Joint Probability Research Articles

Use of Bayesian probabilistic model approach in common bean varietal recommendation

AbstractRecommendation of new varieties is supported by value for cultivation and use (Valor de Cultivo e Uso [VCU]) trials. For a more reliable recommendation, it is necessary to identify methodologies that make better use of the genotype‐by‐environment interaction (GEI). The methodology proposed by Dias et al. is an alternative to take advantage of the GEI; it considers concepts of Bayesian models and probability methods of adaptation and stability analysis in a single model, classifying the genotypes regarding possible success based on a defined selection intensity. Thus, the aim of the present study was to explore the use of Bayesian probabilistic method for the purpose of recommend common bean (Phaseolus vulgaris L.) varieties. To that end, we used grain yield data from 15 genotypes of common bean evaluated in 42 environments distributed over different crop seasons, years, and locations in regard to VCU trials conducted from 2016 to 2018. Under a predefined selection intensity of 30%, the genotypes with greater marginal probability of superior performance were G01, G14, G07, G11, and G02. The genotypes with greater marginal probability of superior stability were G06, G07, G04, G03, and G12. Considering the joint probability of superior performance and yield stability, the genotypes G07, G14, G01, G11, and G04 stand out. Therefore, the use of the Bayesian probabilistic method showed promise in recommendation of common bean varieties.

Characterizing the nonmonotonic behavior of mutual information along biochemical reaction cascades.

Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal populations even in identical environments. Experimentally observed joint probability distributions can then be used to quantify the covariability and mutual information between molecular abundances along signaling cascades. However, because stationary state abundances along stochastic biochemical reaction cascades are not conditionally independent, their mutual information is not constrained by the data-processing inequality. Here, we report the conditions under which the mutual information between stationary state abundances increases along a cascade of biochemical reactions. This nonmonotonic behavior can be intuitively understood in terms of noise propagation and time-averaging stochastic fluctuations that are short-lived compared to an extrinsic signal. Our results reemphasize that mutual information measurements of stationary state distributions of cellular components may be of limited utility for characterizing cellular signaling processes because they do not measure information transfer.

Managing uncertainty in product and process design for the circular factory

Abstract In the circular factory, uncertain attributes of object instances and process steps are found at diverse occasions. Even if uncertainty can also be found to some extent in linear production, the high variation of product attributes of used objects causes the process steps in the circular factory to generate a much higher variability of the properties of the objects handled in circular processes. In consequence, a methodology is needed to model, handle and manage uncertainties at all relevant situations within the circular factory. In contrast to linear production, the uncertainty of attributes cannot be extended to an object class (with the same production history), but must be assigned to each object instance (with its own history) individually. In this contribution, the basic concepts for managing uncertainty in the circular factory are introduced. As a common basis, probabilities are used to express uncertainty, thus being compatible with the traditional and proven concepts of measurement science and stochastics. To describe the individual information state of object instances, it is complemented with a joint probability distribution describing all relevant object attributes. Some examples for processes within the circular factory demonstrate how uncertainty is considered to manage the uncertainty related challenges of used objects.

Layer-Wise Mutual Information Meta-Learning Network for Few-Shot Segmentation.

The goal of few-shot segmentation (FSS) is to segment unlabeled images belonging to previously unseen classes using only a limited number of labeled images. The main objective is to transfer label information effectively from support images to query images. In this study, we introduce a novel meta-learning framework called layer-wise mutual information (LayerMI), which enhances the propagation of label information by maximizing the mutual information (MI) between support and query features at each layer. Our approach involves the utilization of a LayerMI Block based on information-theoretic co-clustering. This block performs online co-clustering on the joint probability distribution obtained from each layer, generating a target-specific attention map. The LayerMI Block can be seamlessly integrated into the meta-learning framework and applied to all convolutional neural network (CNN) layers without altering the training objectives. Notably, the LayerMI Block not only maximizes MI between support and query features but also facilitates internal clustering within the image. Extensive experiments demonstrate that LayerMI significantly enhances the performance of baseline and achieves competitive performance compared to state-of-the-art methods on three challenging benchmarks: PASCAL-5 i , COCO-20 i , and FSS-1000.

Bayesian seismic 4D inversion for lithology and fluid prediction

Seismic data acquired at different times over the same area can provide insight into changes in an oil/gas reservoir. Probabilities for pore fluid will typically change while the lithology remains stable over time. This implies significant correlations across the vintages. We have developed a methodology for Bayesian prediction of joint probabilities for discrete lithology-fluid classes (LFCs) for two vintages, simultaneously considering the seismic AVO data of both vintages. By taking into account cross-vintage correlations of elastic and seismic properties, the simultaneous invertion ensures that the individual results for both vintages as well as their differences are consistent and constrained by the seismic data of both vintages. The method relies on prior geological knowledge of stratigraphic layering, possible lithologies and fluids within each layer, and possible cross-vintage changes in lithology and pore fluid. Multiple LFCs can be used to represent different strengths of dynamic cross-vintage changes. We have tested the algorithm on a synthetic data set and on data from the Edvard Grieg field in the central North Sea. Synthetic results demonstrate that the algorithm is able to use dual-vintage data together with a prior model specifying their correlations to calculate joint LFC posterior probabilities for both vintages with a lower degree of uncertainty than independent single-vintage inversions. The Edvard Grieg results indicate that the underlying model is sufficiently general to explain 4D variations in seismic data using a reasonably simple prior model of 4D LFC changes.

Occurrence and risk assessment of quinolones and sulfonamides in freshwater aquaculture ponds in Northeast Zhejiang, China

Antibiotics play an essential role in the aquaculture industry, but their overuse and weak degradability inevitably lead to light to severe residues in natural and aquaculture environments. Most studies were interested in the occurrence, distribution, and ecological risks of a limited number of antibiotics in natural environments (rivers, lakes, and coastal regions) with a minor focus on antibiotic presence in either water, sediments, or organisms in aquaculture environments located in specific regions. In this study, we conducted a comprehensive investigation into the occurrence and distribution of up to 32 antibiotics [including 15 quinolones (QNs) and 17 sulfonamides (SAs)] in organisms and their corresponding environmental matrices from 26 freshwater aquaculture ponds in Northeast Zhejiang, China. A total of 13, 9, 7, and 7 antibiotics were detected in pond water, sediments, feeds, and aquaculture organisms, respectively, with concentration ranges of 0.6–92.2 ng/L, 0.4–1169.3 ng/g dw, <LOD–17.5 ng/g dw, and < LOD–234.3 ng/g ww, respectively, where enrofloxacin (ENR) was the main component in different matrix samples, with a proportion range of 51 %–88 %. There were differences in the predominant antibiotic and concentration abundance among fishponds, shrimp ponds, crab ponds, and turtle ponds. Feed was likely one of the most essential source of antibiotics in freshwater aquaculture ponds. The risk quotient (RQ) results revealed that ciprofloxacin (CIP) and ENR showed high risks to algae in water at the maximum measured concentrations and norfloxacin (NOR), CIP, ENR, and ofloxacin (OFL) exhibited high risks in sediments. However, the joint probability curve (JPC) showed acceptable risk in water. On the basis of the calculated hazard quotients (HQ < 1), the risk of human antibiotic ingestion through aquaculture organisms was acceptable. These results suggest that the rational control of antibiotic use is necessary for human health and ecological security.

Trace elements and heavy metal(loid)s triggering ecological risks in a heavily polluted river-reservoir system of central Mexico: Probabilistic approaches

The contamination of trace elements and heavy metal(loid)s in water bodies has emerged as a global environmental concern due to their high toxicity at low concentrations to both biota and humans. This study aimed to evaluate the ecological risk associated with the occurrence and spatial distribution of Mn, Fe, Co, Cd, Ni, Zn, Sb, As, Tl, Cu, Pb, U, and V in the heavily polluted waters of an important river-reservoir system (Atoyac River Basin) in central Mexico, using two-level tired probabilistic approaches: Risk Quotient based on Species Sensitivity Distribution (RQSSD) and Joint Probability Curves (JPCs). The concentrations of these elements varied widely, ranging from 0.055 μg L−1 to 9200 μg L−1 and from 0.056 μg L−1 to 660 μg L−1, in both total and dissolved fractions, respectively. Although geogenic and anthropogenic sources contribute to the presence of these elements in waters, the discharge of untreated or poorly treated industrial wastewater is the main source of contamination. In this regard, the RQSSD results indicated high ecological risk for Mn, Fe, Co, Ni, Zn, and Sb, and medium or low ecological risk for As, Tl, U, and V at almost all sampling sites. The highest RQSSD values were found downstream of a large industrial corridor for Co, Zn, Tl, Pb, and V, with Tl, Pb, and V escalating to higher risk levels, highlighting the negative impact of industrial contamination on biota. The JPC results for these elements are consistent with the RQSSD approach, indicating an ecological risk to species from Mn, Fe, Co, Ni, Zn, and Sb in waters of the Atoyac River Basin. Therefore, the results of this study offer a thorough assessment of pollution risk, providing valuable insights for legislators on managing and mitigating exposure.

The multiple birth properties of multi-type Markov branching processes

The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time t is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given.

Bounds on galaxy stochasticity from halo occupation distribution modeling

The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce REDMAGIC-like galaxy catalogs within the ABACUSSUMMIT suite of N-body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.

Distribution and ecological risk assessment of perfluoroalkyl carboxylic acids (PFCAs) in the coastal river, China

Perfluoroalkyl carboxylic acids (PFCAs) enter surface waters through wastewater discharge and atmospheric deposition, accumulating within aquatic ecosystems and organisms, causing dysfunction or mortality. This study investigates the migration, sources and ecological risks of six PFCAs in the coastal Wulong River basin and the estuary along the eastern coast of China. The six PFCAs detected in the Wulong River included, at concentrations ranging from 17.36 to 57.92 ng/L. The distribution of PFCAs concentrations throughout the estuary were as follows: Northeast China (414.07 ng/L) > North China (325.97 ng/L) > East China (249.53 ng/L) > South China (63.61 ng/L), with perfluorooctanoic acid (PFOA) being the dominant PFCA. Toxicity data was collected for all detected PFCAs and the species sensitivity distribution (SSD) method was used to derive the predicted no effect concentrations (PNECs) for all six PFCAs. The risk quotient (RQ) method showed that the risk posed to aquatic organisms in the river basin from all six PFCAs was relatively low (RQ < 1). However, joint probability curve (JPC) analysis revealed that the probability of perfluoropentanoic acid (PFPeA) causing harm to 5% of aquatic species reached 41.13%. Considering the frequency of occurrence and persistence of PFCAs in aquatic environments, these findings indicate they have the potential to induce serious toxic effects on aquatic organisms.

Joint identity among loci under mutation and regular inbreeding

This study describes a compact method for determining joint probabilities of identity-by-state (IBS) within and between loci in populations evolving under genetic drift, crossing-over, mutation, and regular inbreeding (partial self-fertilization). Analogues of classical indices of associations among loci arise as functions of these joint identities. This coalescence-based analysis indicates that multi-locus associations reflect simultaneous coalescence events across loci. Measures of association depend on genetic diversity rather than allelic frequencies, as do linkage disequilibrium and its relatives. Scaled indices designed to show monotonic dependence on rates of crossing-over, inbreeding, and mutation may prove useful for interpreting patterns of genome-scale variation.

Practical method for evaluating wind influence on autonomous ship operations (2nd report)

AbstractRecently, a considerable number of research and development projects have focused on automatic vessels. A highly realistic simulator is needed to validate control algorithms for autonomous vessels. For instance, when considering the automatic berthing/unberthing of a vessel, the effect of wind in such low-speed operations cannot be ignored because of the low rudder performance during slow harbor maneuvers. Therefore, a simulator used to validate an automatic berthing/unberthing control algorithm should be able to reproduce the time histories of wind speed and wind direction realistically. Therefore, in our first report on this topic, to obtain the wind speed distribution, we proposed a simple algorithm to generate the time series and distribution of wind speed only from the mean wind speed. However, for wind direction, the spectral distribution could not be determined based on our literature surveys, and hence, a simple method for estimating the coefficients of the stochastic differential equation (SDE) could not be proposed. In this study, we propose a new methodology for generating the time history of wind direction based on the results of Kuwajima et al.’s work. They proposed a regression equation of the standard deviation of wind direction variation for the mean wind speed. In this study, we assumed that the wind direction distribution can be represented by a linear filter as in our previous paper, and its coefficients are derived from Kuwajima’s proposed equation. Then, as in the previous report, the time series of wind speed and wind direction can be calculated easily by analytically solving the one-dimensional SDE. The joint probability density functions of wind speed and wind direction obtained by computing them independently agree well with the measurement results.

Axiomatization of interventional probability distributions

Abstract Causal intervention is an essential tool in causal inference. It is axiomatized under the rules of do-calculus in the case of structure causal models. We provide simple axiomatizations for families of probability distributions to be different types of interventional distributions. Our axiomatizations neatly lead to a simple and clear theory of causality that has several advantages: it does not need to make use of any modelling assumptions such as those imposed by structural causal models; it only relies on interventions on single variables; it includes most cases with latent variables and causal cycles; and more importantly, it does not assume the existence of an underlying true causal graph as we do not take it as the primitive object; moreover, a causal graph is derived as a by-product of our theory. We show that, under our axiomatizations, the intervened distributions are Markovian to the defined intervened causal graphs, and an observed joint probability distribution is Markovian to the obtained causal graph; these results are consistent with the case of structural causal models, and as a result, the existing theory of causal inference applies. We also show that a large class of natural structural causal models satisfy the theory presented here. The aim of this paper is axiomatization of interventional families, which is subtly different from causal modelling.

Optimizing Distributions for Associated Entropic Vectors via Generative Convolutional Neural Networks.

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed.

Impossibility of adversarial self-testing and secure sampling

Self-testing is the task where spatially separated Alice and Bob cooperate to deduce the inner workings of untrusted quantum devices by interacting with them in a classical manner. We examine the task above where Alice and Bob do not trust each other which we call adversarial self-testing. We show that adversarial self-testing implies secure sampling—a simpler task that we introduce where distrustful Alice and Bob wish to sample from a joint probability distribution with the guarantee that an honest party's marginal is not biased. By extending impossibility results in two-party quantum cryptography, we give a simple proof that both of these tasks are impossible in all but trivial settings. Published by the American Physical Society 2024

Predicting the Performance of Ensemble Classification Using Conditional Joint Probability

In many machine learning applications, there are many scenarios when performance is not satisfactory by single classifiers. In this case, an ensemble classification is constructed using several weak base learners to achieve satisfactory performance. Unluckily, the construction of the ensemble classification is empirical, i.e., to try an ensemble classification and if performance is not satisfactory then discard it. In this paper, a challenging analytical problem of the estimation of ensemble classification using the prediction performance of the base learners is considered. The proposed formulation is aimed at estimating the performance of ensemble classification without physically developing it, and it is derived from the perspective of probability theory by manipulating the decision probabilities of the base learners. For this purpose, the output of a base learner (which is either true positive, true negative, false positive, or false negative) is considered as a random variable. Then, the effects of logical disjunction-based and majority voting-based decision combination strategies are analyzed from the perspective of conditional joint probability. To evaluate the forecasted performance of ensemble classifier by the proposed methodology, publicly available standard datasets have been employed. The results show the effectiveness of the derived formulations to estimate the performance of ensemble classification. In addition to this, the theoretical and experimental results show that the logical disjunction-based decision outperforms majority voting in imbalanced datasets and cost-sensitive scenarios.

A Robust Wind Turbine Component Health Status Indicator

Wind turbine components’ failure prognosis allows wind farm owners to apply predictive maintenance techniques to their fleets. Determining the health status of a turbine’s component typically requires verifying many variables that should be monitored simultaneously. The scope of this study is the selection of the more relevant variables and the generation of a health status indicator (Failure Index) to be considered as a decision criterion in Operation and Maintenance activities. The proposed methodology is based on Gaussian Mixture Copula Models (GMCMs) combined with a smoothing method (Cubic spline smoothing) to define a component’s health index based on the previous behavior and relationships between the considered variables. The GMCM allows for determining the component’s status in a multivariate environment, providing the selected variables’ joint probability and obtaining an easy-to-track univariate health status indicator. When the health of a component is degrading, anomalous behavior becomes apparent in certain Supervisory Control and Data Acquisition (SCADA) signals. By monitoring these SCADA signals using this indicator, the proposed anomaly detection method could capture the deviations from the healthy working state. The resulting indicator shows whether any failure is likely to occur in a wind turbine component and would aid in a preventive intervention scheduling.

Correlation analysis and joint probability density function model of wind pressures: Focusing on multivariate wind loads field on low-rise building under typhoon climate

The characteristics of the multivariate wind loads field on the roof are crucial to the wind-resistant design of low-rise buildings, which contain the correlation characteristics in space and probability characteristics in the time domain. This paper proposes a framework for constructing a Joint Probability Density Function (Joint PDF) model for a multivariate wind loads field. It provides a detailed correlation analysis for the first time. This paper employs wind pressure data collected from the roof of a low-rise building during Typhoon Muifa. It was found that the correlation becomes more robust with increasing roof pitch and the wind pressures are strongly correlated with a correlation coefficient exceeding 0.50 when the roof pitch is above 15°. The mixture distribution model is applied to the probability density function fitting procedure of wind pressure time series under typhoon climate, and the fitting effect is significantly better than other classical probability density functions. The optimal copula function is determined according to the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for estimating the Joint PDF. The results reveal that Gumbel-copula and Student-copula have the highest proportion in optimal copula functions, accounting for over 90% of the total copula functions. Then, a bivariate Joint PDF for wind pressures are established with the optimal copula function. Additionally, the comparison between measured bivariate Joint PDF and that constructed using copula functions verifies the accuracy of the proposed framework for constructing Joint PDFs. The Joint PDF of wind pressures can enhance the understanding of the stochastic characteristics of local wind load fields on roofs, and the correlation characteristics in space provide crucial references for improving the accuracy of wind load random field simulation and saving the cost of wind resistance design.

Survival probability surfaces of hysteretic fractional order structures exposed to non-stationary code-compliant stochastic seismic excitation

A novel first-passage probability stochastic incremental dynamics analysis (SIDA) methodology tailored for hysteretic fractional order structural systems under a fully non-stationary seismic excitation vector consistently designated with contemporary aseismic codes provisions (e.g., Eurocode 8) is developed. Specifically, the vector of the imposed seismic excitations is characterised by evolutionary power spectra that stochastically align with aseismic codes elastic response acceleration spectra, defined for specified modal damping ratios and scaled ground accelerations. Leveraging the concepts of stochastic averaging and statistical linearization, the approximative non-stationary response displacement joint probability density function (PDF) is derived, retaining the particularly coveted attribute of computational efficacy. Subsequently, the coupling with the survival probability model allows for the efficient determination of the response first-passage time probability density surfaces and the survival probability surfaces across various limit-state rules and scalable intensity measures. The first-passage time probability serves as a robust engineering demand parameter, effectively monitoring structural behaviour by considering both intensity and timing information, while inherently aligned with pertinent limit-state requirements. Notably, the associated low computational cost and the ability to handle a wide range of complex nonlinear/hysteretic structural behaviours, coupled with its compliance with modern aseismic codes, underscore its potential for applications in the fields of structural and earthquake engineering. A nonlinear system endowed with fractional derivative elements is used to exemplify the method’s reliability. The accuracy of the proposed method is validated in a Monte Carlo-based context, conducting nonlinear response time–history analyses with an extensive ensemble of accelerograms compatible with Eurocode 8 response acceleration spectra.

Multi-Channel Multi-Scale Convolution Attention Variational Autoencoder (MCA-VAE): An Interpretable Anomaly Detection Algorithm Based on Variational Autoencoder.

With the rapid development of industry, the risks factories face are increasing. Therefore, the anomaly detection algorithms deployed in factories need to have high accuracy, and they need to be able to promptly discover and locate the specific equipment causing the anomaly to restore the regular operation of the abnormal equipment. However, the neural network models currently deployed in factories cannot effectively capture both temporal features within dimensions and relationship features between dimensions; some algorithms that consider both types of features lack interpretability. Therefore, we propose a high-precision, interpretable anomaly detection algorithm based on variational autoencoder (VAE). We use a multi-scale local weight-sharing convolutional neural network structure to fully extract the temporal features within each dimension of the multi-dimensional time series. Then, we model the features from various aspects through multiple attention heads, extracting the relationship features between dimensions. We map the attention output results to the latent space distribution of the VAE and propose an optimization method to improve the reconstruction performance of the VAE, detecting anomalies through reconstruction errors. Regarding anomaly interpretability, we utilize the VAE probability distribution characteristics, decompose the obtained joint probability density into conditional probabilities on each dimension, and calculate the anomaly score, which provides helpful value for technicians. Experimental results show that our algorithm performed best in terms of F1 score and AUC value. The AUC value for anomaly detection is 0.982, and the F1 score is 0.905, which is 4% higher than the best-performing baseline algorithm, Transformer with a Discriminator for Anomaly Detection (TDAD). It also provides accurate anomaly interpretation capability.