Conditional Probability Research Articles

Evolutionary theory of convective organization

Abstract The conceptual landscape of convection has two simple gateways: optimal function and random form. Optimal convection adjusts toward a univariate ideal called neutrality. Convection’s form involves elements (parcels, bubbles, drafts) whose most parsimonious assumption is random. Between these gates lies a wilderness of realizable flow configurations. The only simple principle is natural selection by “fitness”, a scalar whose gradient is a local direction in an abstract configuration space. Random or high-entropy patterns occupy most of configuration space and occur spontaneously. With time, convection can discover less facile but more efficient (“organized”) configurations, by sequential selection. Here two data exercises explore that self-organization process, in shallow and deep moist convection. For shallow convection, causal network postulates are explored in a large set of cyclic-domain large-eddy simulations (LES; the “Cloud Botany” set). When an evolutionary pathway (mainly layer deepening in these simulations) leads to precipitation, mesoscale patterns blossom rapidly. For deep convection, expanding rings of conditional cell probability around prior cells are estimated from satellite imagery over South America and the South Pacific. In a Monte Carlo model iterating such a conditional probability kernel, hundreds of hourly cells take days to discover a self-sustaining “squall” configuration the kernel affords. Larger-scale implications include overshoots (redefinition of neutrality) and tens-of-hours timescales to both adjustment and noise (indeterminacy). If functional organization can be inferred from horizontal patterns, the abundance of horizontal texture information in satellite cloud imagery could find quantitative value.

H∞ Filtering for 2-D Discrete-Time Periodic Markov Jump Systems With Multiplicative Noise: A Periodic HMM Approach.

This article presents the implementation of an asynchronous ${\mathcal {H}}_{\infty }$ filter for 2-D discrete-time periodic Markov jump systems with multiplicative noise. The study addresses the issue of missing measurements, which is treated as a stochastic variable following the Bernoulli random distribution. To account for the nonsynchronous phenomenon between the system and filter due to the loss of mode information, the periodic hidden Markov model (HMM) is introduced. Moreover, the transition rate matrix of the system and the conditional probability matrix of the filter are general, allowing for transition probabilities in fully known, partly known or fully unknown cases. The objective is to implement an asynchronous ${\mathcal {H}}_{\infty }$ filter based on periodic HMM that guarantees the filtering error system is mean-square asymptotically stable while maintaining a specified ${\mathcal {H}}_{\infty }$ disturbance attenuation performance. In the light of linear matrix inequalities, the article offers sufficient conditions for filter to exist and provides a solution for the parameters of the filter. Ultimately, a demonstration of the validity of the presented design technique is provided through the Darboux equation.

Resilience Analysis of Airport Systems Based on Improved Bayesian Networks

Modern airports, as pivotal nodes in global transportation networks, face increasing resilience challenges from compound threats such as extreme weather events and cyberattacks. However, current assessment methods primarily rely on subjective evaluations and lack probabilistic reasoning to account for the dynamic interdependencies among resilience factors. To address this gap, this study presents a hybrid Bayesian network–best worst method (BN–BWM) framework aimed at improving the accuracy and practicality of airport system resilience assessments. While Bayesian networks are effective for modeling complex probabilistic dependencies, expert-based probability assignments often introduce subjectivity. To mitigate this, we apply the best worst method (BWM) to conduct systematic pairwise comparison. Building on this, we leverage the BWM’s systematic pairwise comparisons, conducted with 10 aviation experts, to generate conditional probability tables for the Bayesian network. The results indicate that large airports demonstrate higher resilience levels (84–85%), whereas medium-sized airports exhibit moderate resilience (79%). Sensitivity analysis identifies key factors influencing resilience, including emergency repair systems and personnel capabilities, thereby offering actionable insights into improving airport operations. This study presents a robust, data-driven framework that enhances the objectivity and accuracy of resilience evaluations, providing theoretical support for sustainable airport management and operational safety.

Adverse childhood experiences are associated with job burnout in nursing interns: the mediation role of sleep duration

BackgroundAdverse childhood experiences (ACEs) have been linked to a higher probability of adverse physical and emotional conditions. Yet, there remains limited understanding regarding the correlation between ACEs and job burnout, and the role of sleep duration as a potential mediator in this relationship remains largely understudied.MethodsFrom December 2023 to February 2024, a convenience sampling method was used to recruit nursing interns from multiple hospitals in Hunan Province, China. Adverse Childhood Experiences International Questionnaire and Maslach Burnout Inventory-General Survey were used to collect data. Logistic regression was employed to analyze the association between ACEs and job burnout, while mediation analysis was used to investigate the potential mediating role of sleep duration in the relationship between ACEs and job burnout.ResultsAmong the 1055 participants, 412 (39.1%) reported experiencing at least one type of ACE, with 124 (11.7%) reporting four or more type of ACEs. A total of 265 interns were identified as experiencing job burnout. After adjusting for potential covariates, participants with high ACE exposure (≥ 4) showed significantly higher odds of job burnout compared to those with low ACE exposure (0–1) (OR: 1.69, 95%CI: 1.10, 2.57). In addition, each unit increase in ACEs was associated with decreased sleep duration (β: -3.14, 95%CI: -5.60, -0.69). Mediation analysis confirmed that sleep duration partially mediated the association between ACEs and job burnout (indirect effect: 0.0019, 95%CI: 0.0004, 0.004; direct effect: 0.0116, 95%CI: 0.0013, 0.0214), accounting for 13.62% of the total effect.ConclusionsThis study suggests more ACE exposure was associated with an increased likelihood of job burnout among nursing interns, with sleep duration playing a partial mediating role in this relationship.Clinical Trial numberNot applicable.

Probabilities of conditionals: The relevance effect might be confounded by the existence of boundary cases

Probabilities of conditionals: The relevance effect might be confounded by the existence of boundary cases

Deep learning based time-dependent reliability analysis of an underactuated lower-limb robot exoskeleton for gait rehabilitation.

This study evaluates the reliability of an underactuated wearable lower-limb exoskeleton designed to assist with gait rehabilitation. Recognizing the complexity of system reliability, a deep learning framework augmented with Long short-term Memory (LSTM) was utilized for the time-dependent reliability analysis of dynamic systems. The research commenced with the development of a lower-limb gait robot, modeled on a Stephenson III six-bar linkage mechanism. Following the mechanical design, computer-aided design (CAD) tools were employed to conceptualize a lower-limb robotic exoskeleton for rehabilitation purposes. The design incorporated two metallic materials (aluminum and steel), and a composite material (carbon fiber) tested using SolidWorks®. The prototype achieved a lightweight design (~1.63 kg) for carbon fiber material. An LSTM-enhanced deep neural network algorithm was implemented to predict the time-dependent reliability of joint displacements and end-effector trajectories. Finally, conditional probability methods were applied to complete the time-dependent system reliability assessment. The designed mechanical system for gait rehabilitation demonstrated high reliability (R ≈ 0.87). Over 200 simulation runs, reliability trends showed consistent and robust predictions.

Short-Term Forecasting of Crop Production for Sustainable Agriculture in a Changing Climate

Globally, crop productive systems exhibit climatic adaptation, resulting in increased overall yields over the past century. Nevertheless, inter-annual fluctuations in production can lead to food price volatility, raising concerns about food security. Within this framework, short-term crop yield predictions informed by climate observations may significantly contribute to sustainable agricultural development. In this study, we discuss the criteria for historical monitoring and forecasting of the productive system response to climatic fluctuations, both ordinary and extreme. Here, forecasting is intended as an assessment of the conditional probability distribution of crop yield, given the observed value of a key climatic index in an appropriately chosen month of the year. Wheat production in the Teramo province (central Italy) is adopted as a case study to illustrate the approach. To characterize climatic conditions, this study utilizes the Standardized Precipitation Evapotranspiration Index (SPEI) as a key indicator impacting wheat yield. Validation has been carried out by means of Monte Carlo simulations, confirming the effectiveness of the method. The main findings of this study show that the model describing the yield–SPEI relationship has time-varying parameters and that the study of their variation trend allows for an estimate of their current values. These results are of interest from a methodological point of view, as these methods can be adapted to various crop products across different geographical regions, offering a tool to anticipate production figures. This offers effective tools for informed decision-making in support of both agricultural and economic sustainability, with the additional benefit of helping to mitigate price volatility.

BaLNet: A probabilistic Bayesian neural network for solar wind speed forecasting

Machine Learning has gained favor as a tool for space weather event forecasting over the last few years. In the context of solar wind forecasting, efforts have been primarily focused on forecasting the bulk speed of solar wind. Although steps have been taken in improving the accuracy of forecasts, a common concern from an operational point of view has been determining the reliability of any given prediction. In this work, we present BaLNet, a variational neural network with a normal probability distribution output as a tool for providing operational forecasts of solar wind speed with uncertainty quantification. For a lead time of five days, we find reductions in root mean squared error by between 38\% and 55\%, depending on the test set, when compared to state-of-the-art neural networks. Similarly, for the same lead time, we obtain a correlation coefficient between prediction and observation of 0.89 to 0.94, compared to the correlation coefficient of 0.15 obtained by state-of-the-art models. Cross-validation results confirm robust generalization across temporal variations, maintaining consistent superiority over baseline methods. We also leverage the properties of the Bayesian inference process supporting the resulting model to estimate the degree and sources of uncertainty for any given forecast. We provide a 95\% confidence interval for each prediction computed from the standard deviation of the forecasted normal distribution. For a lead time of five days, BaLNet's prediction interval coverage probability is of 95\% in the test set, evidencing that the target conditional probability distribution is being succesfully extracted. The method presented allows for a full training of the model to converge in a span of 2.17h in CPU. This process can be further accelerated by using a GPU to reduce the training time to an average of 15 minutes.

Conditional Probability of Observing a Poor Night According to Sleep Depth Among Individuals With Insomnia.

The present study aims at verifying whether the conditional probability of observing a poor night after one, two, or three consecutive poor nights is associated with sleep depth or sleep self-estimation. Online sleep diaries were collected for 21 consecutive nights from 30 adults with insomnia. Participants completed seven consecutive nights of home polysomnography starting on night 1, 8, or 15 of the sleep diary. The conditional probabilities of observing a poor night after one, two, or three consecutive poor nights were computed for each participant. Sleep depth was measured with the Odds Ratio Product. K-Means Cluster Analyses were computed to derive sleep patterns. Pearson's correlation tests and ANOVAs were conducted to verify the existence of relations with conditional probabilities of observing poor nights and characterise identified sleep patterns. The conditional probability of observing a poor night after one, two, or three consecutive poor nights increased with objective and self-reported WASO, self-reported TWT, and sleepiness before bedtime. The probability increased on sleep depth; thus, the lack of sleep depth was more pronounced. Conversely, the probability increased as subjective SE decreased. Two sleep patterns in insomnia were derived from sleep diaries. Individuals for whom the conditional probability of having consecutive poor nights is high and constant tend to exhibit a reduced sleep depth. Cortical and physiological arousal might play a key role in the development and maintenance of sleep patterns in insomnia. Sleep self-estimation does not appear to be influenced by the conditional probability of experiencing a poor night after consecutive poor nights.

Univariate deep learning framework for short-term SST forecasting at high spatio-temporal scales

Abstract We present a univariate hybrid machine learning framework to predict daily high resolution Sea Surface Temperature (SST) near the Gulf of Kutch region at a resolution of ~ 5.5 km. The hybrid model integrates Intrinsic Mode Functions (IMF) derived from variational mode decomposition with a Long Short-Term Memory (LSTM) network to augment predictive skill. The predicted SST demonstrates impressive performance up to lead times of 7 days. Using statistical metrics like Kullback-Leibler divergence and mutual information, we show that the SST predicted from the hybrid model with a lead time of 3 days decisively outperforms the high-resolution GLORYS SST reanalysis let alone forecast skills of a data-assimilated dynamical model. Using conditional probability, we show that the SST forecasts from the hybrid model are quite reliable over the entire range of SST observations in the study domain. In contrast, the reliability of GLORYS falters in the lower range of SST observations. Also, the hybrid model excels in capturing fine-scale SST features, such as SST fronts, and detecting Marine Heatwaves (MHWs) up to 3 days in advance. These capabilities hold significant applications for Potential Fishing Zone identification and coral bleaching alerts. The hybrid model framework is also adept at forecasting location specific high frequency (3 hourly) SST with a lead time of a day.

Evaluating medical AI systems in dermatology under uncertain ground truth.

Evaluating medical AI systems in dermatology under uncertain ground truth.

Probabilistic memory auto-encoding network for abnormal behavior detection in surveillance video.

Probabilistic memory auto-encoding network for abnormal behavior detection in surveillance video.

Oarfish: enhanced probabilistic modeling leads to improved accuracy in long read transcriptome quantification.

Long-read sequencing technology is becoming an increasingly indispensable tool in genomic and transcriptomic analysis. In transcriptomics in particular, long reads offer the possibility of sequencing full-length isoforms, which can vastly simplify the identification of novel transcripts and transcript quantification. However, despite this promise, the focus of much long-read method development to date has been on transcript identification, with comparatively little attention paid to quantification. Yet, due to differences in the underlying protocols and technologies, lower throughput (i.e. fewer reads sequenced per sample compared to short-read technologies), as well as technical artifacts, long-read quantification remains a challenge, motivating the continued development and assessment of quantification methods tailored to this increasingly prevalent type of data. We introduce a new method and corresponding user-friendly software tool for long-read transcript quantification called oarfish. Our model incorporates a novel coverage score, which affects the conditional probability of fragment assignment in the underlying probabilistic model. We demonstrate, in both simulated and experimental data, that by accounting for this coverage information, oarfish is able to produce more accurate quantification estimates than existing long-read quantification tools. oarfish is implemented in the Rust programming language and is made available as free and open-source software under the BSD 3-clause license. The source code is available at https://www.github.com/COMBINE-lab/oarfish.

Target low-carbon conditional probability for low-carbon structural design

Target low-carbon conditional probability for low-carbon structural design

Optimizing student engagement detection using facial and behavioral features

Abstract In recent years, computer vision and machine learning have achieved remarkable advancements across health care, autonomous systems, and robotics sectors. However, the educational domain, particularly the automated detection of student engagement in online and offline learning environments, remains rich in research opportunities. Detecting student engagement is inherently complex and requires sophisticated interpretive capabilities. This paper introduces a novel approach to automatically detect and classify student engagement by integrating facial images with behavioral and facial features, providing a comprehensive solution to enhance engagement recognition. This study begins by extracting behavioral features and correlating them with pre-defined engagement labels to perform engagement classification using machine learning techniques. In parallel, deep learning models are trained and validated on both image and behavioral features, offering a complementary approach. Additionally, the relationship between facial action units (AUs) and engagement labels is analyzed using three distinct metrics: conditional activation probability, relative activation ratio, and the statistical discriminant coefficient (SDC). The study utilizes publicly available datasets (WACV and DAiSEE) to perform extensive evaluations. Experimental results demonstrate that integrating action units significantly enhances model performance, with XGBoost achieving the highest accuracy (82.9%) among traditional models and EfficientNet reaching the best performance (47.2%) in deep learning experiments. These findings highlight the potential of multimodal approaches in improving real-time engagement detection, offering valuable insights into educational technologies and pedagogy.

Testing an Expanded Model of Deterrence Applied to Guilty Plea Decision Making

Perceptions of certainty of arrest, prosecution, and conviction are all constituent pieces of certainty of punishment, which is a key component of deterrence scholarship and broader work on offending. Nagin discusses these elements as a sequence of conditional probabilities, but the offender decision making literature has nearly exclusively focused upon certainty of arrest. Plea decision making scholars are similarly concerned with certainty perceptions, but more limited to the likelihood of conviction, and how that perception shapes willingness to take a plea deal, often under a ‘shadow of the trial’ model. We seek to employ certainty perceptions as a construct-based linkage to bridge the offender decision making and plea decision making scholarships, enabling us to test the expanded model of deterrence in the context of plea decision making. We found strong support for this theoretical application and discuss our results in the dual contexts of offender and defendant decision making.

Long-term variability of Altocumulus lenticularis clouds in Katowice and atmospheric circulation conditions

The aim of this paper is to analyse the annual and long-term variability in the occurrence of these clouds in the Silesian Upland (on the example of Katowice) as well as to indicate its causes related to atmospheric circulation. The source material comes from the IMGW-PIB. The paper uses data on mid-level cloud cover in Katowice in the years 1971-2020. Altocumulus lenticularis (Ac len) clouds, coded CM = 4, were analysed for eight time points a day (every 3 hours) during the study period. The study also used data on air masses, weather fronts, and types of atmospheric circulation based on the Calendar of atmospheric circulation types for southern Poland compiled by Niedźwiedź (2024). Most occurrences of Ac len were observed in autumn, and least in summer. The highest average number of days and number of cases of Ac len were recorded in October and November, while the lowest in April. In terms of the diurnal distribution, these clouds occurred most frequently between 6:00 and 15:00 UTC. Based on a 50-year dataset, a statistically significant decreasing trends for both number of cases and number of days were found for this type of cloud cover (-2.7 days per 10 years). The maximum number of occurrences was found in 1975, and the minimum in 2016. The highest conditional probability of occurrence of a lenticular cloud in Upper Silesia was found for advection of air masses from the south and southwest in cyclonic pressure systems (>25%) and for advection of a warm polar maritime air mass over southern Poland (20%).

Changes and variability of the physiological air humidity deficit index at Kasprowy Wierch (1971‑2020) and the impact of atmospheric circulation

The paper examines changes and variability of the physiological air humidity deficit index (D) at thesummit of Kasprowy Wierch in the period 1971‑2020. The analysis comprised annual and long-term patterns of the average values, absolute minima and maxima, and the number and share of days with a perception of comfort and dryness. The conditional probability of the occurrence of conditions of perceptibility of air humidity for different air masses was calculated. The highest values of the D index occur at Kasprowy Wierch in winter, the lowest – in summer. The average, maximum and minimum values of the D index in the long-term distribution show a negative trend on an annual basis. Perception of humidity comfort occurs from April to October, peaking in August. Occasionally, days with index values interpreted as sultry do occur. In the long-term period covered in the study, the share of days with perception of physiological comfort of air humidity increases significantly, while days perceived as dry decreases significantly. The conditional probability of perceiving dryness in the air is the highest during the advection of arctic air over southern Poland. For comfortable air humidity it is highest when tropical air passes over southern Poland.The high parts of the Tatra Mountains are unaffected by local anthropogenic impacts. Nevertheless, significant trends in the biometeorological index are observed, linked to air humidity conditions, which are a consequence of global climate change.

The Impact of Foreign Direct Investment on Carbon Emissions in Economies Along the Belt and Road

With China’s emergence as a major global economy, its involvement in tackling climate change and fostering sustainable growth has garnered considerable focus. What impact does global direct investment have on carbon emissions within Belt and Road economies? This study innovatively utilizes a quantile regression model to analyze the varied impacts of international direct investment across distinct carbon emission quantiles, further delving into the conditional probability distribution of the dependent variable to provide a strong theoretical basis for precise policy-making by relevant departments and integrating time and space delays in examining the effects of carbon reduction strategies within the Belt and Road Initiative. Furthermore, this study aims to concentrate its research efforts on the host nations. Findings from this study indicate that global direct investments could escalate carbon emissions in economies with lower carbon emissions; yet, with the rise in the host nation’s carbon emissions, the ripple effect of international direct investments in green technology becomes increasingly evident. Empirical evidence indicates that global direct investment in Belt and Road economies demonstrates a significant mitigating effect on carbon emissions, thereby amplifying the decarbonization benefits associated with such cross-border capital flows.

Research on the Semantic and Pragmatic Reasoning of Chinese Hyperbolic Numerical Idioms Based on the Bayesian Model

Abstract Hyperbolic numerical idioms in modern Chinese are a phenomenon of hyperbolic rhetoric, where numeral words indicate extremely large or small quantities. This study uses Bayesian models to examine the semantic reasoning and pragmatic reasoning processes of hyperbolic numerical idioms. In terms of semantic reasoning, a conditional probability formula is used to demonstrate that hyperbolic quantities can infer any other quantity, leading to the conclusion that the idiomatic events with any quantity are generally valid; in terms of pragmatic reasoning, Bayes’ theorem is employed to show that hyperbolic numerical idioms significantly influence the listener’s numerical cognition, leading to a tendency for the listener’s estimation of the quantity related to the idioms to shift towards hyperbolic quantities. Finally, this study explores the applicable contexts for hyperbolic numerical idioms and analyzes the Bayesian mechanisms behind illegal hyperbolic expressions, pointing out that hyperbolic expressions must carry implications of impossibility and counterfactuality; if the hyperbolic expression conveys a commonplace event, it results in communication failure.