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After a brief review of electronic nose technology, the use of an Australian electronic nose to identify an unknown odour out of a set of known odours is described. Multivariate supervised learning is accomplished by applying Bayes' theorem to data from metal oxide semiconductor sensors responding to each of a number of target odours. An odour from an unknown source is then assigned a probability of membership of each of the training sets by applying either a Naïve Bayes algorithm to the deemed independent data from each sensor, or to a multinormal distribution of the data. A flat prior (equal probabilities of each outcome) is usually adopted, but for particular situations where one odour is known to predominate, then suitably weighted priors can be used. A source 'none of the above', which has a small likelihood covering the space of the possible sensor responses, is included for completeness. This also avoids the assignment to a source that has an extremely small probability but which is greater than that of any other source. Examples are given of a single source (detecting diabetes from a patient's breath), and three sources of unpleasant odours in a meat processing plant. The 18th century cleric Thomas Bayes gave his name to an elegant statement of the probability of an event – in this case identification of an odour – given some evidence: output from a number of metal oxide semiconductor sensors. Knowing the distributions of outputs for target odours, we assign the probabilities of an unknown odour. The greatest probability wins! (Image credit: E-nose Pty Ltd and D. B. Hibbert.) This article belongs to the 10th Anniversary Collection of RACI and AAS Award papers. [ABSTRACT FROM AUTHOR]

The task of incremental learning is to enable machine learning models to continuously learn and adapt to new tasks and data in changing environments while maintaining knowledge of prior tasks. Recently, researchers have proposed a variety of incremental learning methods. Some methods rely on data storage or complex generative models to perform satisfactorily. However, existing incremental learning approaches typically focus on mitigating catastrophic forgetting, with less emphasis on effectively applying old knowledge to facilitate learning new tasks. In this paper, we propose a non-exemplar-based incremental learning approach called Class-Incremental Learning via Prototype Similarity Replay and Similarity-adjusted Regularization (PSSR) to tackle catastrophic forgetting in incremental learning. The essence of PSSR is leveraging prior knowledge of prior tasks to facilitate the acquisition of new tasks. PSSR memorizes a prototype for each old class, representing the class, and learns the new classes based on the similarity between the prototypes and the new class samples during the learning process. The feature space distribution is modified by the old class prototypes to enhance the model's learning of the new classes. Extensive experiments on three benchmark datasets demonstrate the superior incremental performance of PSSR, with classification accuracy improvements of 2.73%, 3.37%, and 4.21% over state-of-the-art methods. Code available at https://github.com/FutureIAI/PSSR. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the state estimation problem and structure identification problem are investigated for an array of complex networks with time‐varying delays and model uncertainty. Model uncertainty is generated by uncertain connections between nodes in complex networks. Combining probabilistic graph model and graph neural network, a probabilistic graph neural network is proposed to deal with the uncertainty, and the multiple linear terms of the errors between nodes are estimated. The purpose of the addressed state estimation problem is to design a state estimator such that, in the presence of the model uncertainty, the estimation error to converge to zero can be guaranteed and the explicit expression of the estimator parameters is given. Based on a Lyapunov function, the parameters of the estimator and the updating laws of the weights of probabilistic graph neural network can be obtained by the solutions to linear matrix inequalities. The purpose of the addressed structure identification problem is to infer a definite graph structure model based on Bayes' theorem in the presence of a stable probabilistic graph neural network and state estimator. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation and structure identification scheme. [ABSTRACT FROM AUTHOR]

Many U.S. states require election workers to check signatures on ballots returned by mail, causing tens of thousands of ballots to be rejected at each general election. This paper applies Bayes' theorem, along with findings from prior research, to show how rejection rates are likely to vary under plausible assumptions about signature checker accuracy and the prevalence of invalid signatures. This approach yields a pair of predictions. On the one hand, given findings from research on handwriting forensics, the Bayesian analysis implies election workers are more likely to wrongly reject valid ballots for purported signature mismatch than to correctly reject invalidly signed returns. On the other hand, research on election workers as problem-solvers suggests they may try to minimize the wrongful rejection of ballots. I find empirical support for each prediction, including signs that election workers learn from past errors to calibrate signature rejection rates downwards. This suggests election worker discretion may be an unexpected source of resilience against laws otherwise liable to disenfranchise eligible voters, although I also discuss conditions under which such discretion may conflict with democratic norms. [ABSTRACT FROM AUTHOR]

In robust parameter design, model parameter uncertainty and quality of experimental data often affect the establishment of response surface models, which in turn affect the acquisition of the optimal operating conditions. This paper proposes a robust multi-response surface modelling and optimisation method based on Bayesian quantile regression, which is a robust regression technique insensitive to outliers, to address the above problems. We first incorporate quantile regression into the Bayesian framework and use Bayes's theorem to obtain posterior inference of model parameters. Then, the Monte Carlo-based expectation maximisation algorithm is used to estimate the model parameters, and the entropy-based overall desirability function is taken asan optimisation objective to obtain the optimal settings. The effectiveness of the proposed method is demonstrated by an additive manufacturing process anda simulation study. Compared with other existing methods, the proposed method can resist the disturbance of outliers, and thus obtain more accurate optimisation results. [ABSTRACT FROM AUTHOR]

Abstract The failure of water pipes in Water Distribution Networks (WDNs) is associated with environmental, economic, and social consequences. It is essential to mitigate these failures by analyzing the historical data of WDNs. The extant literature regarding water pipe failure analysis is limited by the absence of a systematic selection of significant factors influencing water pipe failure and eliminating the bias associated with the frequency distribution of the historical data. Hence, this study presents a new framework to address the existing limitations. The framework consists of two algorithms for categorical and numerical factors influencing pipe failure. The algorithms are employed to check the relevance between the pipe’s failure and frequency distributions in order to select the most significant factors. The framework is applied to Hong Kong WDN, selecting 10 out of 21 as significant factors influencing water pipe failure. The likelihood feature method and Bayes’ theorem are applied to estimate failure probability due to the pipe materials and the factors. The results indicate that galvanized iron and polyethylene pipes are the most susceptible to failure in the WDN. The proposed framework enables decision-makers in the water infrastructure industry to effectively prioritize their networks’ most significant failure factors and allocate resources accordingly.

The increasing proliferation of cyber-attacks threatening the security of computer networks has driven the development of more effective methods for identifying malicious network flows. The inclusion of statistical laws, such as Benford's Law, and distance functions, applied to the first digits of network flow metadata, such as IP addresses or packet sizes, facilitates the detection of abnormal patterns in the digits. These techniques also allow for quantifying discrepancies between expected and suspicious flows, significantly enhancing the accuracy and speed of threat detection. This paper introduces a novel method for identifying and analyzing anomalies within computer networks. It integrates Benford's Law into the analysis process and incorporates a range of distance functions, namely the Mean Absolute Deviation (MAD), the Kolmogorov–Smirnov test (KS), and the Kullback–Leibler divergence (KL), which serve as dispersion measures for quantifying the extent of anomalies detected in network flows. Benford's Law is recognized for its effectiveness in identifying anomalous patterns, especially in detecting irregularities in the first digit of the data. In addition, Bayes' Theorem was implemented in conjunction with the distance functions to enhance the detection of malicious traffic flows. Bayes' Theorem provides a probabilistic perspective on whether a traffic flow is malicious or benign. This approach is characterized by its flexibility in incorporating new evidence, allowing the model to adapt to emerging malicious behavior patterns as they arise. Meanwhile, the distance functions offer a quantitative assessment, measuring specific differences between traffic flows, such as frequency, packet size, time between packets, and other relevant metadata. Integrating these techniques has increased the model's sensitivity in detecting malicious flows, reducing the number of false positives and negatives, and enhancing the resolution and effectiveness of traffic analysis. Furthermore, these techniques expedite decisions regarding the nature of traffic flows based on a solid statistical foundation and provide a better understanding of the characteristics that define these flows, contributing to the comprehension of attack vectors and aiding in preventing future intrusions. The effectiveness and applicability of this joint method have been demonstrated through experiments with the CICIDS2017 public dataset, which was explicitly designed to simulate real scenarios and provide valuable information to security professionals when analyzing computer networks. The proposed methodology opens up new perspectives in investigating and detecting anomalies and intrusions in computer networks, which are often attributed to cyber-attacks. This development culminates in creating a promising model that stands out for its effectiveness and speed, accurately identifying possible intrusions with an F1 of nearly 80 % , a recall of 99.42 % , and an accuracy of 65.84 % . [ABSTRACT FROM AUTHOR]

This paper proposed a prediction algorithm for the degraded actuator taking into account the impact of estimation error of hidden index in the closed-loop system. To this end, a unified prediction framework is established to evaluate the hidden degradation information and recursively update the degradation model parameters simultaneously. The advantage is that the prediction framework can comprehensively compensate the estimation error of hidden degradation index caused by system uncertainty. To jointly estimate the degradation information in avoidance of the impact of system uncertainty, a modified adaptive Kalman filter is designed, and the proof of stability is provided. With the priori estimate from the filter, the degradation model parameters are updated by the inverse filtering probability based on Bayes' theorem. It is followed by the computation of the remaining useful life (RUL) prediction utilizing aforementioned hidden degradation information and the latest degradation model. The effectiveness of the proposed RUL prediction algorithm is demonstrated by the degraded actuator in the continuous casting process. • A novel prediction framework is designed for degraded actuator in closed-loop system. • Adaptive degradation model is established by modified adaptive Kalman filter. • The estimation error of hidden degradation index is integrated. • The stability of optimized adaptive Kalman filter is proven. • Recursive prediction algorithm is performed without full life data. [ABSTRACT FROM AUTHOR]

End-to-end (E2E) automatic speech recognition (ASR) models, which consist of deep learning models, are able to perform ASR tasks using a single neural network. These models should be trained using a large amount of data; however, collecting speech data which matches the targeted speech domain can be difficult, so speech data is often used that is not an exact match to the target domain, resulting in lower performance. In comparison to speech data, in-domain text data is much easier to obtain. Thus, traditional ASR systems use separately trained language models and HMM-based acoustic models. However, it is difficult to separate language information from an E2E ASR model because the model learns both acoustic and language information in an integrated manner, making it very difficult to create E2E ASR models for specialized target domain which are able to achieve sufficient recognition performance at a reasonable cost. In this paper, we propose a method of replacing the language information within pre-trained E2E ASR models in order to achieve adaptation to a target domain. This is achieved by deleting the "implicit" language information contained within the ASR model by subtracting the source-domain language model trained with a transcription of the ASR's training data in a logarithmic domain. We then integrate a target domain language model through addition in the logarithmic domain. This subtraction and addition to replace of the language model is based on Bayes' theorem. In our experiment, we first used two datasets of the Corpus of Spontaneous Japanese (CSJ) to evaluate the effectiveness of our method. We then we evaluated our method using the Japanese Newspaper Article Speech (JNAS) and CSJ corpora, which contain audio data from the read speech and spontaneous speech domain, respectively, to test the effectiveness of our proposed method at bridging the gap between these two language domains. Our results show that our proposed language model replacement method achieved better ASR performance than both non-adapted (baseline) ASR models and ASR models adapted using the conventional Shallow Fusion method. [ABSTRACT FROM AUTHOR]

Reliable drought prediction should be preceded to prevent damage from potential droughts. In this context, this study developed a hydrological drought prediction method, namely ensemble drought prediction (EDP) to reflect drought-related information under the ensemble streamflow prediction framework. After generating an ensemble of standardized runoff index by converting the ensemble of generated streamflow, the results were adopted as the prior distribution. Then, precipitation forecast and soil moisture were used to update the prior EDP. The EDP + A model included the precipitation forecast with the PDF-ratio method, and the observed soil moisture index was reflected in the former EDP and EDP + A via Bayes' theorem, resulting in the EDP + S and EDP + AS models. Eight basins in Korea with more than 30 years of observation data were applied with the proposed methodology. As a result, the overall performance of the four EDP models yielded improved results than the climatological prediction. Moreover, reflecting soil moisture yielded improved evaluation metrics during short-term drought predictions, and in basins with larger drainage areas. Finally, the methodology presented in this study was more effective during periods with less intertemporal variabilities. [ABSTRACT FROM AUTHOR]

Decision makers are often interested in assigning alternatives to preference classes under multiple criteria instead of choosing the best alternative or ranking all the alternatives. Firms need to categorize suppliers based on performance, credit agencies need to classify customers according to their risks, and graduate programs need to decide who to admit. In this article, we develop an interactive Bayesian algorithm to aid a decision maker (DM) with a multicriteria sorting problem by learning about her preferences and using that knowledge to sort alternatives. We assume the DM has a linear value function and value thresholds for preference classes. Our method specifies an informative prior distribution on the uncertain parameters. At each stage of the process, we compare the expected cost of stopping with the expected cost of continuing to consult the DM. If it is optimal to continue, we select an alternative to present to the DM and, given the DM's response, we update the prior distribution using Bayes' Theorem. The goal of the algorithm is to minimize expected total cost. We develop lower bounds on the optimal cost and study the performance of a heuristic policy that presents the DM alternatives with the highest expected cost of misplacement. [ABSTRACT FROM AUTHOR]

Studying cloud-to-ground lightning strokes and ground-strike points provides an alternative method of lightning mapping for lightning risk assessment. Various k-means algorithms have been used to verify the ground-strike points from lightning locating systems, producing results with room for improvement. This paper proposes using Bayesian networks (BNs), a model not previously used for this purpose, to classify lightning ground-strike points. A Bayesian network is a probabilistic graphical model that uses Bayes' theorem to represent the conditional dependencies of variables. The networks created for this research were trained from the data using a score-based structure-learning procedure and the Bayesian information criterion score function. The models were evaluated using confusion matrices and kappa indices and produced accuracy values ranging from 86% to 94% and kappa indices of up to 0.76. While BN models do not outperform k-means algorithms, they offer an alternative by not requiring predetermined distances. However, the easy implementation of the k-means approach means that no significant gain is made by implementing the more complex Bayesian network approach. [ABSTRACT FROM AUTHOR]

The total aviation effective radiative forcing is dominated by non-CO2 effects. The largest contributors to the non-CO2 effects are contrails and contrail cirrus. There is the possibility of reducing the climate effect of aviation by avoiding flying through ice-supersaturated regions (ISSRs), where contrails can last for hours (so-called persistent contrails). Therefore, a precise prediction of the specific location and time of these regions is needed. But a prediction of the frequency and degree of ice supersaturation (ISS) on cruise altitudes is currently very challenging and associated with great uncertainties because of the strong variability in the water vapour field, the low number of humidity measurements at the air traffic altitude, and the oversimplified parameterisations of cloud physics in weather models. Since ISS is more common in some dynamical regimes than in others, the aim of this study is to find variables/proxies that are related to the formation of ISSRs and to use these in a regression method to predict persistent contrails. To find the best-suited proxies for regressions, we use various methods of information theory. These include the log-likelihood ratios, known from Bayes' theorem, a modified form of the Kullback–Leibler divergence, and mutual information. The variables (the relative humidity with respect to ice, RH iERA5 ; the temperature, T ; the vertical velocity, ω ; the divergence, DIV; the relative vorticity, ζ ; the potential vorticity, PV; the normalised geopotential height, Z ; and the local lapse rate, γ) come from ERA5, and RH iM/I , which we assume as the truth, comes from MOZAIC/IAGOS (Measurement of Ozone and Water Vapour on Airbus In-service Aircraft/In-service Aircraft for a Global Observing System; commercial aircraft measurements). It turns out that RH iERA5 is the most important predictor of ice supersaturation, in spite of its weaknesses, and all other variables do not help much to achieve better results. Without RH iERA5 , a regression to predict ISSRs is not successful. Certain modifications of RH iERA5 before the regression (as suggested in recent papers) do not lead to improvements of ISSR prediction. Applying a sensitivity study with artificially modified RH iERA5 distributions points to the origin of the problems with the regression: the conditional distributions of RH iERA5 (conditioned on ISS and non-ISS, from RH iM/I) overlap too heavily in the range of 70 %–100 %, so for any case in that range, it is not clear whether it belongs to an ISSR or not. Evidently, this renders the prediction of contrail persistence very difficult. [ABSTRACT FROM AUTHOR]

This study presents a cluster-based Bayesian methodology for state estimation under realistic conditions including noisy data from sparse sensors. The proposed approach is interpretable and, building upon previous work on transition networks, explicitly accounts for experimental noise within the data-driven framework by means of data clustering. Experimental measurements are exploited, beyond model training, to quantify the degree of uncertainty (noise) for each trained state. Such noise levels are eventually associated with probability distributions that, when combined with Bayes' theorem, allow us to perform real-time state estimation. The proposed methodology is tested on two cases of challenging flows generated by an accelerating elliptical plate and also a delta wing experiencing gusts. Results specifically indicate that the proposed approach is robust against the number of clusters, enabling state estimation with a significant order reduction, notably decreasing the computational cost while preserving estimation accuracy. Based on the present findings, the proposed data-driven approach can be employed for realistic state estimation in nonlinear systems where noise, sensor sparsity and nonlinearities represent a challenging scenario. [ABSTRACT FROM AUTHOR]

The microbiological monitoring of bivalve mollusk harvesting areas in the Marche region is based on the parameters of Escherichia coli and Salmonella spp. However, Regulation EU/2019/627 stated criteria based on E. coli only to determine the health status of these areas. Therefore, the reason for Salmonella spp. monitoring, as provided in the Marche region, could be aimed at reducing the risk of placing on the market contaminated bivalve mollusks. This study, using the results of microbiological monitoring carried out in the Marche region from 2015 to 2022 and the methods based on Bayes' theorem and Poisson's distribution, evaluated the effectiveness and efficiency of Salmonella spp. monitoring in reducing the risk to the consumer. The results show that i) the use of a single sample unit significantly reduced the possibility of detecting non-compliance with the microbiological safety criterion; ii) the time taken to report positive results (average of approximately 10 days) did not allow the timely implementation of control measures; iii) the prevalence of positive outcomes was quite sporadic: a random trend of positivity is recognizable on a geographical and monthly basis for mussels and a geographical basis for striped clams; iv) considering the predictive value of E. coli against Salmonella spp., the specificity is very high and the negative predictive value versus Salmonella spp. would be >80%. In conclusion, the study shows that the monitoring of Salmonella spp. has a limited effect on reducing the risk to the consumer; however, in the cost/benefit assessment, other aspects not covered by this study should be considered. [ABSTRACT FROM AUTHOR]

This article provides an overview of the German tank problem, which involves estimating the size of a population of tanks based on a random sample. It explains the Bayesian approach to solving the problem, which incorporates prior information and quantifies uncertainty. The article also discusses generalizations and variants of the problem, as well as the use of simulations and linear regression in estimation. It is a valuable resource for researchers and educators interested in statistical estimation and combinatorics. The text also explores the concept of prior distribution and likelihood function, and explains the data-generating process and the sample space of possible outcomes. It discusses the posterior distribution, which assigns a probability to each possible tank population size based on the data and prior beliefs. The text suggests summarizing the posterior distribution with a point estimate and a credible subset of the population size. It also provides an example and discusses the sensitivity of the posterior to the prior and the impact of capturing more tanks on reducing uncertainty. The text concludes with simulations to investigate the behavior of the posterior distribution under a known population size. It also explores the concept of selection bias in the tank-capturing process and suggests alternative methods to reduce vulnerability to serial number analysis. [Extracted from the article]

Strategies for sustaining cooperation and preventing exploitation by selfish agents in repeated games have mostly been restricted to Markovian strategies where the response of an agent depends on the actions in the previous round. Such strategies are characterized by lack of learning. However, learning from accumulated evidence over time and using the evidence to dynamically update our response is a key feature of living organisms. Bayesian inference provides a framework for such evidence-based learning mechanisms. It is therefore imperative to understand how strategies based on Bayesian learning fare in repeated games with Markovian strategies. Here, we consider a scenario where the Bayesian player uses the accumulated evidence of the opponent's actions over several rounds to continuously update her belief about the reactive opponent's strategy. The Bayesian player can then act on her inferred belief in different ways. By studying repeated Prisoner's dilemma games with such Bayesian inferential strategies, both in infinite and finite populations, we identify the conditions under which such strategies can be evolutionarily stable. We find that a Bayesian strategy that is less altruistic than the inferred belief about the opponent's strategy can outperform a larger set of reactive strategies, whereas one that is more generous than the inferred belief is more successful when the benefit-to-cost ratio of mutual cooperation is high. Our analysis reveals how learning the opponent's strategy through Bayesian inference, as opposed to utility maximization, can be beneficial in the long run, in preventing exploitation and eventual invasion by reactive strategies. [ABSTRACT FROM AUTHOR]

Bayesian networks (BNs) are probabilistic graphical models that leverage Bayes' theorem to portray dependencies and cause-and-effect relationships between variables. These networks have gained prominence in the field of health sciences, particularly in diagnostic processes, by allowing the integration of medical knowledge into models and addressing uncertainty in a probabilistic manner. Objectives: This review aims to provide an exhaustive overview of the current state of Bayesian networks in disease diagnosis and prognosis. Additionally, it seeks to introduce readers to the fundamental methodology of BNs, emphasising their versatility and applicability across varied medical domains. Employing a meticulous search strategy with MeSH descriptors in diverse scientific databases, we identified 190 relevant references. These were subjected to a rigorous analysis, resulting in the retention of 60 papers for in-depth review. The robustness of our approach minimised the risk of selection bias. Results: The selected studies encompass a wide range of medical areas, providing insights into the statistical methodology, implementation feasibility, and predictive accuracy of BNs, as evidenced by an average area under the curve (AUC) exceeding 75%. The comprehensive analysis underscores the adaptability and efficacy of Bayesian networks in diverse clinical scenarios. The majority of the examined studies demonstrate the potential of BNs as reliable adjuncts to clinical decision-making. The findings of this review affirm the role of Bayesian networks as accessible and versatile artificial intelligence tools in healthcare. They offer a viable solution to address complex medical challenges, facilitating timely and informed decision-making under conditions of uncertainty. The extensive exploration of Bayesian networks presented in this review highlights their significance and growing impact in the realm of disease diagnosis and prognosis. It underscores the need for further research and development to optimise their capabilities and broaden their applicability in addressing diverse and intricate healthcare challenges. [ABSTRACT FROM AUTHOR]

The article focuses on the importance of understanding why things happen for effective problem-solving, utilizing Bayes' theorem to uncover hidden cause-and-effect relationships. Topics include the challenges of finding true causes; the two ways of thinking about causes and effects (forward and inverse); tools like fishbone diagrams for structured problem-solving; and demonstrating how Bayes' theorem can be applied in root cause analysis, like analyzing inflation causes and medical diagnoses.

The article examines the evaluation of the Kidney Failure Risk Equation (KFRE) in predicting the risk of kidney replacement therapy in patients with chronic kidney disease. The study finds that while the KFRE is effective in identifying patients with a low risk of requiring referral to a nephrologist, it has limitations in accurately predicting high-risk patients. The authors suggest exploring alternative methods to improve the accuracy of risk prediction. The study was funded by commercial partners, and the opinions expressed are those of the authors. [Extracted from the article]

Abstract The individual results of SARS-CoV-2 serological tests measured after the first pandemic wave of 2020 cannot be directly interpreted as a probability of having been infected. Plus, these results are usually returned as a binary or ternary variable, relying on predefined cut-offs. We propose a Bayesian mixture model to estimate individual infection probabilities, based on 81,797 continuous anti-spike IgG tests from Euroimmun collected in France after the first wave. This approach used serological results as a continuous variable, and was therefore not based on diagnostic cut-offs. Cumulative incidence, which is necessary to compute infection probabilities, was estimated according to age and administrative region. In France, we found that a “negative” or a “positive” test, as classified by the manufacturer, could correspond to a probability of infection as high as 61.8% or as low as 67.7%, respectively. “Indeterminate” tests encompassed probabilities of infection ranging from 10.8 to 96.6%. Our model estimated tailored individual probabilities of SARS-CoV-2 infection based on age, region, and serological result. It can be applied in other contexts, if estimates of cumulative incidence are available.

Summary: Opportunistic network (OppNet) belongs to the category of Mobile Ad‐hoc Networks (MANETs), a kind of Delay Tolerant Network (DTN), where the wireless nodes are completely mobile and the data transmission routes are dynamic. The major challenge in developing a routing model for such a network is the unpredictable nature of the movement of the nodes. In this paper, a spatiotemporal prediction model based on human mobility pattern is proposed using Bayesian posterior probability (BPPR) where several clusters are identified within the network and the day and time duration of nodes visiting those clusters are recorded. The Bayesian posterior probability is then used to determine the probability of the neighbor node visiting the destination's cluster. If the calculated probability for that node is higher than a specified threshold, the packet will be forwarded. A comparison of the results obtained on simulation is made with benchmark models—Epidemic, Prophet, HBPR, EDR, NexT, and EBC, to name a few, where it is found that on average the proposed model outperforms the other models in terms of delivery probability, hop count and number of messages dropped by around 23.89%, 24.8%, 24.4%, 37%, 11%, and 42% respectively, with varying number of nodes, TTL, message generation interval, and buffer size. Similar improvements have been observed in terms of the other two metrics. In terms of overhead ratio, the proposed model outperforms Epidemic, Prophet, HBPR, NexT, and EBC. However, as the number of nodes and TTL are varied, BPPR performs better than NexT by around 9% and 12%, respectively, in terms of average latency. [ABSTRACT FROM AUTHOR]

Improved adaptive type-II progressive censoring schemes (IAT-II PCS) are increasingly being used to estimate parameters and reliability characteristics of lifetime distributions, leading to more accurate and reliable estimates. The logistic exponential distribution (LED), a flexible distribution with five hazard rate forms, is employed in several fields, including lifetime, financial, and environmental data. This research aims to enhance the accuracy and reliability estimation capabilities for the logistic exponential distribution under IAT-II PCS. By developing novel statistical inference methods, we can better understand the behavior of failure times, allow for more accurate decision-making, and improve the overall reliability of the model. In this research, we consider both classical and Bayesian techniques. The classical technique involves constructing maximum likelihood estimators of the model parameters and their asymptotic covariance matrix, followed by estimating the distribution's reliability using survival and hazard functions. The delta approach is used to create estimated confidence intervals for the model parameters. In the Bayesian technique, prior information about the LED parameters is used to estimate the posterior distribution of the parameters, which is derived using Bayes' theorem. The model's reliability is determined by computing the posterior predictive distribution of the survival or hazard functions. Extensive simulation studies and real-data applications assess the effectiveness of the proposed methods and evaluate their performance against existing methods. [ABSTRACT FROM AUTHOR]

Studies have demonstrated the potential of satellite thermal infrared observations to detect anomalous signals preceding large earthquakes. However, the lack of well-defined precursory characteristics and inherent complexity and stochasticity of the seismicity continue to impede robust earthquake forecasts. This study investigates the potential of pre-seismic thermal anomalies, derived from five satellite-based geophysical parameters, i.e., skin temperature, air temperature, total integrated column water vapor burden, outgoing longwave radiation (OLR), and clear-sky OLR, as valuable indicators for global earthquake forecasts. We employed a spatially self-adaptive multiparametric anomaly identification scheme to refine these anomalies, and then estimated the posterior probability of an earthquake occurrence given observed anomalies within a Bayesian framework. Our findings reveal a promising link between thermal signatures and global seismicity, with elevated forecast probabilities exceeding 0.1 and significant probability gains in some strong earthquake-prone regions. A time series analysis indicates probability stabilization after approximately six years. While no single parameter consistently dominates, each contributes precursory information, suggesting a promising avenue for a multi-parametric approach. Furthermore, novel anomaly indices incorporating probabilistic information significantly reduce false alarms and improve anomaly recognition. Despite remaining challenges in developing dynamic short-term probabilities, rigorously testing detection algorithms, and improving ensemble forecast strategies, this study provides compelling evidence for the potential of thermal anomalies to play a key role in global earthquake forecasts. The ability to reliably estimate earthquake forecast probabilities, given the ever-present threat of destructive earthquakes, holds considerable societal and ecological importance for mitigating earthquake risk and improving preparedness strategies. [ABSTRACT FROM AUTHOR]

Forensic document examiners are often confronted with questioned documents written with ballpoint pens. Depending on the force applied (or pressure) as well as the angle between the pen and the surface, sister lines running parallel to the inked strokes can be left by the lip of the housing ball. In a real case, sister lines were observed on the left side of inked strokes of a questioned signature. To assess whether the writer of that signature was a left-handed or a right-handed writer based on this result, an experimental study was carried out. Handwritten samples and signatures from 182 right-handed and 18 left-handed writers were collected with different ballpoint pens. For every writer, the presence or absence of sister lines was recorded. Sister lines were observed in 49% of the writers of the studied population (in 50% of the right-handed and ca. 39% of the left-handed writers). Most individuals who left sister lines showed a writing angle of 50°-55°. The location of sister lines was tabulated to inform probabilities of observing sister lines at a given location, if the writer is a right-handed or left-handed writer. In the case at hand, a likelihood ratio of 48 was obtained in support of the proposition of a left-handed writer, rather than a right-handed writer. Applying Bayes' theorem, such value moves the prior probability of 15% that the writer of the questioned signature is left-handed to a posterior probability of 89%. [ABSTRACT FROM AUTHOR]

With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions N (μ , σ 0) , as before, but with a constant σ 0 not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution N m (μ , Σ 0) with a constant variance–covariance matrix Σ 0 not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger's equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of σ 0 , altogether leading to the concept of "intrinsic". Similarly, as in our previous work with the estimator's variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the "intrinsic" Cramér–Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes' theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of "intrinsic" information-theoretic models, which are essential for developing physics. [ABSTRACT FROM AUTHOR]

Hydrogeological models require reliable uncertainty intervals that honestly reflect the total uncertainties of model predictions. The operation of a conventional Bayesian framework only produces realistic (interpretable in the context of the natural system) inference results if the model structure matches the data‐generating process, that is, applying Bayes' theorem implicitly assumes the underlying model to be true. With an imperfect model, we may obtain a too‐narrow‐for‐its‐bias uncertainty interval when conditioning on a long time‐series of calibration data, because the assumption of a quasi‐true model becomes too strict. To overcome the problem of overconfident posteriors, we propose a non‐parametric Bayesian method, called Tau‐averaging method: it applies Bayesian analysis on sliding time windows along the data time series for calibration. Thus, it obtains so‐called transitional posteriors per time window. Then, we average these into a wider predictive posterior. With the proposed routine, we explicitly capture the time‐varying impact of model error on prediction uncertainty. The length of the calibration window is optimized to maximize goal‐oriented statistical skill scores for predictive coverage. Our method loosens the perfect‐model‐assumption by conditioning only on small windows of the data set at a time, that is, it assumes that "the model is sufficient to follow the system dynamics for a smaller duration." We test our method on two cases of soil moisture modeling and show how it improves predictive coverage as compared to the conventional Bayesian approach. Our findings demonstrate that the proposed method convincingly overcomes the overconfidence drawback of Bayesian inference under model misspecification and long calibration time‐series. Plain Language Summary: Mathematical models mimic environmental systems to match what we see, and to predict what will happen. Unfortunately, such models are always simplifications of reality, balancing their complexity between manageability and accuracy. Consequently, interpreting model‐based conclusions requires caution. Assume a model has ten adjustable parameters to make it match with a system. The best‐possible achievable fit to observations is imperfect. Yet, statistical tools indicate we knew these parameters perfectly well after adjustment, especially when adjusting on long data series. Then, we might start believing that this model's adjusted predictions are perfect. We call this "overconfidence." Ways to overcome overconfidence include extending models by statistical components, making them predict intervals and probabilities rather than exact numbers. However, adjusting these additional statistical components has been difficult to date. In our new approach, we force the model only to match short time windows of the data, and move this window through the whole data set. As we use little data per window, we reduce the overconfidence effect. Instead, the model adjusts parameters and predicts outputs differently in each window. To make predictions, we combine the outputs into a more robust result, such that the testing data fall inside the intervals generated by our method. Key Points: We propose a data‐driven Bayesian method to obtain realistic uncertainty estimates despite model errorsOur method builds on a statistically rigorous, time‐windowed Bayesian framework without prior assumptions about error sources or patternsThe method is confirmed to provide realistic predictive coverage with two synthetic test cases and a real‐world lysimeter case study [ABSTRACT FROM AUTHOR]

Most existing poverty research focused on the identification of households in absolute poverty; few studies attempted to identify households in relative poverty (HRP). In this paper, we first developed an improved Bayes's theorem algorithm to sense individuals' spatio-temporal behavior characteristics via integrating mobile phone signaling, electricity consumption, and Points of Interest. We then utilized the improved random forest to identify HRP based on individuals' spatio-temporal behavior characteristics and building properties. A total of 29,370 urban households in Fengchan community, Zhengzhou, China, were selected to conduct this study. The accuracy rate was about 90% when it was verified against the household survey data. Three conclusions can be drawn from our analysis: (1) the individuals' spatio-temporal behavior characteristics played a more critical role in identifying HRP than building properties, (2) the identification accuracy of multi-source data is higher than that of single-source data, (3) mobile phone signaling records and building footprints data are more important in identifying HRP in low-rise buildings, while electricity consumption data is more crucial in the identification in high-rise buildings. Our proposed methods can accurately identify urban HRP, which is helpful to target interventions in the most needed areas. Our findings can inform relief policies in similar cities. [ABSTRACT FROM AUTHOR]

Microarray data have become an integral part of the clinical and drug discovery process. Due to its voluminous and heterogeneous nature, the question arises of the interpretability and stability of the traditional gene selection method. To enhance the stability of the gene selection method, so that the results are better explicable, an ameliorated Extended ReliefF gene selection algorithm is proposed. It encodes gene affinity information using a new mathematical formula based on Bayes' theorem and Manhattan distance for calculating the nearest neighbor in a pooled sample. It works in four aspects: initializing sample gene weight, improving gene weight, maximizing sample gene weight and finally adopting mutation operation. The proposed method selects the most informative genes which are highly perceptive to the prognosis of the disease. Further, to accomplish the accuracy and stability of the algorithm, soft classification is performed on Relieved_F, STIR, VLS-RelifF, I-RelieF, conventional ReliefF and proposed extended ReliefF algorithms using three classifiers namely Support Vector Machine (SVM), Multilayer Perceptron (MLP) and Random Forest (RF) on ten microarray datasets. According to the findings, MLP training times are much longer than those of RF and SVM. From a network perspective, SVM is much faster at training, whereas MLP excels in terms of accuracy. With a rise in gene similarity among the genes selected from the multiple training sets, the approach becomes more stable. As a result, it can be seen that the recommended gene selection algorithm greatly outperforms the other feature selection methods in terms of accuracy and stability. [ABSTRACT FROM AUTHOR]

The individual results of SARS-CoV-2 serological tests measured after the first pandemic wave of 2020 cannot be directly interpreted as a probability of having been infected. Plus, these results are usually returned as a binary or ternary variable, relying on predefined cut-offs. We propose a Bayesian mixture model to estimate individual infection probabilities, based on 81,797 continuous anti-spike IgG tests from Euroimmun collected in France after the first wave. This approach used serological results as a continuous variable, and was therefore not based on diagnostic cut-offs. Cumulative incidence, which is necessary to compute infection probabilities, was estimated according to age and administrative region. In France, we found that a "negative" or a "positive" test, as classified by the manufacturer, could correspond to a probability of infection as high as 61.8% or as low as 67.7%, respectively. "Indeterminate" tests encompassed probabilities of infection ranging from 10.8 to 96.6%. Our model estimated tailored individual probabilities of SARS-CoV-2 infection based on age, region, and serological result. It can be applied in other contexts, if estimates of cumulative incidence are available. [ABSTRACT FROM AUTHOR]

In robust parameter design for blocked experiments, the correlation of response observations within each block and model parameter uncertainty often impact acquiring ideal operating conditions. In this paper, a Bayesian mixed regression-based multi-response surface modeling and optimization method is suggested to address the above issues. Firstly, the mixed effects model is incorporated into the Bayesian framework, and posterior distributions of the model parameters are derived using Bayes' theorem. Secondly, the hybrid Monte Carlo algorithm is employed to calculate the model parameters. Thirdly, the expected quality loss function satisfying the specification is constructed to lessen the impact of outliers on the results of optimization, and the optimal factor settings are obtained by the hybrid genetic algorithm. In addition, the posterior probability is used to assess the conformance of the optimization results. Finally, a simulated study and real-world example of the additive manufacturing process are used to illustrate the viability of the proposed method. Compared with the current techniques, the proposed method can reduce the impact of model uncertainty on the modeling and optimization results, leading to more conformant and robust optimization results. • The correlation of observations within block and model parameter uncertainty are considered. • The priors of covariance of random effect and standard deviation of random error are extended to non-conjugate priors. • Compared with MCMC, the HMC algorithm improves efficiency. • In the blocked experiment, both quality loss and the conformance of optimization results are simultaneously considered. • On the application side, the problem of quality design for multiple 3D printers printing simultaneously is solved. [ABSTRACT FROM AUTHOR]

The following game of two persons is formalized and solved in the paper. Player 1 is asked a question. Player 2 knows the correct answer. Moreover, both players know all possible answers and their a priori probabilities. Player 2 must choose a subset of the given cardinality of deception answers. Player 1 chooses one of the proposed answers. Player 1 wins one from Player 2 if he/she guessed the correct answer and zero otherwise. This game is reduced to a matrix game. However, the game matrix is of large dimension, so the classical method based on solving a pair of dual linear programming problems cannot be implemented for each individual problem. Therefore, it is necessary to develop a method to radically reduce the dimension. The whole set of such games is divided into two classes. The superuniform class of games is characterized by the condition that the largest of the a priori probabilities is greater than the probability of choosing an answer at random, and the subuniform class corresponds to the opposite inequality—each of the a priori probabilities when multiplied by the total number of answers presented to Player 1 does not exceed one. For each of these two classes, the solving the extended matrix game is reduced to solving a linear programming problem of a much smaller dimension. For the subuniform class, the game is reformulated in terms of probability theory. The condition for the optimality of a mixed strategy is formulated using the Bayes theorem. For the superuniform class, the solution of the game uses an auxiliary problem related to the subuniform class. For both classes, we prove results on the probabilities of guessing the correct answer when using optimal mixed strategies by both players. We present algorithms for obtaining these strategies. The optimal mixed strategy of Player 1 is to choose an answer at random in the subuniform class and to choose the most probable answer in the superuniform class. Optimal mixed strategies of Player 2 have much more complex structure. [ABSTRACT FROM AUTHOR]

This work contributes to the comprehension of Bayes’ theorem inclusive Bayesian probabilities and Bayesian inferencing within the framework of STEM (Science, Technology, Engineering, Arts, and Mathematics) and cognitive learning w.r.t Bloom’s taxonomy (BT). Bayes’ theorem is taken as a crucial statistical instrument employed in the development of intelligent systems and the management of risks, commonly utilized by engineers for tasks in machine learning and managerial decision-making. The fundamental concept behind Bayes’ theorem revolves around comprehending the degree of truth within the confines of an explicit perspective. This involves partitioning the entire sample space of possible evidence and utilizing the subset containing the relevant perspective to estimate the uncertainty of an event or the reliability of a model. However, it is often found difficult for students to understand Bayes’ theorem to the level of applying it to real-world problems. Considering this, the proposed learning method in this paper elucidated the acquisition of Bayes’ mathematical formulation by leveraging computational thinking, leading to the development of a computational model. The proposed model is named the Bayesian Computational Learning Model (BCLM). Subsequently, we have probed the utility of BCLM in the design and plan of learning activities, coherent to the STEM paradigm and BT cognitive learning hierarchy.

Empirical life tests are used for reliability demonstration and determination of the actual reliability of the product. Therefore, engineers are faced with the challenge of selecting the most suitable test strategy out of the possible many and also the optimal parameter setting, e.g. sample size, in order to realize reliability demonstration with limited costs, time and with their available testing resources. It becomes even more challenging due to the stochastic nature of failure times and necessary cost and time being dependent on those. The considerations and guidelines in this paper are intended to simplify this process. Even simple products can fail due to several causes and mechanisms and usually have several components and subsystems. Therefore, this paper provides test planning options for single critical failure mechanisms as well as for systems with multiple failure mechanisms. For this purpose, the Probability of Test Success (Statistical Power of a life test) is used as a central, objective assessment metric. It is capable of indicating the probability of a successful reliability demonstration of a test and thus allows, for example, to answer the question of the required sample size for failure-based tests. The main planning resource is prior knowledge, which is mandatory due to the stochastic lifetime, in order to provide estimates for the Probability of Test Success at all. Therefore, it is also shown how to deal with uncertain prior knowledge and how the underlying information can additionally be used to increase the Probability of Test Success using Bayes’ theorem. The guidelines show how the most efficient test can be identified in the individual case and for individual boundary conditions.

The total aviation effective radiative forcing is dominated by non − CO2 effects. The largest contributors to the non − CO2 effects are contrails and contrail cirrus. There is the possibility of reducing the climate effect of aviation by avoiding flying through ice supersaturated regions (ISSRs), where contrails can last for hours (so-called persistent contrails). Therefore, a precise prediction of the specific location and time of these regions is needed. But a prediction of the frequency and degree of ice supersaturation (ISS) on cruise altitudes is currently very challenging and associated with great uncertainties because of the strong variability of the water vapour field, the low number of humidity measurements at air traffic altitude, and the oversimplified parameterisations of cloud physics in weather models. Since ISS is more common in some dynamical regimes than in others, the aim of this study is to find variables/proxies that are related to the formation of ISSRs and to use these for a regression method to predict persistent contrails. To find the best suited proxies for regressions, we use various methods of information theory. These include the log-likelihood ratios, known from the Bayes' theorem, a modified form of the Kullback-Leibler divergence and the mutual information. The variables (the relative humidity with respect to ice RHi ERA5, the temperature T , the vertical velocity ω, the divergence DIV , the relative vorticity ζ, the potential vorticity PV , the normalised geopotential height Z and the local lapse rate γ) come from ERA5 and RHi M/I, which we assume as the truth, comes from MOZAIC/IAGOS (commercial aircraft measurements). It turns out, that RHi ERA5 is the most important predictor of ice supersaturation, in spite of its weaknesses, and all other variables do not help much to achieve better results. Without RHi ERA5, a regression to predict ISSRs is not successful. Certain modifications of RHi ERA5 before the regression (as suggested in recent papers) do not lead to improvements of ISSR prediction. Applying a sensitivity study with artificially modified RHi ERA5 distributions point to the origin of the problems with the regression: the conditional distributions of RHi ERA5 (conditioned on ISS and non-ISS, from RHi M/I) overlap too heavily in the range 70–100 %, such that for any case in that range it is not clear whether it belongs to an ISSR or not. Evidently, this renders the prediction of contrail persistence very difficult. [ABSTRACT FROM AUTHOR]

The American Statistical Association has highlighted problems with null hypothesis significance testing and outlined alternative approaches that may 'supplement or even replace P -values'. One alternative is to report the false positive risk (FPR), which quantifies the chance the null hypothesis is true when the result is statistically significant. We reviewed single-centre, randomised trials in 10 anaesthesia journals over 6 yr where differences in a primary binary outcome were statistically significant. We calculated a Bayes factor by two methods (Gunel, Kass). From the Bayes factor we calculated the FPR for different prior beliefs for a real treatment effect. Prior beliefs were quantified by assigning pretest probabilities to the null and alternative hypotheses. For equal pretest probabilities of 0.5, the median (inter-quartile range [IQR]) FPR was 6% (1–22%) by the Gunel method and 6% (1–19%) by the Kass method. One in five trials had an FPR ≥20%. For trials reporting P -values 0.01–0.05, the median (IQR) FPR was 25% (16–30%) by the Gunel method and 20% (16–25%) by the Kass method. More than 90% of trials reporting P -values 0.01–0.05 required a pretest probability >0.5 to achieve an FPR of 5%. The median (IQR) difference in the FPR calculated by the two methods was 0% (0–2%). Our findings suggest that a substantial proportion of single-centre trials in anaesthesia reporting statistically significant differences provide limited evidence of real treatment effects, or, alternatively, required an implausibly high prior belief in a real treatment effect. PROSPERO (CRD42023350783). [ABSTRACT FROM AUTHOR]

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Among the numerous techniques followed to learn a linear classifier through the discriminative dictionary and sparse representations learning of signals, the techniques to learn a nonparametric Bayesian classifier jointly and discriminately with the dictionary and the corresponding sparse representations have drawn considerable attention from researchers. These techniques jointly learn two sets of sparse representations, one for the training samples over the dictionary and the other for the corresponding labels over the dictionary classifier. At the prediction stage, the representations of the test samples computed over the learned dictionary do not truly represent the corresponding labels, exposing weakness in the joint learning claim of these techniques. We mitigate this problem and strengthen the joint by learning a set of weights over the dictionary to represent the training data and further optimizing the same weights over the dictionary classifier to represent the labels of the corresponding classes of the training data. Now, at the prediction stage, the representation weights of the test samples computed over the learned dictionary also represent the labels of the corresponding classes of the test samples, resulting in the accurate reconstruction of the labels of the classes by the learned dictionary classifier. Overall, a reduction in the size of the Bayesian model's parameters also improves training time. We analytically and nonparametrically derived the posterior conditional probabilities of the model from the overall joint probability of the model using Bayes' theorem. We used the Gibbs sampler to solve the joint probability of the model using the derived conditional probabilities, which also supports our claim of efficient optimization of the coupled/joint dictionaries and the sparse representation parameters. We demonstrated the effectiveness of our approach through experiments on the standard datasets, i.e., the Extended YaleB and AR face databases for face recognition, Caltech-101 and Fifteen Scene Category databases for categorization, and UCF sports action database for action recognition. We compared the results with the state-of-the-art methods in the area. The classification accuracies, i.e., 93.25%, 89.27%, 94.81%, 98.10%, and 95.00%, of our approach on the datasets have increases of 0.5 to 2% on average. The overall average error margin of the confidence intervals in our approach is 0.24 compared with the second-best approach, JBDC, for which it is 0.34. The AUC–ROC scores of our approach are 0.98 and 0.992, which are better than those of others, i.e., 0.960 and 0.98, respectively. Our approach is also computationally efficient. [ABSTRACT FROM AUTHOR]

In this paper we introduce probabilistic measure which takes values in bihyperbolic numbers and generalize Kolmogorov's system of axioms. We study the zero divisors of the set of bihyperbolic numbers and keeping it in mind, we define conditional bihyperbolic probability and prove bihyperbolic analogues of the multiplication theorem, of the law of total probability and Bayes' theorem. [ABSTRACT FROM AUTHOR]