIA) source, and an ozone-associated secondary aerosol source were identified, characterized and quantified. The dispersion correction did not considerably change the profiles, diel variations or patterns of the sources, while it substantially modified the relative shares of the nucleation source in all seasons. The mean relative contributions of the traffic emissions (60 %) indicate that on-road motor vehicles were the leading source of particle numbers. The nucleation was responsible for 24 % of the PNC annually as a lower estimate. It exhibited a compound character consisting of photochemically induced nucleation and traffic-related nucleation. Its contributions were the highest in spring and the lowest in winter. The shares of the urban diffuse and SIA source types were the largest in autumn and winter and in spring and summer, respectively, but they were typically ⪅ 10 %. The O3-associated secondary aerosol made up the smallest (⪅ 3 %) contributions. The conditional bivariate probability function analysis showed considerable spatial variations in the source origin. The combination of the size-segregated particle number concentrations, wide overall range of the size channels, considerably long dataset, dispersion correction and modelling over separate seasons led jointly to a unique adaptation of the source apportionment and yielded novel and valuable insights into the urban aerosol sources and processes both for Budapest and in general.

Day–night variation, size distribution, source identification, and health risk of polycyclic aromatic hydrocarbons in particulate matter in Ulsan, South Korea

Particulate matter (PM) in 11 different sizes was collected at a semi-rural site in Ulsan, a multi-industrial city in South Korea, over one year from 2019 to 2020 to investigate the temporal patterns in size distribution and potential sources of polycyclic aromatic hydrocarbons (PAHs). The mean concentration of Σ21 PAHs was higher in winter (0.29 and 0.45 ng/m3 for coarse and fine PM, respectively) than in summer (0.06 and 0.07 ng/m3). Although there was no statistically significant difference between day and night for the concentration of individual PAHs in both coarse and fine PM, the concentrations were generally higher during the day than at night. During the day, Σ21 PAHs had two distinct peaks (0.056–0.10 μm and 3.20–5.60 μm) in winter, but they tended to partition to larger particles (1.00–1.80 μm and >18.0 μm) in summer. This result suggests that the volatilization of PAHs in smaller particles was enhanced by high-temperature conditions in summer, followed by their condensation onto larger particles. At night, Σ21 PAH peaks were mainly around the size of 0.7 μm (droplet mode), suggesting the importance of heterogeneous-aqueous reactions. The results of the conditional bivariate probability function and concentration-weighted trajectory indicate that the high concentrations of PAHs in summer and winter were more affected by local pollution and long-range atmospheric transport, respectively. The results of the health risk assessment demonstrate that PAHs in fine PM contributed significantly to cancer risk compared to those in coarse PM. In conclusion, investigating the size distribution of PAHs in particles is necessary to understand their environmental behaviors and evaluate potential health risks.

Dynamic Bayesian game optimization method for multi-energy hub systems with incomplete load information

The interconnection of Energy Hub can enhance the energy efficiency and reliability associated with the independent operation of energy systems. However, the traditional optimal scheduling methods are hard to tackle the situation with the incomplete load information and competitive constraints of a multi-Energy Hub. This paper proposes a dynamic Bayesian game optimization scheduling strategy considering incomplete information on users’ load-side demand. First, a load forecast error coefficient is introduced to handle the conditional probability problem caused by incomplete information through the Bayesian rule. The constraint relationship among multi-Energy Hub under the dynamic price mechanism is analyzed to meet the economic and environmental coordination goals under load uncertainty. Second, extending from Nash equilibrium to Bayes Nash equilibrium proves the existence and uniqueness of Nash equilibrium solutions in Bayesian game models. The decision game algorithm is used to optimize the scheduling of the multi-Energy Hub and subsequently ensure the autonomous scheduling of the system and solve the information barriers. Finally, an Integrated Energy System composed of three Energy Hubs was used to validate the effectiveness and superiority of the proposed optimization method. Results show that under the Bayesian game decision, the multi-Energy Hub game model has reduced the total cost of the Integrated Energy System by 0.78 %, which can improve the economic benefit and address the environmental pollution problem.

Probabilistic Causal Network Modeling of Southern Hemisphere Jet Subseasonal to Seasonal Predictability

Abstract Skillful prediction of the Southern Hemisphere (SH) eddy-driven jet is crucial for representation of mid-to-high-latitude SH climate variability. In the austral spring-to-summer months, the jet and the stratospheric polar vortex variabilities are strongly coupled. Since the vortex is more predictable and influenced by long-lead drivers 1 month or more ahead, the stratosphere is considered a promising pathway for improving forecasts in the region on subseasonal to seasonal (S2S) time scales. However, a quantification of this predictability has been lacking, as most modeling studies address only one of the several interacting drivers at a time, while statistical analyses quantify association but not skill. This methodological gap is addressed through a knowledge-driven probabilistic causal network approach, quantified with seasonal ensemble hindcast data. The approach enables to quantify the jet’s long-range predictability arising from known late-winter drivers, namely, El Niño–Southern Oscillation (ENSO), Indian Ocean dipole (IOD), upward wave activity flux, and polar night jet oscillation, mediated by the vortex variability in spring. Network-based predictions confirm the vortex as determinant for skillful jet predictions, both for the jet’s poleward shift in late spring and its equatorward shift in early summer. ENSO, IOD, late-winter wave activity flux, and polar night jet oscillation only provide moderate prediction skill to the vortex. This points to early spring submonthly variability as important for determining the vortex state leading up to its breakdown, creating a predictability bottleneck for the jet. The method developed here offers a new avenue to quantify the predictability provided by multiple, interacting drivers on S2S time scales. Significance Statement Predictions of the Southern Hemisphere midlatitude jet stream are crucial for skillful forecasts of the austral mid-to-high latitudes. Several oceanic and atmospheric phenomena could, if better represented in models, improve spring-to-summer jet predictions on subseasonal to seasonal time scales. However, the combined potential skill arising from the inclusion of such phenomena has not been quantified. This study does so by using a probabilistic causal network model, representing the connections between those drivers and the jet with conditional probabilities, trained on large sets of model data. The stratospheric polar vortex is confirmed as crucial predictor of jet variability but is itself hard to predict a month in advance due to submonthly variability, creating a predictability bottleneck for the jet.

Study on the distribution of average wind speeds at a mountainous bridge site for structural durability design

Conventional wind speed distribution methods (e.g., Rayleigh distribution and Weibull distribution) may not adequately capture complex characteristics of wind fields in mountainous areas. To address this problem, this study proposes a semi-parametric mix method for modeling the distribution of average wind speeds based on the combination of nonparametric Kernel Density Estimation (KDE) and Generalized Pareto Distribution (GPD). In the proposed method, KDE focuses on capturing the distribution in the main part of average wind speeds, while GPD aims at performing the distribution in terms of those in the extreme part. The segment point (i.e., the threshold) between KDE and GPD distributions is determined based on the combination of conditional mean excesses criterion and empirical rule. Meanwhile, the selection of modeling parameters should ensure that the mix distribution model is continuous and differentiable at the identified threshold point. Then, the commonly-used conditional probability model is further introduced to describe the wind direction distribution. Finally, a case study based on the measured 10-min average wind speeds at a mountainous bridge site is employed to demonstrate the effectiveness of the proposed method. The results indicate that: (1) the distribution of omnidirectional average wind speeds in the mountainous bridge site exhibits an obviously single-peak characteristic, while those considering wind directionality present a certain bimodal characteristic; (2) the proposed method can effectively describe wind speed distributions with different statistical characteristics, and the fitting accuracy outperforms the frequently-employed Weibull distribution model.

Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games

Abstract We propose a new sequential Efficient Pseudo-Likelihood (k-EPL) estimator for dynamic discrete choice games of incomplete information. k-EPL considers the joint behaviour of multiple players simultaneously, as opposed to individual responses to other agents’ equilibrium play. This, in addition to reframing the problem from conditional choice probability (CCP) space to value function space, yields a computationally tractable, stable, and efficient estimator. We show that each iteration in the k-EPL sequence is consistent and asymptotically efficient, so the first-order asymptotic properties do not vary across iterations. Furthermore, we show the sequence achieves higher-order equivalence to the finite-sample maximum-likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum-likelihood estimator at a nearly superlinear rate when the data are generated by any regular Markov perfect equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, k-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression. Monte Carlo simulations demonstrate the theoretical results and show k-EPL’s good performance in finite samples in both small- and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data. We apply the estimator to analyse competition in the U.S. wholesale club industry.

Investigation of odor pollution by utilizing selected ion flow tube mass spectrometry (SIFT-MS) and principal component analysis (PCA).

Odor pollution, also referred to as odor nuisance, is a growing environmental concern that is significantly associated with mental health. Once emitted into the air, the concentration of odorous substances varies considerably with wind conditions, leading to difficulties in timely sampling. In the present study, we employed selected ion flow tube mass spectrometry (SIFT-MS) to measure 22 odor-producing molecules continuously in an urban-rural complex city. In addition, we applied statistical analyses, principal component analysis (PCA), and a conditional probability function (CPF) to the datasets obtained from SIFT-MS to identify the odor characteristics at two study sites. At site A, odorants related to livestock farming and industry showed high factor loadings on principal components (PCs) from the PCA. In contrast, we estimated that the odorous gaseous chemicals affecting site B were closely related to sewage treatment and municipal solid waste disposal. Similar CPF patterns of grouped substances from the PCA supported the association between potential odor sources and specific odorants at site B, which helped estimate possible source locations. Consequently, our findings indicate that continuous monitoring of odorous substances using SIFT-MS can be an effective way to provide sufficient information on odor-producing molecules, leading to the clear identification of odor characteristics despite the high variability of odorous substances.

The sensitivity of legal proof

The proof paradox results from conflicting intuitions concerning different types of fallible evidence in a court of law. We accept fallible individual evidence but reject fallible statistical evidence even when the conditional probability that the defendant is guilty given the evidence is the same, a seeming inconsistency. This paper defends a solution to the proof paradox, building on a sensitivity account of checking and settling a question. The proposed sensitivity account of legal proof not only requires sensitivity simpliciter but sensitivity of each relevant step of the proof procedure and/or sensitivity concerning all relevant alternatives. This account avoids problems that have been identified for other sensitivity views of legal proof. Moreover, it is argued that sensitivity, rather than safety, is the crucial modal condition for legal proof. It is, finally, shown that the provided account can fruitfully support very different existing views on the relationship between knowledge and legal proof.

Hidden Markov model–based asynchronous fault-tolerant control for mode-dependent time-delayed Markovian jump systems with uncertain conditional probability

In control engineering, time-delayed systems are quite common. Modern industrial systems often involve delays due to complicated network environments, the accuracy of sensors and actuators, or signal processing. Speaking of Markovian jump systems, such systems undergo discrete mode changes caused by a Markov process. Hence, it is reasonable to consider the mode-dependent time delays. In this paper, the asynchronous fault-tolerant controller is developed for mode-dependent time-delayed Markovian jump systems. First, the estimations of states and actuator fault are provided by designing an intermediate observer. Then, based on these estimations, the asynchronous fault-tolerant controller is designed by virtue of the hidden Markov process with uncertain conditional probability. Finally, the existence conditions of both the designed observer and fault-tolerant controller are given in terms of linear matrix inequalities. In the meantime, a numerical example is illustrated to validate the effectiveness and potential of the proposed method.

Enhancing Time-Series Prediction with Temporal Context Modeling: A Bayesian and Deep Learning Synergy

In time-series classification, conventional deep learning methods often treat continuous signals as discrete windows, each analyzed independently without considering the contextual information from adjacent windows. This study introduces a novel, lightweight Bayesian meta-classification approach designed to enhance prediction accuracy by integrating contextual label information from neighboring windows. Alongside training a deep learning model, we construct a Conditional Probability Table (CPT) during training to capture label transitions. During inference, these CPTs are utilized to adjust the predicted class probabilities of each window, taking into account the predictions of preceding windows. Our experimental analysis, focused on Human Activity Recognition (HAR) time series datasets, demonstrates that this approach not only surpasses the baseline performance of standalone deep learning models but also outperforms contemporary state-of-the-art methods that integrate temporal context into time series prediction.

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

Educating 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.

Research On the Role and Influencing Factors of Momentum in Tennis Matches Based on Linear Conditional Probability Model and Support Vector Machine

This research investigates the role and influencing factors of momentum in tennis matches using a Linear Conditional Probability Model (LCPM) and Support Vector Machine (SVM). The study begins with data preprocessing to address outliers and standardize scoring notations, followed by an analysis of the momentum's role in tennis, which is defined in relation to consecutive points, games won, and service breaks. The principal component analysis (PCA) is employed to synthesize key factors reflecting momentum, including consecutive scores, untouchable shots, aces, and net points, with a focus on their Markovian properties. A momentum formula is constructed, accounting for the sliding average of scoring differentials and the mutual cancellation of momentum between players. The study further examines the stochasticity of swings in play and runs of success, challenging the notion that these elements are random. The results of the Wald Wolfowitz Run Test and Granger Causality Test indicate that momentum significantly influences the probability of winning points and is not a random phenomenon. A PCA-SVM-SHAP model is developed to predict momentum fluctuations, achieving an 81.26% accuracy rate in the validation set. The model identifies net skills, serving skills, and untouchable shots as the most influential factors on momentum changes. The research extends the model's application to unknown tennis matches and other sports events, demonstrating its generalization ability with varying degrees of accuracy.

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.

PREDICTION OF ELECTROCHEMICAL PROCESSES OF LOCAL DISSOLUTION OF STAINLESS STEELS. PART 2. ANALYTICAL AND SIMULATION MODELING OF PROCESS DYNAMICS

To analyze the process of pitting corrosion, a state graph was used, which displays the possible states of local dissolution of chromium-nickel steels, taking into account the additional state "unstable passivation of macropitting". The developed analytical model for calculating the process before the formation of stable pitting is based on homogeneous Markov chains. The calculation of conditional probabilities of system changes from one possible state to another determines the time in the VisualStudio 2010 environment on the platform of NetFramework using the C# programming language. A comparison of the calculation of states with “unstable passivation of macropitting” (UPM) and without it allowed us to establish for stainless steels (12X18N10T, 10X17N13M2T, 08X22N6T) that the formation time of stable pitting taking into account UPM is less than the formation time without it, but more for 08X22N6T steel, which is due to the increased chromium content in its composition. A simulation model (SM) has been created, which is based on the Monte Carlo method, in which a random number generator is used to implement random processes of local dissolution due to SM, a sequence of states in which the system is located before its transition to a stable state is obtained. Also, due to this model, it became possible to consider the change in the potential of the system in the process of local dissolution of the studied steels. The use of two modeling approaches taking into account the state of the UPM allowed us to establish that IT is better consistent with experimental results both on a quantitative and qualitative level. An algorithm for selecting the values of the mode parameters is proposed, which became the basis for predicting the formation of macropitting processes. For citation: Vinogradova S.S. Prediction of electrochemical processes of local dissolution of stainless steels Part 2. Analytical and simulation modeling of process dynamics. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol.]. 2024. V. 67. N 6. P. 119-126. DOI: 10.6060/ivkkt.20246706.6972.

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.