Probability Estimation Research Articles

Probabilistic estimation of the source component of seismic hazard in North-Eastern Brazil

Stable continental regions pose unique challenges for conducting Probabilistic Seismic Hazard Analysis because the earthquake activity driving mechanisms are poorly understood. For instance, the lower seismicity (hence the paucity of data) and the absence of well-defined active fault systems complicate accurately determining seismic source parameters. Northeastern Brazil is a stable continental region exhibiting moderate-size events recorded with significant seismic intensities and provoking the collapse of poorly constructed buildings in the last century. Thus, assessing the seismic hazard is critical for seismic risk mitigation. The seismic hazard depends on three components: source, path, and site, and here, we present the probabilistic seismic hazard analysis of the source component for NE Brazil. Spatial aggregation of earthquake sources outlined four areal seismic zones. A goodness-of-fit test rejected the Gutenberg-Richter model of magnitude frequency distribution in one of the studied seismic zones. For this reason, we estimated the magnitude probability distribution function in that zone using a nonparametric adaptive kernel estimator. In other zones the Gutenberg-Richter magnitude frequency model was applied. In either way of the magnitude probability distribution modelling we considered the upper bound for magnitude equal to 6.6 mR, based on the upper bound of a 95 % confidence interval for the standard normal distribution of palaeoearthquake sizes. Our findings suggests that potentially damaging events are likely to occur, and we cannot neglect chances for the occurrence of earthquakes exceeding 5.2 mR. The calculated mean return periods indicate significantly shorter intervals between consecutive large events than palaeoseismic records.

Managing Risk and Uncertainty in the Context of Child Protection Decision Making

Abstract Uncertainty is a concept related to, but distinct from, risk. Risk has been defined as the portion of the continuum from complete certainty to total ignorance that can be estimated using tools of probability. Uncertainty, on the other hand lies in the portion of the continuum of knowability that is incalculable and uncontrollable. It is well established that estimating risk probabilistically in the child protection context is unreliable and prone to error under conditions of high uncertainty—particularly when making decisions on the long-term needs of a child. This is true whether risk is estimated using professional judgement, statistical algorithms or a combination of both. In other disciplines, tools have been developed that transition decision making away from the probabilistic reasoning associated with judgments of risk (the ‘Predict and Act’ paradigm) to procedures that do not rely on the probabilistic estimation of risk (the ‘Monitor and Adapt’ paradigm). A pragmatic approach to adapting existing assessment procedures developed within the Predict and Act paradigm to align more closely with the Monitor and Adapt approach is presented. It is suggested that a key component of such an adaptation would be integrating case formulation into routine child protection practice.

XWaveNet: Enabling uncertainty quantification in short-term ocean wave height forecasts and extreme event prediction

To aid accurate short-term forecast of wave heights and extreme events prediction from buoy data, a deep learning approach is proposed. Wave heights are forecasted up to 72 h in advance from multivariate meteorological and oceanographic data, followed by quantification of uncertainty in the forecasted values, and estimation of exceedance probabilities for extreme event conditions. Using Monte Carlo dropout technique, network regularization and forecast uncertainty assessment were performed. To forecast wave heights, a stacked long short-term memory (LSTM) model was trained on historical buoy data augmented with positionally encoded features. Per comparative evaluation of different models, across the 72 h forecast horizon, positionally encoded temporal attributes resulted in a mean prediction error and forecast uncertainty of only 3 % and 13.5 %, respectively. Contrarily, without temporal feature augmentation mean error was 5 % and uncertainty, 15 %. Therefore, the former model was ensembled with a Random Forest model for exceedance probability estimation. The hybrid model yielded a 21.4 % better separability between the extreme and normal observations in the test data from a nearby buoy in the northern Gulf of Mexico than individual models. All the four extreme events in the test set were correctly predicted with 97 % mean accuracy. Further evaluation of the deep ensemble model on 5 other spatially diverse buoy datasets from the Gulf of Mexico, Atlantic and Pacific coasts, suggested excellent generalizability for short-term wave forecasts and extreme event prediction, with an average maximum error of just 5.2 % across all the 6 buoy test datasets and the entire forecast horizon.

An Efficient Methodology to Identify Relevant Multiple Contingencies and Their Probability for Long-Term Resilience Studies

The selection of multiple contingency scenarios is a key task to perform resilience-oriented long-term planning analyses. However, the identification of relevant multiple contingencies may easily lead to combinatorial explosion issues, even for relatively small systems. This paper proposes an effective methodology for the identification of relevant multiple contingencies and their probabilities, suitable for the long-term resilience analysis of large power systems. The methodology is composed of two main pillars: (1) the clustering of lines that are more likely to fail together, to reduce the computational complexity of the analysis exploiting historical weather data and (2) the probability-based identification of multiple contingencies within each cluster, where the contingency probability is computed applying the copula theory. Tests performed on a portion of the Italian EHV transmission system confirm the validity of the clustering results compared against historical failure events. Moreover, the copula-based algorithm for contingency probability estimation passes the tests carried out on relatively large clusters with very low error tolerance. The method successfully pinpoints critical multiple contingency scenarios and their likelihoods, making it valuable for assessing power system resilience over long-term horizons in support of resilience-oriented planning activities.

Bias correction in species distribution models based on geographic and environmental characteristics

Correcting sampling bias in species distribution models (SDMs) is challenging. The difficulty lies in accurately identifying and quantifying bias and the scarcity of samples, which greatly impedes the implementation of bias correction. Current methods often adjust the distribution of presence or background points within geographic or environmental spaces to correct the sampling bias in probability estimation within SDMs. However, these methods may lead to information loss, rely on subjective assumptions, and often separate geography and environment when correcting for bias. This study proposes a novel and easily implementable method termed “aggregation background.” This method selects background data based on the aggregation degree of presence points in the geographic and environmental feature space, thereby approximating the representation and correction of sampling bias in the presence samples. We compared this new method with other prevalent sampling bias correction methods in the existing literature by analyzing ecological authenticity. Under varying biases and sample sizes, the aggregation background and geographic filtering methods achieved more accurate species distribution predictions compared to the target group background and other methods. Notably, when the sample size was small (≤70), the aggregation background was superior to that obtained using the geographic filtering method. These findings underscore the effectiveness of the aggregation background in improving bias correction using limited available presence sample data, without relying on assumptions about sampling bias. Our method provides a new approach for correcting complex unknown biases in SDMs.

Indications for the Postpartum Oral Glucose Tolerance Test.

Gestational diabetes mellitus (GDM) affects more than 50 000 pregnant women in Germany every year. In postpartum diabetes screening, a 75 g oral glucose tolerance test (OGT) is recommended. This is time-consuming and can have side effects, and only 40% of mothers take it. The determination of pre-test probabilities might obviate the need for OGT except in women who are at particular risk. We analyzed 5444 cases of GDM from the GestDiab registry over the period 2015-2019. The pretest probabilities of a postpartum diagnosis of diabetes mellitus (DM) or prediabetes were calculated on the basis of clinical variables including postpartum venous fasting plasma glucose (FPG) and hemoglobin A1c (HbA1c). In 0.77% of mothers with a history of GDM in whom DM was not detected by FPG or HbA1c, postpartum DM was diagnosed on the basis of the 2-hour value in the OGT. Individual estimation of the pre-test probability of a diagnosis by OGT of postpartum DM or prediabetes was possible with the aid of the FPG and HbA1c values and clinical predictors including insulin treatment during pregnancy, obesity, GDM diagnosed before 24 weeks of gestation, age over 35, and a 1-hour value in the diagnostic OGT during pregnancy of 180 mg/dL (10.0 mmol/L) or above. The pretest probability of postpartum DM in the study group ranged from 0.11% to 4.17%, and that of postpartum prediabetes from 6.4% to 16.3%. The probability of a diagnosis of postpartum diabetes by OGT after GDM can be estimated in postpartum screening on the basis of various parameters. This enables risk-adapted counseling of the affected women along with a long-term strategy for diabetes prevention and follow-up. The findings of our study should be verified by further research.

Imprecise probabilistic inference from sequential data.

Although the Bayesian paradigm is an important benchmark in studies of human inference, the extent to which it provides a useful framework to account for human behavior remains debated. We document systematic departures from Bayesian inference under correct beliefs, even on average, in the estimates by experimental subjects of the probability of a binary event following observations of successive realizations of the event. In particular, we find underreaction of subjects' estimates to the evidence ("conservatism") after only a few observations and at the same time overreaction after longer sequences of observations. This is not explained by an incorrect prior nor by many common models of Bayesian inference. We uncover the autocorrelation in estimates, which suggests that subjects carry imprecise representations of the decision situations, with noise in beliefs propagating over successive trials. But even taking into account these internal imprecisions and assuming various incorrect beliefs, we find that subjects' updates are inconsistent with the rules of Bayesian inference. We show how subjects instead considerably economize on the attention that they pay to the information relevant to the decision, and on the degree of control that they exert over their precise response, while giving responses fairly adapted to the task. A "noisy-counting" model of probability estimation reproduces the several patterns we exhibit in subjects' behavior. In sum, human subjects in our task perform reasonably well while greatly minimizing the amount of information that they pay attention to. Our results emphasize that investigating this economy of attention is crucial in understanding human decisions. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A dynamic risk assessment model based on multidimensional and quantitative inference theory

With the continuous increase in petroleum consumption and the trend towards more refined management, crude oil storage tanks are playing an increasingly crucial role in the petrochemical industry. However, the corrosion issue of crude oil storage tanks has consistently been a major factor limiting their service life, and leaks in crude oil tanks are often attributed to corrosion of the tank bottom. Due to the high cost and complexity associated with tank opening inspections, in this paper, directly observable information and physical quantities are utilized as indirect evidence, combined with Bayesian network, to indirectly determine the probability of tank corrosion. This approach allows for selective internal tank inspections, enabling effective risk assessment while also facilitating cost savings. Some parameters in the Bayesian network model are obtained through a probability estimation model combining expert experience and fuzzy set theory. Finally, the feasibility of the method is demonstrated by citing examples. The current model can offer a relatively reliable reference for evaluating the risks associated with tanks and their ancillary facilities, while also reducing the costs of tank inspections to some extent.

Influence of temporary emigration on wood turtle (Glyptemys insculpta) detectability, with implications for abundance estimation.

Reliable population estimates are important for making informed management decisions about wildlife species. Standardized survey protocols have been developed for monitoring population trends of the wood turtle (Glyptemys insculpta), a semi-aquatic freshwater turtle species of conservation concern throughout its distribution in east-central North America. The protocols use repeated active search surveys of defined areas, allowing for estimation of survey-specific detection probability (p) and site-specific abundance. These protocols assume population closure within the survey area during the survey period, which is unlikely to be met as wood turtles are a highly mobile species. Additionally, current protocols use a single-pass design that does not allow for separation of availability (pa) and detectability (pd). If there are systematic influences on pa or pd that are not accounted for in the survey design or data analysis, then resulting abundance estimates could be biased. The objectives of this study were to determine if pa is a random process and if pa and pd are influenced by demographic characteristics. We modified the wood turtle survey protocol used in the upper Midwest to include a double-pass design, allowing us to estimate pa and pd using a robust design capture-recapture model. The modified protocol was implemented at 14 wood turtle monitoring sites in Minnesota and Wisconsin between 2017 and 2022. Our results indicated that pa was non-random and that pd increased with turtle carapace length. Our study suggests that model assumptions for current wood turtle population models may be violated, likely resulting in an overestimation of abundance. We discuss possible protocol and modeling modifications that could result in more accurate wood turtle abundance estimates.

Self-adaptive sampling for Fourier single-pixel imaging using probability estimation

Self-adaptive sampling for Fourier single-pixel imaging using probability estimation

Isotonic design for single-arm biomarker stratified trials.

In single-arm trials with a predefined subgroup based on baseline biomarkers, it is often assumed that a biomarker defined subgroup, the biomarker positive subgroup, has the same or higher response to treatment compared to its complement, the biomarker negative subgroup. The goal is to determine if the treatment is effective in each of the subgroups or in the biomarker positive subgroup only or not effective at all. We propose the isotonic stratified design for this problem. The design has a joint set of decision rules for biomarker positive and negative subjects and utilizes joint estimation of response probabilities using assumed monotonicity of response between the biomarker negative and positive subgroups. The new design reduces the sample size requirement when compared to running two Simon's designs in each biomarker positive and negative. For example, the new design requires 23%-35% fewer patients than running two Simon's designs for scenarios we considered. Alternatively, the new design allows evaluating the response probability in both biomarker negative and biomarker positive subgroups using only 40% more patients needed for running Simon's design in the biomarker positive subgroup only.

A multi-model evaluation of probabilistic streamflow predictions via residual error modelling

Probabilistic streamflow predictions are valuable tools for predictive uncertainty estimation, hydrologic risk management, and support for decision-making in water resources. Usually, predictive uncertainty quantification is developed and assessed using only a single hydrological model, making it difficult to generalize to other model configurations. To tackle this issue, we assess changes in the model performance ranking of diverse streamflow models by applying a residual error model post-processing approach to multiple basins and multiple models. This assessment employed 141 basins from the Great Lakes watershed covering the USA and Canada, and 13 diverse streamflow models, which are evaluated using deterministic and probabilistic performance metrics. As the first study to implement probabilistic methods to diverse streamflow models applied to a multitude of basins, the analysis here examines the dependence of probabilistic streamflow estimation quality on model quality. Our findings show that streamflow model choice influences the robustness of probabilistic predictions. It was found that moving from deterministic to probabilistic predictions using a post-processing approach does not change the streamflow model performance ranking for the best and worst deterministic models, but models of intermediate rank in deterministic evaluation do not have consistent ranking when evaluated in probabilistic mode. Post-processing residual errors of long short-term memory (LSTM) network models are consistently the best-performing model in terms of deterministic and probabilistic metrics. This study highlights the significance of combining deterministic streamflow model predictions with residual error models for improving the quality and increasing the value of hydrological predictions, quantifying uncertainty, and facilitating decision-making in operational water management. It also clarifies the degree to which probabilistic predictions depend upon good model performance and can compensate for poor model performance.

Capacity estimation of lithium-ion batteries with uncertainty quantification based on temporal convolutional network and Gaussian process regression

Reliable capacity estimation is crucial for safe operation of lithium-ion batteries (LIBs). This work combines the temporal convolutional network (TCN) and Gaussian process regression (GPR) to establish a novel probabilistic capacity estimation method. The proposed TCN-GPR method can not only provide accurate capacity estimation but also quantify the uncertainty of the estimation. Besides, the TCN-GPR method can automatically extract degradation features from partial charging segments, overcoming the limitations of manual experience. In addition, the TCN-GPR method can be applied to different types of LIBs through transfer learning using only a small amount of training data. For validation, the Oxford battery dataset is used to demonstrate the accuracy and robustness of the TCN-GPR method, where a mean absolute percentage error (MAPE) of less than 0.3% can be achieved with only a 15-min partial charging segment. Furthermore, our own experimental dataset is used to demonstrate the generalization ability of the TCN-GPR method through transfer learning, where a MAPE of less than 0.7% can be achieved by using only one battery cell as the training sample.

Estimation of Probabilities of Transitions of a Markov Binary Input Signal of a Nonlinear System

Estimation of Probabilities of Transitions of a Markov Binary Input Signal of a Nonlinear System

Statistical inference for multivariate extremes via a geometric approach

Abstract A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, and the geometric approach itself has not been fully exploited for statistical inference. We outline a method for parametric estimation of the limit set shape, which includes a useful non-/semi-parametric estimate as a pre-processing step. More fundamentally, our approach provides a new class of asymptotically motivated statistical models for the tails of multivariate distributions, and such models can accommodate any combination of simultaneous or non-simultaneous extremes through appropriate parametric forms for the limit set shape. Extrapolation further into the tail of the distribution is possible via simulation from the fitted model. A simulation study confirms that our methodology is very competitive with existing approaches and can successfully allow estimation of small probabilities in regions where other methods struggle. We apply the methodology to two environmental datasets, with diagnostics demonstrating a good fit.

Comparative Analysis of Local Differential Privacy Schemes in Healthcare Datasets

In the rapidly evolving landscape of healthcare technology, the critical need for robust privacy safeguards is undeniable. Local Differential Privacy (LDP) offers a potential solution to address privacy concerns in data-rich industries. However, challenges such as the curse of dimensionality arise when dealing with multidimensional data. This is particularly pronounced in k-way joint probability estimation, where higher values of k lead to decreased accuracy. To overcome these challenges, we propose the integration of Bayesian Ridge Regression (BRR), known for its effectiveness in handling multicollinearity. Our approach demonstrates robustness, manifesting a noteworthy reduction in average variant distance when compared to baseline algorithms such as LOPUB and LOCOP. Additionally, we leverage the R-squared metric to highlight BRR’s advantages, illustrating its performance relative to LASSO, as LOPUB and LOCOP are based on it. This paper addresses a relevant concern related to datasets exhibiting high correlation between attributes, potentially allowing the extraction of information from one attribute to another. We convincingly show the superior performance of BRR over LOPUB and LOCOP across 15 datasets with varying average correlation attributes. Healthcare takes center stage in this collection of datasets. Moreover, the datasets explore diverse fields such as finance, travel, and social science. In summary, our proposed approach consistently outperforms the LOPUB and LOCOP algorithms, particularly when operating under smaller privacy budgets and with datasets characterized by lower average correlation attributes. This signifies the efficacy of Bayesian Ridge Regression in enhancing privacy safeguards in healthcare technology.

A probabilistic neural twin for treatment planning in peripheral pulmonary artery stenosis.

The substantial computational cost of high-fidelity models in numerical hemodynamics has, so far, relegated their use mainly to offline treatment planning. New breakthroughs in data-driven architectures and optimization techniques for fast surrogate modeling provide an exciting opportunity to overcome these limitations, enabling the use of such technology for time-critical decisions. We discuss an application to the repair of multiple stenosis in peripheral pulmonary artery disease through either transcatheter pulmonary artery rehabilitation or surgery, where it is of interest to achieve desired pressures and flows at specific locations in the pulmonary artery tree, while minimizing the risk for the patient. Since different degrees of success can be achieved in practice during treatment, we formulate the problem in probability, and solve it through a sample-based approach. We propose a new offline-online pipeline for probabilistic real-time treatment planning which combines offline assimilation of boundary conditions, model reduction, and training dataset generation with online estimation of marginal probabilities, possibly conditioned on the degree of augmentation observed in already repaired lesions. Moreover, we propose a new approach for the parametrization of arbitrarily shaped vascular repairs through iterative corrections of a zero-dimensional approximant. We demonstrate this pipeline for a diseased model of the pulmonary artery tree available through the Vascular Model Repository.

A Unifying Generator Loss Function for Generative Adversarial Networks.

A unifying α-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN) that uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a symmetric class probability estimation type function, Lα, and the resulting GAN system is termed Lα-GAN. Under an optimal discriminator, it is shown that the generator's optimization problem consists of minimizing a Jensen-fα-divergence, a natural generalization of the Jensen-Shannon divergence, where fα is a convex function expressed in terms of the loss function Lα. It is also demonstrated that this Lα-GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, least squares GAN (LSGAN), least kth-order GAN (LkGAN), and the recently introduced (αD,αG)-GAN with αD=1. Finally, experimental results are provided for three datasets-MNIST, CIFAR-10, and Stacked MNIST-to illustrate the performance of various examples of the Lα-GAN system.

Educational Status as a Mediator of Intergenerational Social Mobility in Europe: A Positional Analysis Approach

This paper investigates the transmission of educational attainment from parents to offspring as a mediator of intergenerational class mobility in Europe. The study covers the last two decades with data drawn from a cross-national large-scale sample survey, namely the European Social Survey (ESS), for the years 2002–2018. Interest has focused on the question of the persistence of inequality of educational opportunities by examining the attainment of nominal levels of education and the association between the educational attainment of the parent with the highest level of education and their descendants. The study also covers new trends in social mobility that consider education as a “positional good”, and a novel method of incorporating educational expansion into the transition probabilities is proposed, providing answers to whether the rising accessibility of educational qualifications attenuates the association between social origin and educational attainment. Therefore, the concept of positionality is taken into account in the estimation of intergenerational transition probabilities, and to complement the analysis, mobility measures are provided for both methods, nominal and positional. The proposed positional method is validated through a correlation analysis between the upward mobility scores (nominal and positional) with the Education Expansion Index (EEI) for the respective years. The upward mobility scores estimated via the positional method are more highly correlated with the EEI for all years, indicating a better alignment with the broader trends in educational participation and achievement.

Cognitive Biases in High-Stakes Decision-Making: Implications for Joint Pediatric Cardiology and Cardiothoracic Surgery Conference.

Extensive research has consistently demonstrated that humans frequently diverge from rational decision-making processes due to the pervasive influence of cognitive biases. This paper conducts an examination of the impact of cognitive biases on high-stakes decision-making within the context of the joint pediatric cardiology and cardiothoracic surgery conference, offering practical recommendations for mitigating their effects. Recognized biases such as confirmation bias, availability bias, outcome bias, overconfidence bias, sunk cost fallacy, loss aversion, planning fallacy, authority bias, and illusion of agreement are analyzed concerning their specific implications within this conference setting. To counteract these biases and enhance the quality of decision-making, practical strategies are proposed, including the implementation of a no-interruption policy until all data is reviewed, leaders refraining from immediate input, requiring participants to formulate independent judgments prior to sharing recommendations, explicit probability estimations grounded in base rates, seeking external opinions, and promoting an environment that encourages dissenting perspectives.