Distributional Assumptions Research Articles

A Non-Stochastic Special Model of Risk Based on Radon Transform

The concept of risk is fundamental in various scientific fields, including physics, biology and engineering, and is crucial for the study of complex systems, especially financial markets. In our research, we introduce a novel risk model that has a natural transactional–financial interpretation. In our approach, the risk of holding a financial instrument is related to the measure of the possibility of its loss. In this context, a financial instrument is riskier the more opportunities there are to dispose of it, i.e., to sell it. We present a model of risk understood in this way, introducing, in particular, the concept of financial time and a financial frame of reference, which allows for associating risk with the subjective perception of the observer. The presented approach does not rely on statistical assumptions and is based on the transactional interpretation of models. To measure risk, we propose using the Radon transform. The financial concept of risk is closely related to the concepts of uncertainty, entropy, information, and error in physics. Therefore, the well-established algorithmic aspects of the computed tomography method can be effectively applied to the broader field of uncertainty analysis, which is one of the foundational elements of experimental physics.

Accounting for adaptation when projecting climate change impacts on health: a review of methods

Abstract Exposure to high and low temperatures can cause harm to health. Temperature related health effects are likely to increase in the future, due to global warming, unless populations can adapt to a warming environment. Adaptation occurs through multiple mechanisms, however, the amount that populations may adapt to rising temperatures is unclear. There are currently a variety of methods used to include adaptation in projections, but it is unclear how underlying assumptions are made and whether they are based on evidence. With increasing interest from decisionmakers around implementation of adaptation strategies, an important step in responding to climate change will be to understand how adaptation can statistically be incorporated when estimating future health burdens. A systematic scoping review was conducted to identify all quantitative methods to include adaptation in studies projecting future temperature-related health impacts under climate change. Approaches employed in studies were coded into methodological categories. Advantages and disadvantages of each method were also explored, along with the empirical basis for model assumptions. Eight methodological categories were identified from the included fifty-nine studies. More recent methods of including adaptation in projections use a combination of approaches or modelling adaptation based on specific adaptation strategies or socioeconomic conditions. The most used approaches in the literature to model adaptation are heat threshold shifts and reductions in the exposure-response slope. Just under 20% of studies were categorised as using an empirical basis for statistical assumptions. Including adaptation in projections considerably reduced the projected temperature-mortality burden in the future. Researchers should ensure that all future impact assessments include adaptation uncertainty in projections and assumptions are based on empirical evidence where possible. Key messages • Including adaptation in future projections considerably affects temperature-related mortality numbers. • All future impact assessments should include adaptation uncertainty and assumptions should be based on evidence where possible.

Estimating reference intervals from an IPD meta-analysis using quantile regression

BackgroundReference intervals, which define an interval in which a specific proportion of measurements from a healthy population are expected to fall, are commonly used in medical practice. Synthesizing information from multiple studies through meta-analysis can provide a more precise and representative reference interval than one derived from a single study. However, the current approaches for estimating the reference interval from a meta-analysis mainly rely on aggregate data and require parametric distributional assumptions that cannot always be checked.MethodsWith the availability of individual participant data (IPD), non-parametric methods can be used to estimate reference intervals without any distributional assumptions. Furthermore, patient-level covariates can be introduced to estimate personalized reference intervals that may be more applicable to specific patients. This paper introduces quantile regression as a method to estimate the reference interval from an IPD meta-analysis under the fixed effects model.ResultsWe compared several non-parametric bootstrap methods through simulation studies to account for within-study correlation. Under fixed effects model, we recommend keeping the studies fixed and only randomly sampling subjects with replacement within each study. ConclusionWe proposed to use the quantile regression in the IPD meta-analysis to estimate the reference interval. Based on the simulation results, we identify an optimal bootstrap strategy for estimating the uncertainty of the estimated reference interval. An example of liver stiffness measurements, a clinically important diagnostic test without explicitly established reference range in children, is provided to demonstrate the use of quantile regression in estimating both overall and subject-specific reference intervals.

Bayesian Empirical Likelihood Regression for Semiparametric Estimation of Optimal Dynamic Treatment Regimes.

We propose a semiparametric approach to Bayesian modeling of dynamic treatment regimes that is built on a Bayesian likelihood-based regression estimation framework. Methods based on this framework exhibit a probabilistic coherence property that leads to accurate estimation of the optimal dynamic treatment regime. Unlike most Bayesian estimation methods, our proposed method avoids strong distributional assumptions for the intermediate and final outcomes by utilizing empirical likelihoods. Our proposed method allows for either linear, or more flexible forms of mean functions for the stagewise outcomes. A variational Bayes approximation is used for computation to avoid common pitfalls associated with Markov Chain Monte Carlo approaches coupled with empirical likelihood. Through simulations and analysis of the STAR*D sequential randomized trial data, our proposed method demonstrates superior accuracy over Q-learning and parametric Bayesian likelihood-based regression estimation, particularly when the parametric assumptions of regression error distributions may be potentially violated.

Fast Iterative Sample Transfer Identification Method for Dynamic Systems Under Non‐identical Distribution

ABSTRACTThis paper proposes a method to improve the identification performance of linear dynamic systems by utilizing knowledge from samples of non‐identical distribution systems. Traditional identification methods heavily rely on the quality of the dataset, such as sample length and noise level, which constrains their performance due to the assumption of identical distribution. Motivated by the concept of sample‐based transfer learning, we propose a sample transfer identification method and derive the condition to avoid negative transfer. We develop a fast iterative transfer identification method for low storage costs, considering the computational burden imposed by the sample size from the source system. Additionally, based on the fast iterative transfer identification method, considering the need to update the current measurement data model in real time, a fast iterative online sample transfer identification method is explored. Through simulations, we validate the effectiveness and superiority of the proposed methods. The results show that sample transfer identification is superior to non‐transfer identification and fast iterative sample transfer identification effectively reduces the calculation amount when dealing with low quality measurement data.

Simplified methods for variance estimation in microbiome abundance count data analysis

The complex nature of microbiome data has made the differential abundance analysis challenging. Microbiome abundance counts are often skewed to the right and heteroscedastic (also known as overdispersion), potentially leading to incorrect inferences if not properly addressed. In this paper, we propose a simple yet effective framework to tackle the challenges by integrating Poisson (log-linear) regression with standard error estimation through the Bootstrap method and Sandwich robust estimation. Such standard error estimates are accurate and yield satisfactory inference even if the distributional assumption or the variance structure is incorrect. Our approach is validated through extensive simulation studies, demonstrating its effectiveness in addressing overdispersion and improving inference accuracy. Additionally, we apply our approach to two real datasets collected from the human gut and vagina, respectively, demonstrating the wide applicability of our methods. The results highlight the efficacy of our covariance estimators in addressing the challenges of microbiome data analysis. The corresponding software implementation is publicly available at https://github.com/yimshi/robustestimates.

Sulfur dioxide in white sugar: Source of income, reference values

Sulfur dioxide is one of the classic essential technological processing aids used in modern technology for the production of white beet sugar. The technological and safe use of sulfites (sulfur dioxide, sodium sulfite and sodium hydrosulfite) in the formation of the food system of the sugar production process flow has been substantiated, and their functional effect is shown. It has been established that the change in the content of sulfur dioxide in white sugar under the influence of an antifoam, antiscale agent and decolorant in the doses used in massecuite occurred in accordance with the principle of additivity. The presence of the additive property was confirmed by the maximum approximation of the algebraic sum of the effects of each agent, amounting to 5.6%, to the range of variation in the values of the sulfur dioxide content (5.9) at a significance level of p=0.05. The dependence of the sulfur dioxide content in white sugar in a range of 0 to 6.5 mg/kg on the influence of the decolorant and defoamer in a dose range of 100 to 200 and of 4 to 6 g/t of massecuite was established. It has been revealed that increasing the minimum optimal dose of the decolorant to the maximum leads to an increase in the content of sulfur dioxide in white sugar by 1.7 times. Confidence intervals for the general mean were calculated based on the assumption of normal data distribution and a significance level of p=0.05. The reference values for the sulfur dioxide content in white sugar of the four categories were 1.28–2.69 mg/kg, and the upper limit level with consideration for the confidence interval was 1.39–3.01 mg/kg. The established reference values can be used at sugar factories in the production control system, and also provide an evidence base for comparison and assessment of this indicator of the white sugar safety for industrial consumers.

Evaluating interseismic deformation patterns in the North Tabriz Fault (Iran) using enhanced fitting of velocity field and analysis of surface deformation

Understanding the mechanisms and locations of interseismic strain accumulation along faults is essential for assessing earthquake hazards. However, the mechanical response during the transition from deep fault locking to creep behavior remains uncertain. Estimating the slip deficit within these transition zones is challenging. This study challenges the assumption of a constant depth distribution of interseismic slip rate along the fault over time and proposes variable locking depths as an alternative model. By rejecting the constant locking depth assumption, singularity issues during stress theorem resolution are resolved. To address this, we employ a methodology considering creep propagation within a fully elastic medium. This approach incorporates long-term deformation resulting from viscoelastic flow in the upper mantle and lower crust. Including viscoelastic effects improves the fit to interseismic deformation rates, yielding lower locking depths compared to fully elastic models. To conduct the investigation, the GPS velocity field is recovered using the forward problem and the boundary element method. Subsequently, a physics-based inversion approach, deep interseismic creep, is employed to determine interseismic deformation patterns on a strike-slip fault. Furthermore, this study examined the correlation between the dislocation parameters and their relationship, as well as established the probability distributions associated with each faulting parameter. This research highlights the importance of considering variable locking depths in understanding interseismic strain accumulation and the transition to creep behavior along faults. The findings contribute to improved earthquake hazard assessment and mitigation strategies by providing valuable insights into fault behavior mechanics along the North Tabriz Fault.

Bayesian Ensemble Kalman Filter for Gaussian Mixture Models

AbstractInverse theory and data assimilation methods are commonly used in earth and environmental science studies to predict unknown variables, such as the physical properties of underground rocks, from a set of measured geophysical data, like geophysical seismic or electromagnetic data. A new Bayesian approach based on the ensemble Kalman filter using Gaussian mixture models is presented to overcome the assumption of Gaussian distribution of the unknown variables commonly used in the data assimilation literature and to generalize the algorithm to inverse problems with multimodal probability distributions. In applications of subsurface characterization, the multimodality of the unknown variables is generally due to the presence of different rock types, also known as geological facies. In the proposed method, the weights of the Gaussian mixture model represent the facies proportions, and they follow a Markov chain model. The proposed Bayesian model generates the unknown model parameters conditioned on measured data using a Markov chain Monte Carlo sampler. The validity of the method is demonstrated on a data assimilation problem where the goal is to estimate the posterior distribution of the unknown rock density from a set of repeated measurements of acoustic wave velocity measured at different times. The proposed method provides accurate estimates with efficient computational times.

Cokernel statistics for walk matrices of directed and weighted random graphs

Abstract The walk matrix associated to an $n\times n$ integer matrix $\mathbf{X}$ and an integer vector $b$ is defined by ${\mathbf{W}} \,:\!=\, (b,{\mathbf{X}} b,\ldots, {\mathbf{X}}^{n-1}b)$ . We study limiting laws for the cokernel of $\mathbf{W}$ in the scenario where $\mathbf{X}$ is a random matrix with independent entries and $b$ is deterministic. Our first main result provides a formula for the distribution of the $p^m$ -torsion part of the cokernel, as a group, when $\mathbf{X}$ has independent entries from a specific distribution. The second main result relaxes the distributional assumption and concerns the ${\mathbb{Z}}[x]$ -module structure. The motivation for this work arises from an open problem in spectral graph theory, which asks to show that random graphs are often determined up to isomorphism by their (generalised) spectrum. Sufficient conditions for generalised spectral determinacy can, namely, be stated in terms of the cokernel of a walk matrix. Extensions of our results could potentially be used to determine how often those conditions are satisfied. Some remaining challenges for such extensions are outlined in the paper.

Small Area Estimation of Household Economic Indicators under Unit-Level Generalized Additive Models for Location, Scale and Shape

Abstract We propose a small area estimation model based on Generalized Additive Models for Location, Scale and Shape (SAE-GAMLSS) for the estimation of household economic indicators. SAE-GAMLSS relax the exponential family distributional assumption and allow each distributional parameter to depend on covariates. A bootstrap approach to estimate the MSE is proposed. The SAE-GAMLSS estimator shows a largely better performance than the well-known Empirical Best Linear Unbiased Predictor (EBLUP) under various simulated scenarios. Per-capita consumption of Italian and foreign households in Italian regions, in urban and rural areas, is estimated using SAE-GAMLSS. Results show that the well-known Italian North–South divide does not hold for foreigners.

Deep Neural Network-Based Accelerated Failure Time Models Using Rank Loss.

An accelerated failure time (AFT) model assumes a log-linear relationship between failure times and a set of covariates. In contrast to other popular survival models that work on hazard functions, the effects of covariates are directly on failure times, the interpretation of which is intuitive. The semiparametric AFT model that does not specify the error distribution is sufficiently flexible and robust to depart from the distributional assumption. Owing to its desirable features, this class of model has been considered a promising alternative to the popular Cox model in the analysis of censored failure time data. However, in these AFT models, a linear predictor for the mean is typically assumed. Little research has addressed the non-linearity of predictors when modeling the mean. Deep neural networks (DNNs) have received much attention over the past few decades and have achieved remarkable success in a variety of fields. DNNs have a number of notable advantages and have been shown to be particularly useful in addressing non-linearity. Here, we propose applying a DNN to fit AFT models using Gehan-type loss combined with a sub-sampling technique. Finite sample properties of the proposed DNN and rank-based AFT model (DeepR-AFT) were investigated via an extensive simulation study. The DeepR-AFT model showed superior performance over its parametric and semiparametric counterparts when the predictor was nonlinear. For linear predictors, DeepR-AFT performed better when the dimensions of the covariates were large. The superior performance of the proposed DeepR-AFT was demonstrated using three real datasets.

PATH ANALYSIS OF FACTORS INFLUENCING CASHLESS SOCIETY DEVELOPMENT USING BOOTSTRAP RESAMPLING

Path analysis can be applied to various fields, one of which is the field of banking economics. This study is aimed to examine what factors significantly affect the development of cashless society both directly and indirectly. There are many studies related to the development of cashless society but there has been no research that analyzes the relationship between marketing mix variables, such as product, price and promotion, with the development of cashless society. The data used came from the results of questionnaires with respondents of bank customers in Jakarta. Direct influence tests are carried out using bootstrap resampling hypothesis tests so that they are free from data distribution assumptions. It was found that product and digitalization of electronic money had a significant direct effect on the development of cashless society while price had a significant indirect effect on the development of cashless society.

Target Trial Emulation for Evaluating Health Policy.

Target trial emulation is an approach to designing rigorous nonexperimental studies by "emulating" key features of a clinical trial. Most commonly used outside of policy contexts, this approach is also valuable for policy evaluation as policies typically are not randomly assigned. In this article, we discuss the application of the target trial emulation framework in a policy evaluation context. The policy trial emulation framework includes 7 components: the units and eligibility criteria, definitions of the exposure and comparison conditions, assignment mechanism, baseline ("time zero") and follow-up, outcomes, causal estimand, and statistical analysis and assumptions. Policy evaluations that emulate a randomized trial across these dimensions can yield estimates of the causal effects of the policy on outcomes. Using the policy trial emulation framework to conduct and report on research design and methods supports transparent assessment of threats to causal inference in nonexperimental studies intended to assess the effect of a health policy on clinical or population health outcomes.

Artificial Intelligence and Machine Learning with Moment Generating Functions to Enhance Biological Count Data Analysis

This research presents artificial intelligence with supervised machine learning to determine the median count given training data from biological laboratory experimentation. After determining the central moment of the median, machine learning is then used to predict the population median value. When computer programs learn they access available data, then autonomously analyze the information to make informed, data-driven decisions. Moment generating function restrictions identify a parameter of interest by restricting the expected value of the moment generating function. This research proposes a theoretical foundation for achieving such predictions. A summary of the key elements underlying the statistical power of the Mann– Whitney test, a nonparametric hypothesis test for the median of count data, is also presented. A nonparametric approach allows for accurate predictions while relaxing distributional assumptions such as normality.

Joint modeling of zero-inflated longitudinal measurements and time-to-event outcomes with applications to dynamic prediction.

In this article, we present a joint modeling approach for zero-inflated longitudinal count measurements and time-to-event outcomes. For the longitudinal sub-model, a mixed effects Hurdle model is utilized, incorporating various distributional assumptions such as zero-inflated Poisson, zero-inflated negative binomial, or zero-inflated generalized Poisson. For the time-to-event sub-model, a Cox proportional hazard model is applied. For the functional form linking the longitudinal outcome history to the hazard of the event, a linear combination is used. This combination is derived from the current values of the linear predictors of Hurdle mixed effects. Some other forms are also considered, including a linear combination of the current slopes of the linear predictors of Hurdle mixed effects as well as the shared random effects. A Markov chain Monte Carlo method is implemented for Bayesian parameter estimation. Dynamic prediction using joint modeling is highly valuable in personalized medicine, as discussed here for joint modeling of zero-inflated longitudinal count measurements and time-to-event outcomes. We assess and demonstrate the effectiveness of the proposed joint models through extensive simulation studies, with a specific emphasis on parameter estimation and dynamic predictions for both over-dispersed and under-dispersed data. We finally apply the joint model to longitudinal microbiome pregnancy and HIV data sets.

Combining Biomarkers to Improve Diagnostic Accuracy in Detecting Diseases With Group-Tested Data.

We consider the problem of combining multiple biomarkers to improve the diagnostic accuracy of detecting a disease when only group-tested data on the disease status are available. There are several challenges in addressing this problem, including unavailable individual disease statuses, differential misclassification depending on group size and number of diseased individuals in the group, and extensive computation due to a large number of possible combinations of multiple biomarkers. To tackle these issues, we propose a pairwise model fitting approach to estimating the distribution of the optimal linear combination of biomarkers and its diagnostic accuracy under the assumption of a multivariate normal distribution. The approach is evaluated in simulation studies and applied to data on chlamydia detection and COVID-19 diagnosis.

Use of the Win Ratio for Analysis of Stroke Trials: Description, Illustration, and Planned Use in the Second European Carotid Surgery Trial (ECST-2).

Randomized trials in stroke often focus on outcomes beyond a single clinical event. Trials of stroke prevention commonly use composite outcomes that include multiple components (eg, death, stroke, or myocardial infarction). A major limitation is that all events count equally but may differ markedly in terms of clinical severity. Trials in acute stroke often use ordinal outcomes or scale scores. Limitations include the requirement for statistical assumptions and the difficulty of handling the competing risk of death. We introduce the win ratio as an alternative method. It works by placing components of a composite into a hierarchy, whereby clinically more important outcomes take priority over less important ones. We illustrate how it works using data from 2 major stroke trials: the ICSS (International Carotid Stenting Study, a trial in stroke prevention) and the MR CLEAN (Multicenter Randomized Clinical Trial of Endovascular Treatment for Acute Ischemic Stroke in the Netherlands). Potential benefits of the win ratio approach include the possibility to (1) emphasize the clinically most important outcomes, (2) combine components of different outcome types into a composite (eg, a mixture of time-to-event, continuous, and categorical), and (3) naturally handle the competing risk of death in analyses of quantitative outcomes. The win ratio will be used in the upcoming analysis of the ECST-2 (Second European Carotid Surgery Trial), which has a hierarchical primary outcome of (1) time to perioperative death, fatal stroke, or fatal myocardial infarction (most important); (2) time to nonfatal stroke; (3) time to nonfatal myocardial infarction (excluding silent infarcts); and (4) new silent cerebral infarct on brain imaging (least important). The win ratio provides a useful clinically relevant method for analyzing trial outcomes. It has some advantages over conventional methods, and we recommend its wider application in future stroke trials.

A [formula omitted]-means triangular synthesis large margin classifier with unified pinball loss for imbalanced data

Large Margin Distribution Machine (LDM) improves the Support Vector Machine (SVM) by integrating the marginal distribution of samples into the objective function, which exhibits excellent classification and generalization performance. However, most of the existing LDM-based models exhibit inherent flaws: (1) The assumption of a category uniform distribution, resulting in an inability to effectively address the issue of class imbalance. (2) The inheritance of the hinge loss in SVM, leading to inferior anti-noise performance. Given the shortcomings above, this paper constructs a novel K-means Triangular Synthesis (KTS) method for imbalanced data classification and introduces Unified Pinball (UP) loss to ensure robust performance, demonstrated as a novel KTS large margin classifier with UP Loss (KTS-UPLMC) model. Specifically, the KTS method utilizes the triangular synthesis and generates samples based on the cluster density, effectively mitigating the problems of introducing noise samples and strip-shaped sample distribution in the traditional synthetic minority oversampling technique, further alleviating the LDM’s classification line offset. In addition, the UP Loss considers quantile distance, improving the anti-noise performance of the model. Comparative experiments on artificial datasets and benchmark datasets validate the effectiveness and noise resistance of the proposed KTS-UPLMC in imbalanced data classification problems. Furthermore, the stability of the KTS-UPLMC is substantiated by the parameter sensitivity analysis experiment. In conclusion, the KTS method effectively addresses category imbalance, while the integration of the UP Loss enhances noise resistance.

Net-zero carbon emission oriented Bi-level optimal capacity planning of integrated energy system considering carbon capture and hydrogen facilities

The integrated energy system (IES) is considered an efficient energy provision paradigm to improve the utilization efficiency of renewable generation (RG), reduce energy cost and improve energy supply reliability. However, the multi-dimensional uncertainties and the hydrogen utilization have posed enormous challenges to the optimal planning of the IES. This paper proposes a net-zero carbon emission oriented bi-level optimal planning model for the IES with full consideration of the multiple operational uncertainties in the IES (RG, multiple demands). The upper level is an optimal capacity configuration model, and the economic costs, energy selling profits, the penalty for power abandonment and energy supply shortage are settled as the objectives. The lower level is an optimal energy dispatch model with the objective function of minimizing the total operating cost of the IES on typical days. An integrated energy system framework consisting of multiple energy flows is formulated in the presence of carbon capture system (CCS) and hydrogen-to-power (H2P) facilities. To fully characterize the uncertainties of RG and multiple demands, a data-driven scenario generation method is adopted to expand the operational scenarios, in which probability distribution assumptions and prior knowledge are not necessary. Finally, the effectiveness of the proposed solution is extensively demonstrated through numerical simulation, and a sensitivity analysis is carried out to assess the impact of changes in electricity and gas prices on the IES planning results.