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Two-stage conditional probability density function estimators are proposed and studied. Specifically, the Nadaraya-Watson (NW) and local linear (LL) conditional distribution function estimators have been smoothed using Bernstein polynomials in the first stage. Second, the proposed estimators are obtained by differentiating NW and LL estimators. The asymptotic properties of these estimators are established such as asymptotic bias, variance, and normality. Finally, a simulation study is carried out to assess the relative advantage of our estimators compared to other competitors. In addition, the well-known Old Faithful Geyser data is analyzed using the proposed estimators. [ABSTRACT FROM AUTHOR]

The auditory system has an amazing ability to rapidly encode auditory regularities. Evidence comes from the popular oddball paradigm, in which frequent (standard) sounds are occasionally exchanged for rare deviant sounds, which then elicit signs of prediction error based on their unexpectedness (e.g., MMN and P3a). Here, we examine the widely neglected characteristics of deviants being bearers of predictive information themselves; naive participants listened to sound sequences constructed according to a new, modified version of the oddball paradigm including two types of deviants that followed diametrically opposed rules: one deviant sound occurred mostly in pairs (repetition rule), the other deviant sound occurred mostly in isolation (non‐repetition rule). Due to this manipulation, the sound following a first deviant (either the same deviant or a standard) was either predictable or unpredictable based on its conditional probability associated with the preceding deviant sound. Our behavioral results from an active deviant detection task replicate previous findings that deviant repetition rules (based on conditional probability) can be extracted when behaviorally relevant. Our electrophysiological findings obtained in a passive listening setting indicate that conditional probability also translates into differential processing at the P3a level. However, MMN was confined to global deviants and was not sensitive to conditional probability. This suggests that higher‐level processing concerned with stimulus selection and/or evaluation (reflected in P3a) but not lower‐level sensory processing (reflected in MMN) considers rarely encountered rules. Our results indicate that processing at the level of sensory analysis (MMN) is foremost shaped by the frequency of rule encounters (global probability) rather than their precision (conditional probability). Yet, higher‐level processes (P3a) appear to be sensitive to conditional probability even when associated with rarely encountered deviants. Deviants are powerful tools to elicit prediction errors, yet our findings suggest that deviants can be relevant predictors themselves. [ABSTRACT FROM AUTHOR]

Remote sensing image fusion is dedicated to obtain a high-resolution multispectral (HRMS) image without spatial or spectral distortion compared to the single source image. In this paper, a novel fusion algorithm based on Bayesian estimation for remote sensing images is proposed from the new perspective of risk decisions. In this study, an observation model based on Bayesian estimation for remote sensing image fusion is constructed. Three categories of probabilities including prior, conditional and posterior probabilities are calculated after an intensity-hue-saturation (IHS) transformation is applied to the original low-resolution MS image. To obtain the desired HRMS image, with the corrected posterior probability, a fusion rule based on Bayesian decisions is designed to estimate which pixels to select from the panchromatic (PAN) image and the intensity component of the MS image. The selected pixels constitute a new component that will participate in an IHS inverse transformation to yield the fused image. Extensive experiments were performed on the Pleiades, WorldView-3, and IKONOS datasets, and the results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The Large Area Telescope (LAT) onboard the Fermi gamma-ray observatory continuously scans the sky in an energy range from 50 MeV to 1 TeV. The telescope has identified over 6000 gamma-ray emitting sources, approximately half of which are classified as active galactic nuclei (AGN). However, not all of these gamma-ray sources have known redshift values for the reason that redshift estimation following traditional methods can be an expensive, challenging task. Alternatively, as an effort to robustly predict the AGN redshift values, many researchers have recently turned to machine learning methods. However, while the focus has primarily been on predicting specific values, real-world data often allows us only to predict conditional probability distributions, constrained by conditional entropy [ H (Y | X)]. In our study, we employ the Hierarchical Correlation Reconstruction approach to inexpensively predict complex conditional probability distributions, including multimodal ones. This is achieved through independent Mean Squared Error estimation of multiple moment-like parameters, combined into reconstruction of the conditional distribution. By employing linear regression for this purpose, we can develop interpretable models where coefficients describe the contributions of features to conditional moments. This article extends the original approach by incorporating Canonical Correlation Analysis for feature optimization and l1 'lasso' regularization. Our primary focus is on the practical problem of predicting the redshift of AGN using data from the Fourth Fermi -LAT Data Release 3 (4LAC-DR3) data set. [ABSTRACT FROM AUTHOR]

The framework of elementary probabilistic operations (EPO) explains the structure of elementary probabilistic reasoning tasks as well as people's performance on these tasks. The framework comprises three components: (a) Three types of probabilities: joint, marginal, and conditional probabilities; (b) three elementary probabilistic operations: combination, marginalization, and conditioning, and (c) quantitative inference schemas implementing the EPO. The formal part of the EPO framework is a computational level theory that provides a problem space representation and a classification of elementary probabilistic problems based on computational requirements for solving a problem. According to the EPO framework, current methods for improving probabilistic reasoning are of two kinds: First, reduction of Bayesian problems to a type of probabilistic problems requiring less conceptual and procedural competencies. Second, enhancing people's utilization competence by fostering the application of quantitative inference schemas. The approach suggests new applications, including the teaching of probabilistic reasoning, using analogical problem solving in probabilistic reasoning, and new methods for analyzing errors in probabilistic problem solving. [ABSTRACT FROM AUTHOR]

In probabilistic coastal hazard assessments based on the Joint Probability Method, historical storm data is used to build distribution models of tropical cyclone atmospheric parameters (i.e., central pressure deficit, forward velocity, radius of maximum wind, and heading direction). Recent models have used a range of assumptions regarding the dependence structure between these random variables. This research investigates the performance of a series of joint distribution models based on assumptions of parameter independence, partial-dependence (i.e., dependence between only central pressure deficit and radius of maximum wind), and full dependence (i.e., dependence between each pair of tropical cyclone atmospheric parameters). Full dependence models consider a range of copula models, such as the Gaussian copula and vine copulas that combine linear-circular copulas with Gaussian or Frank copulas. The consideration of linear-circular copulas allows for the characterization of correlation between linear variables (e.g., central pressure deficit) and circular variables (e.g., heading direction). The sensitivity of the results to different joint distribution models is assessed by comparing hazard curves at representative locations in New Orleans, LA (USA). The stability of hazard curves generated using a Gaussian copula considering variation in the selection of the zero-degree convention is also assessed. The tail dependence between large central pressure deficit and large radius of maximum wind associated with various copula models are also compared using estimated conditional probability. It is found that the linear-circular Frank vine copula model improve the stability of hazard curves and maximize tail dependence between large central pressure deficit and large radius of maximum wind. However, the meta-Gaussian copula model exhibits performance within this study region that was generally consistent with the tested vine copulas and have the advantage of being easier to implement. [ABSTRACT FROM AUTHOR]

• A fusion-driven Bayesian network fault diagnosis method is proposed. • Broad learning system-based benchmark model is developed to learn prior structure. • Fuzzy logic systems-based knowledge evaluation method is developed for structuring optimization. • Fusion field observation information to improve the accuracy and reliability of fault diagnosis. • The method was experimented on a chiller. Timely diagnosis and maintenance of faults in chiller units is beneficial for reducing energy consumption in buildings. In order to improve the diagnostic accuracy and provide reasonable explanations for fault occurrences of the heating, ventilation, and air conditioning (HVAC) systems in buildings, a fusion-driven Bayesian network fault diagnosis method is proposed based on broad learning system and fuzzy expert knowledge. Firstly, from the data-driven perspective, an efficient broad learning system is developed as benchmarking model to build the prior Bayesian network structure. Secondly, from the knowledge-driven perspective, the fuzzy logic system is used to fuzz expert knowledge, which then used to optimize the Bayesian network. Finally, the information obtained by experts on-site is incorporated into the optimized Bayesian network as new evidence nodes to determine the Bayesian network. The parameters of the Bayesian network are learned through Noisy-MAX processing of the conditional probability table. The performance of the proposed method is evaluated based on the fault diagnosis of a chiller system. The results demonstrate that the Bayesian network established through this method combines the advantages of data-driven and knowledge-driven approaches. It not only performs well in terms of diagnostic accuracy, with accuracy rates above 98 % for six typical faults, but also provides effective explanations for the underlying mechanisms of the faults through causal relationship diagrams. [ABSTRACT FROM AUTHOR]

Multiregional clinical trials (MRCTs) have become increasingly common during the development of new drugs to obtain simultaneous drug approvals worldwide. When planning MRCTs, a major statistical challenge is determination of the regional sample size. In general, the regional sample size must be determined as the sample size such that the regional consistency probability, defined as the probability of meeting the regional consistency criterion, is greater than a prespecified value. The Japanese Ministry of Health, Labour and Welfare proposed two criteria for regional consistency. Moreover, many researchers have proposed corresponding closed‐form formulas for calculating regional consistency probabilities when the primary outcome is continuous. Although some researchers have argued that those formulas are also applicable to cases with binary outcomes, it remains questionable whether such an argument can be true. Based on simulation results, we demonstrate that the existing formulas are inappropriate for binary cases, even when the regional sample size is sufficiently large. To address this issue, we develop alternative formulas and use simulation to show that they provide accurate regional consistency probabilities. Furthermore, we present an application of our proposed formulas for an MRCT of advanced or metastatic clear‐cell renal cell carcinoma. [ABSTRACT FROM AUTHOR]

According to the Ray-Knight description, the Brownian local time in some conditional probability space is a diffusion process with respect to spatial variable. This diffusion has a local time. Thus the following definition of local time of the original Brownian local time seems to be natural: such a process is called the second-order Brownian local time. The paper studies the Laplace transform of the distribution of the Brownian local time of the second order. [ABSTRACT FROM AUTHOR]

The H ∞ control problem is studied for discrete-time Markov jump systems with both discrete and distributed delays. The controller to be designed allows for mode mismatch with the plant, and the mode mismatch behavior is described by a hidden Markov model. The conditional probabilities are permitted to be uncertain, which belong to an interval with precise upper and lower bounds. A sufficient condition that ensures the stochastic stability and H ∞ disturbance-attenuation performance of the system is derived by employing a Lyapunov functional involving multiple quadratic items associated with the system modes. Then, two design methods are proposed for the desired controller. The first method does not utilize the property that the row sum of the conditional probability matrix is one, while the second method incorporates this property into the design process. The scenario where all the conditional probabilities are known in advance is also investigated, and corresponding controller design methods are presented. Finally, two examples are applied to validate the effectiveness of the design methods. [ABSTRACT FROM AUTHOR]

Baseflow is a critical hydrological variable linked to a variety of environmental factors. The construction of a dam may modify baseflow generation and adjust its environmental dependence via the regulation of discharge. However, its effects on the relationships among air temperature, water temperature, and baseflow remain unclear. Here, we use copula functions to explore the relationships among these variables in the Yangtze River and show how they have changed in response to the Three Gorges Dam (TGD). Because of the buffering effects of the baseflow, baseflow is negatively correlated to water temperature, and the relationship between baseflow and water temperature lessens as air temperature rises. Construction of the TGD attenuates the relationship between baseflow and water temperature when air temperature is low, and this attenuation is especially prominent in winter and spring. Our findings will enhance environmental protection in the Yangtze River and improve the ecological operations of the TGD. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Groundwater serves as the primary source of freshwater in arid and semi-arid regions, rendering them resilient against precipitation scarcity. Various aspects of the drought phenomenon necessitate the application of multivariate analysis and composite drought indices. These composite indices afford a more comprehensive understanding of various drought types. However, few studies have considered the integration of meteorological and groundwater drought information. This research delves into determining a threshold for triggering the transition from meteorological drought to groundwater drought in an arid region (Minab plain). It introduces the Joint Deficit Meteo-Groundwater Drought Index, a result of combining two droughts based on copula function. Furthermore, trivariate drought frequency analysis (severity-duration-peak) is conducted based on three scenarios in three clusters of the Minab Plain. Drought risk is then assessed using conditional probability. The results indicate that the northern and central parts of the Minab Plain face a high risk of meteo-groundwater drought. With increasing drought duration and severity, the peak also rises, placing the entire region at risk of widespread drought. A comprehensive understanding of meteo-groundwater drought and an assessment of its characteristics provide insights into the signals of propagation from meteorological drought to groundwater, facilitating the management of groundwater and surface water resources to mitigate the effects of drought. [ABSTRACT FROM AUTHOR]

The design flood for a coastal basin based on model simulations can be impacted by various conditions other than design storm, such as tide level. However, the design storm and tide level are usually investigated separately, and the relation between them has not been sufficiently studied, which may have unexpected impacts on model simulations. This paper presents a bivariate assessment framework that aims to evaluate the coordination between design storm and tide level using a copula-based joint distribution to derive the conditional probability of coincidences between design storm and tide level intervals. We apply this framework to the Tai Lake Basin (TLB) in the eastern coast of China and investigate what tide level along its coastline is appropriate for guiding flood control planning. Our findings reveal that the currently-used tide level along the southern coast of TLB is too low and should be raised by approximately 0.35 m and 0.12 m under maximum 1-day and 3-day storms, respectively. Meanwhile, the tide levels for the north and east coasts are appropriate. This paper provides a comprehensive understanding of the interplay between design storm and tide level in a large coastal basin, offering insights into the design of flood protection systems. [ABSTRACT FROM AUTHOR]

In the interval-valued intuitionistic fuzzy environment, a new multi-attribute three-way decision-making model is proposed to address the problems that the relative loss function in the existing multi-attribute three-way decision-making model does not consider the degree of hesitancy, and the alternative conditional probabilities are given subjectively by the authors, which lacks objectivity. First, three types of ideal solutions are introduced, and the correlation coefficients between the evaluated values and ideal solutions are utilized to construct alternative relative loss functions. Second, the ELECTRE-I method is generalized to the interval-valued intuitionistic fuzzy environment to establish the outranking relation and a method for estimating the conditional probability of alternatives is given. Finally, the model is used to experimentally analyze examples to illustrate the effectiveness and rationality of the model. [ABSTRACT FROM AUTHOR]

In the United States, overhalf a million delinquency cases are opened annually. Of those cases, an estimated 26% involve detention in some manner. Adolescents who have been adjudicated delinquent are detained based on their display of illegal behavior. This repertoire, which includes illegal behavior, may give rise to challenging behavior while residing in the detention facility. Moreover, challenging behavior displayed by adolescents in detention facilities often gives rise to severe consequences including physical or psychological harm, facility instability, increased duration of detention, and parole denial. The present study is a descriptive assessment of behavioral data collected by dormitory staff at a juvenile residential treatment facility. We used conditional probabilities and statistical analyses to identify conditional events that predict increased likelihood of challenging behavior (e.g. days of the week, time of day). The findings may allow clinicians and administrators within the facility to allocate resources strategically to prevent and respond to challenging behavior effectively. Implications, limitations, and future directions are discussed. Challenging behavior within juvenile residential facilities is a ubiquitous problem for administrators. Problem behavior by one resident can have dynamic effects on other residents and staff members. Conditional probabilities can assist administrators in making decisions about intervention resources for staff members and residents of juvenile facilities. [ABSTRACT FROM AUTHOR]

This paper describes estimation of the regression parameters and prediction of the cumulative incidence functions under the cause-specific proportional hazards model when some of covariates are not fully observed. Assuming that missingness mechanism is missing at random, we propose the augmented inverse probability weighted method for estimation and inference procedures. A nonparametric regression approach is adapted for estimating selection probabilities and conditional expectations of missing covariates in the augmented estimating function. We establish the asymptotic properties of the predicted cumulative incidence functions under the cause-specific proportional hazards model with missing covariates and derive consistent variance estimators of the predicted cumulative incidence functions. Simulation studies show that the procedures perform well. The proposed methods are illustrated with stage IV breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute. [ABSTRACT FROM AUTHOR]

Over the past decades, the process of the traditional drug discovery study spent tremendous time and resources. More and more studies have shown that genetic determinants may mediate variability among persons in the response to a drug. In this article, the proposed method is considered for genetic heterogeneity in Simon's two-stage design for a phase II clinical trial. We try to propose the method to employ the phase II clinical trial based on the existence of the epidemiological evidence for genetic heterogeneity. For our proposed method, Simon's two-stage design is conditional on the probability of the genetic heterogeneity. The example is used to illustrate how to calculate sample size in given parameters. [ABSTRACT FROM AUTHOR]

The aim of device-independent quantum key distribution (DIQKD) is to study protocols that allow the generation of a secret shared key between two parties under minimal assumptions on the devices that produce the key. These devices are merely modeled as black boxes and mathematically described as conditional probability distributions. A major obstacle in the analysis of DIQKD protocols is the huge space of possible black box behaviors. De Finetti theorems can help to overcome this problem by reducing the analysis to black boxes that have an iid structure. Here we show two new de Finetti theorems that relate conditional probability distributions in the quantum set to de Finetti distributions (convex combinations of iid distributions) that are themselves in the quantum set. We also show how one of these de Finetti theorems can be used to enforce some restrictions onto the attacker of a DIQKD protocol. Finally we observe that some desirable strengthenings of this restriction, for instance to collective attacks only, are not straightforwardly possible. [ABSTRACT FROM AUTHOR]

We propose a Markov Chain Monte Carlo Conditional Maximum Likelihood (MCMC-CML) estimator for the two-way fixed-effects logit model for dyadic data, typically used in network analyses. The proposed MCMC approach, based on a Metropolis algorithm, allows us to overcome the computational issues of evaluating the probability of the outcome conditional on nodes in- and out-degrees, which are sufficient statistics for the incidental parameters. Under mild regularity conditions, the MCMC-CML estimator converges to the exact CML one and is asymptotically normal. Moreover, it is more efficient than the existing pairwise CML estimator. We study the finite sample properties of the proposed approach by means of an extensive simulation study and three empirical applications, where we also show that the MCMC-CML estimator can be applied to logit models for binary panel data with both subject and time-fixed effects. Results confirm the expected theoretical advantage of the proposed approach, especially with small, concentrated, and sparse networks or with rare events in panel data. [ABSTRACT FROM AUTHOR]

Multi-arm trials are increasingly of interest because for many diseases; there are multiple experimental treatments available for testing efficacy. Several novel multi-arm multi-stage (MAMS) clinical trial designs have been proposed. However, a major hurdle to adopting the group sequential MAMS routinely is the computational effort of obtaining stopping boundaries. For example, the method of Jaki and Magirr for time-to-event endpoint, implemented in R package MAMS, requires complicated computational efforts to obtain stopping boundaries. In this study, we develop a group sequential MAMS survival trial design based on the sequential conditional probability ratio test. The proposed method is an improvement of the Jaki and Magirr's method in the following three directions. First, the proposed method provides explicit solutions for both futility and efficacy boundaries to an arbitrary number of stages and arms. Thus, it avoids complicated computational efforts for the trial design. Second, the proposed method provides an accurate number of events for the fixed sample and group sequential designs. Third, the proposed method uses a new procedure for interim analysis which preserves the study power. [ABSTRACT FROM AUTHOR]

In recent decades, several randomization designs have been proposed in the literature as better alternatives to the traditional permuted block design (PBD), providing higher allocation randomness under the same restriction of the maximum tolerated imbalance (MTI). However, PBD remains the most frequently used method for randomizing subjects in clinical trials. This status quo may reflect an inadequate awareness and appreciation of the statistical properties of these randomization designs, and a lack of simple methods for their implementation. This manuscript presents the analytic results of statistical properties for five randomization designs with MTI restriction based on their steady‐state probabilities of the treatment imbalance Markov chain and compares them to those of the PBD. A unified framework for randomization sequence generation and real‐time on‐demand treatment assignment is proposed for the straightforward implementation of randomization algorithms with explicit formulas of conditional allocation probabilities. Topics associated with the evaluation, selection, and implementation of randomization designs are discussed. It is concluded that for two‐arm equal allocation trials, several randomization designs offer stronger protection against selection bias than the PBD does, and their implementation is not necessarily more difficult than the implementation of the PBD. [ABSTRACT FROM AUTHOR]

Background: The impact of electricity access on all-cause premature mortality is unknown. Methods: We use a national dataset from India to compare districts with high access to electricity (>90% of households) to districts with middle (50–90%) and low (<50%) access to electricity and estimate the effect of lack of electricity access on all-cause premature mortality. Results: In 2014, out of 597 districts in India, 174 districts had high access, 228 had middle access, and 195 had low access to electricity. When compared to districts with high access, districts with low access had higher rates of age-standardized premature mortality in both women (2.09, 95% CI: 1.43–2.74) and men (0.99, 0.10–1.87). Similarly, these districts had higher rates of conditional probability of premature death in both women (9.16, 6.19–12.13) and men (4.04, 0.77–7.30). Middle access districts had higher rates of age-standardized premature mortality and premature death in women, but not men. The total excess deaths attributable to reduced electricity access were 444,225 (45,195 in middle access districts and 399,030 in low access districts). In low access districts, the proportion of premature adult deaths attributable to low electricity access was 21.3% (14.4%– 28.1%) in women and 7.9% (1.5%– 14.3%) in men. Conclusion: Poor access to electricity is associated with nearly half a million premature adult deaths. One out of five premature deaths in adult women were linked to low electricity access making it a major social determinant of health. [ABSTRACT FROM AUTHOR]

Target threat assessment provides support for combat decision making. The multi-target threat assessment method based on a three-way decision can obtain threat classification while receiving threat ranking, thus avoiding the limitation of traditional two-way decisions. However, the heterogeneous situation information, attribute relevance, and adaptive information processing needs in complex battlefield environment bring challenges to existing methods. Therefore, this paper proposes a new multi-target three-way threat assessment method with heterogeneous information and attribute relevance. Firstly, dynamic assessment information is represented by heterogeneous information, and attribute weights are calculated by heterogeneous Criteria Importance Through Intercriteria Correlation (CRITIC). Then, the conditional probability is calculated by the heterogeneous weighted Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the adaptive risk avoidance coefficients are constructed by calculating the uncertainty of the assessment value, and then the relative loss function matrices are constructed. Finally, the comprehensive loss function matrices are obtained by the weighted Heronian mean (HM) operator, and the comprehensive thresholds are calculated to obtain the three-way rules. The case study shows that compared with the existing methods, the proposed method can effectively handle the heterogeneous information and attribute relevance, and obtain the risk avoidance coefficients without presetting or field subjective settings, which is more suitable for the complex mission environment. [ABSTRACT FROM AUTHOR]

Sequence-level data offers insights into biological processes through the interaction of two or more genomic features from the same or different molecular data types. Within motifs, this interaction is often explored via the co-occurrence of feature genomic tracks using fixed-segments or analytical tests that respectively require window size determination and risk of false positives from over-simplified models. Moreover, methods for robustly examining the co-localization of genomic features, and thereby understanding their spatial interaction, have been elusive. We present a new analytical method for examining feature interaction by introducing the notion of reciprocal co-occurrence, define statistics to estimate it and hypotheses to test for it. Our approach leverages conditional motif co-occurrence events between features to infer their co-localization. Using reverse conditional probabilities and introducing a novel simulation approach that retains motif properties (e.g. length, guanine-content), our method further accounts for potential confounders in testing. As a proof-of-concept, motif co-localization (MoCoLo) confirmed the co-occurrence of histone markers in a breast cancer cell line. As a novel analysis, MoCoLo identified significant co-localization of oxidative DNA damage within non-B DNA-forming regions that significantly differed between non-B DNA structures. Altogether, these findings demonstrate the potential utility of MoCoLo for testing spatial interactions between genomic features via their co-localization. [ABSTRACT FROM AUTHOR]

Illusory causation is a phenomenon in which people mistakenly perceive a causal relationship between a cue and outcome even though the contingency between them is actually zero. Illusory causation studies typically use a unidirectional causal rating scale, where one endpoint refers to no relationship and the other to a strongly positive causal relationship. This procedure may bias mean causal ratings in a positive direction, either by censoring negative ratings or by discouraging participants from giving the normative rating of zero which is at the bottom extreme of the scale. To test this possibility, we ran two experiments that directly compared the magnitude of causal illusions when assessed with a unidirectional (zero—positive) versus a bidirectional (negative—zero—positive) rating scale. Experiment 1 used high cue and outcome densities (both 75%), whereas Experiment 2 used neutral cue and outcome densities (both 50%). Across both experiments, we observed a larger illusory causation effect in the unidirectional group compared with the bidirectional group, despite both groups experiencing the same training trials. The causal illusions in Experiment 2 were observed despite participants accurately learning the conditional probabilities of the outcome occurring in both the presence and absence of the cue, suggesting that the illusion is driven by the inability to accurately integrate conditional probabilities to infer causal relationships. Our results indicate that although illusory causation is a genuine phenomenon that is observable with either a undirectional or a bidirectional rating scale, its magnitude may be overestimated when unidirectional rating scales are used. [ABSTRACT FROM AUTHOR]

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or "associational") languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. [ABSTRACT FROM AUTHOR]

For supervised classification we propose to use restricted multidimensional unfolding in a multinomial logistic framework. Where previous research proposed similar models based on squared distances, we propose to use usual (i.e., not squared) Euclidean distances. This change in functional form results in several interpretational advantages of the resulting biplot, a graphical representation of the classification model. First, the conditional probability of any class peaks at the location of the class in the Euclidean space. Second, the interpretation of the biplot is in terms of distances towards the class points, whereas in the squared distance model the interpretation is in terms of the distance towards the decision boundary. Third, the distance between two class points represents an upper bound for the estimated log-odds of choosing one of these classes over the other. For our multinomial restricted unfolding, we develop and test a Majorization Minimization algorithm that monotonically decreases the negative log-likelihood. With two empirical applications we point out the advantages of the distance model and show how to apply multinomial restricted unfolding in practice, including model selection. [ABSTRACT FROM AUTHOR]

A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

Multiple-point geostatistics (MPS) has more advantages than two-point geostatistics in reproducing the continuity of geobodies in subsurface reservoir modeling. For fluvial reservoir modeling, the more continuous a channel, the more consistent it is with geological knowledge in general, and fluvial continuity is also of paramount importance when simulating fluid flow. Based on the pixel-based MPS algorithm Snesim, this study proposes a method that utilizes multiple search trees (MSTs) to enhance simulation continuity in 2D fluvial reservoir modeling. The objective of the MST method is to capture complete data events from a training image (TI), which aims to achieve enhanced continuity in fluvial reservoir sublayer modeling. By resorting to search neighborhoods based on their proximity to the central node of the data template, multiple data templates that correspond to the MSTs will be generated. Here, four data templates were generated by arranging the relative search neighborhood coordinates in ascending and descending order with respect to the central node. Parallel computing was tried for the construction of the search trees. This work calculated the conditional probability distribution function (CPDF) of the simulating nodes by averaging the CPDFs derived from the MSTs, and double retrieval was employed to filter out the search trees that possessed an inaccurate local CPDF for the simulating nodes. In addition, the connected component labeling (CCL) method was introduced to evaluate the simulation continuity in MPS. The results indicated that the MST method can enhance the simulation continuity of the Snesim algorithm by reproducing the fine connectivity of channel facies in 2D fluvial reservoir modeling. [ABSTRACT FROM AUTHOR]

In this article, I extend the use of probability of success calculations, previously developed for fixed sample size studies to group sequential designs (GSDs) both for studies planned to be analyzed by standard frequentist techniques or Bayesian approaches. The structure of GSDs lends itself to sequential learning which in turn allows us to consider how knowledge about the result of an interim analysis can influence our assessment of the study's probability of success. In this article, I build on work by Temple and Robertson who introduced the idea of conditional probability of success, an idea which I also treated in a recent monograph. [ABSTRACT FROM AUTHOR]

The problem of probabilities of conditionals is one of the long‐standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate standard probability theory. This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. We address two common objections to Adams' view: that the relevant probabilities are 'probabilities only in name', and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. [ABSTRACT FROM AUTHOR]

Subseasonal droughts including flash droughts have occurred frequently in recent years, which are accompanied by heatwaves or wildfires that raise a wide concern on environmental risk. However, the changing characteristics of subseasonal drought propagation, and the possible climate and environmental drivers remain unknown. This study quantifies the propagation characteristics from meteorological drought to soil drought using a Copula‐based Bayesian framework, and shows that higher propagation risks mainly occur in more humid regions with denser vegetation cover. Trends in drought propagation risk vary regionally, with a global increase of 2%/decade (p < 0.01) during 1980–2022. Vegetation greening and climate warming are the key drivers over >71% of the global vegetated lands, with mean contribution rates of 39.5% and 36.5% respectively. Other climatic factors including vapor pressure deficit and precipitation also paly critical roles, which closely correlate with temperature and vegetation. These findings highlight the importance of vegetation greening on subseasonal drought propagation dynamics. Plain Language Summary: Changing characteristics of seasonal‐interannual drought propagation have been well studied at watershed scales, and they were found to be principally ruled by climate divers and moderately affected by vegetation factors. In a changing environment, subseasonal droughts have occurred frequently worldwide, showing different characteristics and environmental responses with long‐term droughts. However, how climate and environment factors affect the subseasonal drought propagation characteristics remains unknown. This study investigates the propagation risk from meteorological drought to soil drought at subseasonal timescales based on a conditional probability method. We found that higher subseasonal drought propagation risks were mainly located in more humid vegetated regions, and the propagation risk showed an overall increasing trend (p < 0.01) from a global perspective but with significant spatial variations during 1980–2022. Climatic and vegetation factors jointly affect the trends in subseasonal drought propagation risks. Among them, vegetation greening and climate warming were the most important drivers over >71% of global vegetated regions. Key Points: Higher propagation risk from subseasonal meteorological to soil drought mainly occurred in humid regions with denser vegetation coverTrends in subseasonal drought propagation risk varied regionally, with a global mean increase of 2%/decade during 1980–2022Greening and warming were the key drivers of the trends, with global mean contribution rates of 39.5% and 36.5% respectively [ABSTRACT FROM AUTHOR]

This study aimed at modelling the underlying predictor of ASCVD through the Bayesian network (BN). Data for the AZAR Cohort Study, which evaluated 500 healthcare providers in Iran, was collected through examinations, and blood samples. Two BNs were used to explore a suitable causal model for analysing the underlying predictor of ASCVD; Bayesian search through an algorithmic approach and knowledge-based BNs. Results showed significant differences in ASCVD risk factors across background variables' levels. The diagnostic indices showed better performance for the knowledge-based BN (Area under ROC curve (AUC) = 0.78, Accuracy = 76.6, Sensitivity = 62.5, Negative predictive value (NPV) = 96.0, Negative Likelihood Ratio (LR−) = 0.48) compared to Bayesian search (AUC = 0.76, Accuracy = 72.4, Sensitivity = 17.5, NPV = 93.2, LR− = 0.83). In addition, we decided on knowledge-based BN because of the interpretability of the relationships. Based on this BN, being male (conditional probability = 63.7), age over 45 (36.3), overweight (51.5), Mets (23.8), diabetes (8.3), smoking (10.6), hypertension (12.1), high T-C (28.5), high LDL-C (23.9), FBS (12.1), and TG (25.9) levels were associated with higher ASCVD risk. Low and normal HDL-C levels also had higher ASCVD risk (35.3 and 37.4), while high HDL-C levels had lower risk (27.3). In conclusion, BN demonstrated that ASCVD was significantly associated with certain risk factors including being older and overweight male, having a history of Mets, diabetes, hypertension, having high levels of T-C, LDL-C, FBS, and TG, but Low and normal HDL-C and being a smoker. The study may provide valuable insights for developing effective prevention strategies for ASCVD in Iran. [ABSTRACT FROM AUTHOR]

The use of Synthetic Aperture Sonar (SAS) in autonomous underwater vehicle (AUV) surveys has found applications in archaeological searches, underwater mine detection and wildlife monitoring. However, the easy confusability of natural objects with the target object leads to high false positive rates. To improve detection, the combination of SAS and optical images has recently attracted attention. While SAS data provides a large-scale survey, optical information can help contextualize it. This combination creates the need to match multimodal, optical–acoustic image pairs. The two images are not aligned, and are taken from different angles of view and at different times. As a result, challenges such as the different resolution, scaling and posture of the two sensors need to be overcome. In this research, motivated by the information gain when using both modalities, we turn to statistical exploration for feature analysis to investigate the relationship between the two modalities. In particular, we propose an entropic method for recognizing matching multimodal images of the same object and investigate the probabilistic dependency between the images of the two modalities based on their conditional probabilities. The results on a real dataset of SAS and optical images of the same and different objects on the seafloor confirm our assumption that the conditional probability of SAS images is different from the marginal probability given an optical image, and show a favorable trade-off between detection and false alarm rate that is higher than current benchmarks. For reproducibility, we share our database. [ABSTRACT FROM AUTHOR]

Accurate measurement and interpretation of serum levels of troponin (Tn) is a central part of the clinical workup of a patient presenting with chest pain suspicious for acute coronary syndrome (ACS). Knowledge of the molecular characteristics of the troponin complex and test characteristics of troponin measurement assays allows for a deeper understanding of causes of false positive and false negative test results in myocardial injury. In this review, we discuss the molecular structure and functions of the constituent proteins of the troponin complex (TnT, TnC, and TnI); review the different isoforms of Tn and where they are from; survey the evolution of clinical Tn assays, ranging from first-generation to high-sensitivity (hs); provide a primer on statistical interpretation of assay results based on different clinical settings; and discuss potential causes of false results. We also summarize the advances in technologies that may lead to the development of future Tn assays, including the development of point of care assays and wearable Tn sensors for real-time continuous measurement. [ABSTRACT FROM AUTHOR]

As an important extension of classical rough sets, local rough set model can effectively process data with noise. How to effectively calculate three approximation regions, namely positive region, negative region and boundary region, is a crucial issue of local rough sets. Existing calculation methods for approximation regions are based on conditional probability, the time complexity is O (|X||U||C|). In order to improve the computational efficiency of three approximation regions of local rough sets, we propose a double-local conditional probability based fast calculation method. First, to improve the computational efficiency of equivalence class, we define the double-local equivalence class. Second, based on the double-local equivalence class, we define the double-local conditional probability. Finally, given the probability thresholds and a local equivalence class, the monotonicity of double-local conditional probability is proved, on this basis, a double-local conditional probability based fast calculation method for approximation regions of local rough sets is proposed, and the time complexity is O (MAX (|X|2|C|, |X||XC||C|)). Experimental results based on 9 datasets from UCI demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

To comprehend the empirical seismic vulnerability capability of various typical structures in towns and suburbs, this study considers, as the research background, the structural damage data observation from the Mw 7.1 Yushu earthquake that occurred on 2010 April 14th in China. The proposed research activity sorts out the actual investigation data (7156 buildings) of five types of typical structures in towns and villages and establishes the vulnerability and seismic fragility evaluation model of a group of buildings considering multidimensional parameters by using the Chinese macroseismic intensity standard. Using spatial modal, numerical calculation, and regression analysis methods, an updated lognormal distribution vulnerability and resilience assessment model based on multidimensional quantitative parameters is performed. Based on the principle of the conditional probability and damage quantification model, an innovative model (domain, point cloud, curve, surface, matrix, and function) is established for regional vulnerability and seismic resilience assessment of typical group buildings. A logarithmic relationship model considering both the updated Chinese macroseismic intensity and three-dimensional composite peak ground acceleration as intensity measures is proposed, and an empirical vulnerability assessment model for typical rural buildings is established. The traditional average earthquake loss index calculation model is updated, and an innovative regional domain vulnerability assessment model is conducted. Taking the samples of various typical structures surveyed in the Yushu earthquake, regional group structure vulnerability domain comparison models of various structures are performed. Ultimately, depending on the typical damage characteristics of structures, the actual damage features and mechanisms of various structures are analysed. [ABSTRACT FROM AUTHOR]

Reliability analysis aims at quantitatively assessing the risks of structures and infrastructure systems considering various sources of aleatory or epistemic uncertainties. This concept can be interpreted as reliability updating (RU) to track the change of risks, fusing new data emerged in the operation period. Optimal allocation of resources can be therefore prepared for reasonable maintenance and rehabilitation. In the state-of-the-art method for RU with equality information, auxiliary random variables are introduced to transform the problem into an inequality one. However, the joint events derived in aforementioned approach are typically very rare, which can be computationally cumbersome via simulation techniques. To enhance the performance of RU with equality information, this paper proposes a new reliability updating approach that decomposes the joint event term into two separate multipliers and subsequently computes conditional probability through subset simulation (SS). Moreover, this work analyzes the statistical properties for RU through SS. An adaptive manner is proposed to dynamically adjust the batch sample size for each subset so that the consistency of simulation results can be ensured. Compared to past SS-based reliability updating approaches, the proposed method is computationally easier to handle and substantially more robust. Three numerical examples together with a practical application of structural health monitoring are investigated to demonstrate the computational superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study properties of a series–parallel system. The component lifetimes may be dependent and non-identically distributed (DNID) discrete random variables. We consider the number of failed components upon system failure. We derive the probability mass function and the expected value of this quantity. In addition, we find the conditional probabilities corresponding to this variate given some partial information about the system failure. We also provide a numerical example to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

Introduction: Software to predict the impact of aging on physical appearance is increasingly popular. But it does not consider the complex interplay of factors that contribute to skin aging. Objectives: To predict the +15‐year progression of clinical signs of skin aging by developing Causal Bayesian Belief Networks (CBBNs) using expert knowledge from dermatologists. Material and methods: Structures and conditional probability distributions were elicited worldwide from dermatologists with experience of at least 15 years in aesthetics. CBBN models were built for all phototypes and for ages ranging from 18 to 65 years, focusing on wrinkles, pigmentary heterogeneity and facial ptosis. Models were also evaluated by a group of independent dermatologists ensuring the quality of prediction of the cumulative effects of extrinsic and intrinsic skin aging factors, especially the distribution of scores for clinical signs 15 years after the initial assessment. Results: For easiness, only models on African skins are presented in this paper. The forehead wrinkle evolution model has been detailed. Specific atlas and extrinsic factors of facial aging were used for this skin type. But the prediction method has been validated for all phototypes, and for all clinical signs of facial aging. Conclusion: This method proposes a skin aging model that predicts the aging process for each clinical sign, considering endogenous and exogenous factors. It simulates aging curves according to lifestyle. It can be used as a preventive tool and could be coupled with a generative AI algorithm to visualize aging and, potentially, other skin conditions, using appropriate images. [ABSTRACT FROM AUTHOR]

The b‐value in earthquake magnitude‐frequency distribution quantifies the relative frequency of large versus small earthquakes. Monitoring its evolution could provide fundamental insights into temporal variations of stress on different fault patches. However, genuine b‐value changes are often difficult to distinguish from artificial ones induced by temporal variations of the detection threshold. A highly innovative and effective solution to this issue has recently been proposed by van der Elst (2021, https://doi.org/10.1029/2020jb021027) by means of the b‐positive estimator, which is based on analyzing only the positive differences in magnitude between successive earthquakes. Here, we demonstrate the robustness of the estimator, which remains largely unaffected by detection issues due to the properties of conditional probability. We illustrate that this robustness can be further improved by considering positive differences in magnitude, not only between successive earthquakes but also between different pairs of earthquakes. This generalized approach, defined as the "b‐more‐positive estimator," enhances efficiency by providing a precise estimate of the b‐value while including a larger number of earthquakes from an incomplete catalog. However, our analysis reveals that the accuracy of the b estimators diminishes when earthquakes below the completeness threshold are included in the catalog. This leads to the paradoxical observation that greater efficiency is achieved when the catalog is more incomplete. To address this, we introduce the "b‐more‐incomplete estimator," where the b‐more‐positive estimator is applied only after artificially filtering the instrumental catalog to make it more incomplete. Our findings show the superior efficiency of the b‐more‐incomplete method. Plain Language Summary: Earthquake magnitudes can vary widely, and the b‐value is a common metric used to measure the frequency of earthquakes with large versus small magnitudes. In addition, the b‐value could serve as an indicator of the stress state of different fault patches, making it a valuable tool in earthquake research. However, since small earthquakes are often obscured by previous larger ones, determining whether changes in the b‐value are genuine or simply caused by detection problems can be challenging. To address this issue, a new approach called the b‐positive estimator has been recently developed. The method only considers positive changes in magnitude between successive earthquakes. In this study, we confirm that the b‐positive estimator is a powerful and effective technique to estimate the b‐value and is largely unaffected by issues related to detecting earthquakes. We extend the method by considering positive differences in magnitude, encompassing not only successive earthquakes but also different pairs of earthquakes. In particular we show that the b‐positive estimator is more efficient when the catalog is more incomplete. This allows us to develop modifications to the b‐positive method providing a more efficient tool to monitor the b‐value in ongoing seismic sequences. Key Points: Conditional probability detecting consecutive earthquakes makes positive magnitude difference distribution weakly affected by incompletenessThe b‐positive estimator can be enhanced by including more earthquake pairs, not only consecutive onesThe b‐positive estimator can be enhanced by making the catalog more incomplete [ABSTRACT FROM AUTHOR]

We propose in this article a new high-dimensional classification method. It is called AFANS and relies on the penalized logistic regression model. It consists of transforming the data using univariate conditional probability functions. The aim is to put more emphasis on the significant features and hence to allow a better classification rule. We estimate the different univariate conditional probability functions using a simple procedure based on the Gini index. In addition to that, we first establish under mild conditions that the misclassification excess risk bound of the sparse logistic regression, with the LASSO penalty, is rate-optimal and then use this to derive the misclassification excess risk bound of AFANS. Finally, a detailed empirical study, to illustrate the advantages of our approach with respect to several competitors, is conducted on both simulated and real data sets. [ABSTRACT FROM AUTHOR]

Recent studies on China's arid and semi-arid regions, particularly the Tarim River Basin (TRB), have shown an increase in the intensity and frequency of extreme weather events. This research examines the link between meteorological droughts, as measured by the Standardized Precipitation Evapotranspiration Index (SPEI), and hydrological droughts, as indicated by the Standardized Runoff Index (SRI) and the Standardized Terrestrial Water Storage Index (STI), over various time scales. Historical data indicate that SPEI drought frequency (DF) was 14.3–21.9%, with prevalent events in the northern oases. SRI DF ranged from 9.0% to 35.8%, concentrated around the Taklamakan and Kumtag Deserts, while STI DF varied between 4.4% and 32.7%, averaging 15% basin-wide. Future projections show an increased DF of SPEI in deserts and a decrease in oases; SRI DF decreased in deserts but increased in oases. STI changes were more moderate. The study also found a higher risk of drought progression from SPEI to SRI in the southwestern and northeastern oases, exceeding 50% probability, while central and eastern TRB had lower risks. The western TRB and inner Taklamakan Desert faced higher risks of SPEI to STI progression, with probabilities over 45%, in contrast to the lower risks in the eastern and central oases. The concurrence of SRI/STI with moderate to extreme SPEI droughts led to a higher probability and area of SRI/STI droughts, whereas consistent SPEI types showed a reduced induced probability and extent of SRI/STI droughts. This study enhances the understanding of drought propagation from meteorological to hydrological droughts in the TRB and contributes to the prevention of hydrological drought to a certain extent. [ABSTRACT FROM AUTHOR]