Distributional Assumptions Research Articles

Supervised Learning-Based Prediction of Lightning Probability in the Warm Season

The accurate prediction of lightning is crucial for forecasters to respond effectively to its related hazards. The rapid development and confined spatial extent of convective storms, in which lightning frequently occurs, pose considerable challenges for accurately predicting their locations using numerical weather prediction (NWP) models. Lightning occurrence is often prognosed using thermodynamic parameters, convective available potential energy (CAPE), the severe weather threat index (SWEAT), the lifted index (LI), etc. A high-resolution NWP model provides a prediction of these thermodynamic parameters at high spatiotemporal resolution with high accuracy for a few hours. However, a complicated algorithm is required to handle all the useful high-resolution variables from the NWP model. The recently emerging machine learning technique can solve this issue by properly handling these “big data” without any model distributional assumption. In this study, we developed a random forest algorithm for nowcasting and very short-range forecasting (useful for ~6 h), named LightningRF. LightningRF was trained by using lightning occurrence as a response variable and characteristic parameters from the NWP as predictors. It was also applied to analysis and forecast fields, showing a high probability of lightning within the observed lightning regions. This highlights the potential of helping forecasters improve their lightning forecasting skills using real-time probabilistic forecasts from a trained model.

Numerical investigation of lean methane flame response to NRP discharges actuation

This study investigates the response of a laminar methane-air flame to Nanosecond Repetitively Pulsed (NRP) discharges in a canonical wall-stabilized burner using a combined experimental and numerical approach. The flow and flame behaviors were modeled using Direct Numerical Simulation (DNS) with an Analytically Reduced Chemistry for a precise chemical description. A phenomenological model incorporating detailed plasma kinetics and experimental observations was developed to simulate plasma effects. Zero-dimensional plasma reactor simulations were used to build up a reduced-order model describing discharge energy distribution in the specific conditions studied. Experimental measurements of electrical profiles identified two discharge regimes: a low-energy Corona discharge and a higher-energy Glow discharge, characterized by distinct spatial energy distributions. Experimental flame response analysis revealed three major phases: marginal response up to 100 pulses, a downstream shift of the flame tip, and stabilization after 400 pulses. Numerical simulations indicated that the Corona regime is crucial for explaining initial flame responses, while the Glow regime influences later stages. Adjustments in the Vibrational-Translational (VT) energy relaxation time and energy deposition ratios between fresh and burnt gases were necessary to match experimental observations. Additionally, an accurate modeling of the transient and steady-state flame responses requires integrating both the specificity of the Corona and the Glow discharge regimes. Future work should focus on measuring or theoretically calculating N2(v) relaxation times in CH4-H2O-CO2 mixtures and analyzing the spatial energy distribution of discharges interacting with flames to enhance plasma-combustion coupled models.Novelty and significanceIn this work, a phenomenological plasma-assisted combustion model has been developed, to investigate a laminar premixed stagnation plate burner, focusing on VT energy relaxation time and spatio-temporal energy distribution modeling. For the first time, not only O2, N2 and O but also the fuel and combustion intermediates and products have been considered in the VT relaxation model. It revealed their strong influence on the overall flame response in a case where the discharge crosses a flame front, highlighting the strong beneficial effect of energy deposited in vibrational form. The study questions and investigates the energy distribution from fresh to burnt gases, challenging the conventional uniform energy distribution assumption. The experimental identification of two specific plasma regimes was necessary to predict the transient flame response. Additionally, energy deposited downstream of the flame, in fresh gases, was found to more efficient than in hot gases to enhance combustion.

Assessing the hierarchical beta-binomial model as a basic information sharing tool in basket trials

ABSTRACT The majority of statistical methods to share information in basket trials are based on a Bayesian hierarchical model with a common normal distribution for the logit-transformed response rates. The methods are of varying complexity, yet they all use this basic model. Generally, complexity is an obstacle for the application in clinical trials and that includes the use of the logit-transformation. The transformation complicates the model and impedes a direct interpretation of the hyperparameters. On the other hand, there exist basket trial designs which directly work on the probability scale of the response rate which facilitates the understanding of the model for many stakeholders. In order to reduce unnecessary complexity, we considered using a hierarchical beta-binomial model instead of the transformed models. This article investigates whether this approach is a practicable alternative to the commonly applied sharing tools based on a logit-transformation of the response rates. For this purpose, we performed a systematic comparison of the two models, starting with the distributional assumptions for the response rates, continuing with the Bayesian behavior together with binomial data in an independent setting and ended with a simulation study for the hierarchical model under various data and prior scenarios. All Bayesian comparisons require equal starting points, wherefore we propose a calibration procedure to choose similar priors for the models. The evaluation of the sharing property additionally required an evaluation measure for simulation results, which we derived in this work. The conclusion of the comparison is that the hierarchical beta-binomial model is a feasible alternative basic model to share information in basket trials.

A statistical evaluation of the sexual dimorphism of the acetabulum in an Iberian population.

Sex estimation is essential for human identification within bioarchaeological and medico-legal contexts. Amongst the sexually dimorphic skeletal elements commonly utilised for this purpose, the pelvis is usually preferred because of its direct relationship with reproduction. Furthermore, the posterior part of the innominate bone has proven to have better preservation within degraded contexts. With the aim of investigating the potential of the vertical acetabular diameter as a sex marker, 668 documented individuals from three different Iberian skeletal collections were randomly divided into training and test samples and eventually analysed using different statistical approaches. Two traditional (Discriminant Function Analysis and Logistic Regression Analysis) and four Machine learning methodologies (Support Vector Classification, Decision Tree Classification, k Nearest Neighbour Classification, and Neural Networks) were performed and compared. Amongst these statistical modalities, Machine Learning methodologies yielded better accuracy outcomes, with DTC garnering highest accuracy percentages of 83.59% and 89.85% with the sex-pooled and female samples, respectively. With males, ANN yielded highest accuracy percentage of 87.70%, when compared to other statistical approaches. Higher accuracy obtained with ML, along with its minimal statistical assumptions, warrant these approaches to be increasingly utilised for further investigations involving sex estimation and human identification. In this line, the creation of a statistical platform with easier user interface can render such robust statistical modalities accessible to researchers and practitioners, effectively maximising its practical use. Future investigations should attempt to achieve this goal, alongside examining the influence of factors such as age, on the obtained accuracy outcomes.

Double-Layer Distributed and Integrated Fault Detection Strategy for Non-Gaussian Dynamic Industrial Systems.

Currently, with the increasing scale of industrial systems, multisensor monitoring data exhibit large-scale dynamic Gaussian and non-Gaussian concurrent complex characteristics. However, the traditional principal component analysis method is based on Gaussian distribution and uncorrelated assumptions, which are greatly limited in practice. Therefore, developing a new fault detection method for large-scale Gaussian and non-Gaussian concurrent dynamic systems is one of the urgent challenges to be addressed. To this end, a double-layer distributed and integrated data-driven strategy based on Laplacian score weighting and integrated Bayesian inference is proposed. Specifically, in the first layer of the distributed strategy, we design a Jarque-Bera test module to divide all multisensor monitoring variables into Gaussian and non-Gaussian blocks, successfully solving the problem of different data distributions. In the second layer of the distributed strategy, we design a dynamic augmentation module to solve dynamic problems, a K-means clustering module to mine local similarity information of variables, and a Laplace scoring module to quantitatively evaluate the structural retention ability of variables. Therefore, this double-layer distributed strategy can simultaneously combine the different distribution characteristics, dynamism, local similarity, and importance of variables, comprehensively mining the local information of the multisensor data. In addition, we develop an integrated Bayesian inference strategy based on detection performance weighting, which can emphasize the differential contribution of local models. Finally, the fault detection results for the Tennessee Eastman production system and a diesel engine working system validate the superiority of the proposed method.

An adaptive photovoltaic power interval prediction based on multi-objective optimization

Photovoltaic (PV) power interval prediction can provide a variation range of prediction results, which is of great significance to promoting the optimization of power grid dispatching and maintaining the stability of the power system. However, the existing PV interval prediction fails to accurately reflect error fluctuations in their construction process due to dependency on data distribution assumptions and unreasonable estimation of prediction error standard deviations (PEStds). To address these issues, we propose an adaptive interval prediction method based on multi-objective optimization. Firstly, K-means clustering is used to segment similar days. Subsequently, Convolutional Neural Network-Gated Recurrent Unit-Attention (CNN-GRU-Attention) is utilized for point prediction. Furthermore, Grey Relation Analysis (GRA) is used to screen dates similar to the target date under the same weather type, enabling a more precise estimation of prediction error fluctuations. Ultimately, the estimated values are multiplied by non-fixed parameters to construct intervals, which avoids the dependency on data distribution assumptions. Among them, the optimal values for non-fixed parameters are obtained through multi-objective optimization considering interval coverage probability, interval width, and deviation. To verify the effectiveness of the proposed model, we conduct comparative experiments on two datasets with different resolutions. The results demonstrate that the proposed model offers more flexible and higher-quality intervals. Not only does this research improve the accuracy of PV power generation interval prediction, but it also helps to promote the development of smart grid technology and improve the adaptive ability of power systems facing dynamic environments and complex data, which has an important impact on the future energy management and power market.

Simulating multi-scale optimization and variable selection in species distribution modeling

Species distribution modeling (SDM) is a fundamental tool in theoretical and applied ecology. However, relatively little is known about the performance of different approaches for scale optimization, model selection, and algorithmic prediction in the context of nonlinear, multiscale and interactive relationships between environmental variables and species occurrence. Modelers often struggle to optimize a tradeoff between ecological relevance, model robustness, complexity, and overfitting. In this paper, we investigated several methods designed to optimize spatial scale and variable selection in SDMs, in each case evaluating model fitness, parsimony and predictive performance. We used a simulation approach to produce a large pool of alternative underlying habitat relationships that reflect a broad range of realistic habitat associations. We also compared several different modeling algorithms, including logistic regression with a generalized linear model (GLM), Lasso and Elastic-Net Regularized GLMs (GLMNet), and random forest (RF), as well as alternative variable and scale selection methods. We found that GLM methods employing all-subsets dredge routines for variable selection were consistently the best predictors based on all criteria of our model performance assessment and across all attributes of the simulated underlying relationship, including nonlinearity and interaction. We had expected machine learning approaches, such as random forest, to perform better in these more complex forms of species-environment relationships. GLM using dredge variable selection was also the method that included the fewest spurious covariates and included the most correct predictors as a proportion of all predictors. We found that univariate scaling was the most robust method of variable and scale selection, along with Minimal Redundancy Maximal Relevancy (MRMR) which performed equivalently. The simulation experiment presented here provides a robust assessment of simulated multi-species distribution model performance, complexity and fidelity. By simulating a large range of potential habitat relationships with varying spatial scale, effect sizes, linearity, and interactions, we comprehensively evaluated model performance across gradients of complexity of the underlying relationships and violations of classical statistical assumptions. This study provides a valuable assessment and a broader example of the power and utility of controlled simulation experiments in habitat relationships and other ecological spatial predictive modeling.

Mathematical Modeling of Mating Probability and Fertile Egg Production in Helminth Parasites.

In this work, we obtained a general formulation for the mating probability and fertile egg production in helminth parasites, focusing on the reproductive behavior of polygamous parasites and its implications for transmission dynamics. By exploring various reproductive variables in parasites with density-dependent fecundity, such as helminth parasites, we departed from the traditional assumptions of Poisson and negative binomial distributions to adopt an arbitrary distribution model. Our analysis considered critical factors such as mating probability, fertile egg production, and the distribution of female and male parasites among hosts, whether they are distributed together or separately. We show that the distribution of parasites within hosts significantly influences transmission dynamics, with implications for parasite persistence and, therefore, with implications in parasite control. Using statistical models and empirical data from Monte Carlo simulations, we provide insights into the complex interplay of reproductive variables in helminth parasites, enhancing our understanding of parasite dynamics and the transmission of parasitic diseases.

Impact of non-thermal phase-space distributions on dark matter abundance in secluded sectors

Many new physics models include secluded sectors that interact little with the Standard Model and whose internal interactions control the dark matter abundance. If these same interactions are responsible for maintaining kinematic equilibrium within the secluded sector, it is possible that the phase-space distributions will differ considerably from their thermal values during freeze-out. This can potentially result in deviations of the dark matter abundance from that computed under the assumption of thermal distributions. In this paper, we revisit dark matter abundance computations for a benchmark secluded sector by numerically tracking the phase-space distributions. Namely, we show that the dark matter abundance can deviate considerably from standard results during the freeze-out process, but that a longer period of annihilation ultimately leaves only a slight excess.

Using Exact Tests from Algebraic Statistics in Sparse Multi-Way Analyses: An Application to Analyzing Differential Item Functioning

Asymptotic goodness-of-fit methods in contingency table analysis can struggle with sparse data, especially in multi-way tables where it can be infeasible to meet sample size requirements for a robust application of distributional assumptions. However, algebraic statistics provides exact alternatives to these classical asymptotic methods that remain viable even with sparse data. We apply these methods to a context in psychometrics and education research that leads naturally to multi-way contingency tables: the analysis of differential item functioning (DIF). We explain concretely how to apply the exact methods of algebraic statistics to DIF analysis using the R package algstat, and we compare their performance to that of classical asymptotic methods.

Fuzzy Regression Discontinuity Designs With Multiple Control Groups Under One-Sided Noncompliance: Evaluating Extended Time Accommodations

Since its conception by Thistlethwaite and Campbell, a regression discontinuity (RD) design has continuously evolved and progressed in various aspects. This paper explores a novel theoretical advancement in fuzzy RD designs by combining them with multiple control groups under one-sided noncompliance. Within this approach, we estimate the average treatment effect on the treated at the cutoff from the fuzzy RD design and construct its bounds derived from multiple control groups. Using the bounds as a sensitivity check, we examine whether the underlying causal or statistical assumptions for the fuzzy RD design are warranted. We verify the effectiveness of our approach via a simulation study and demonstrate its application by studying the effect of extended time accommodations using data from the National Assessment of Educational Progress.

Theory and Design of Audio Rooms: Physical Formulation

The time-dependent statistical chains of transition matrix B are successfully used to calculate the reverberation time TR and sound energy density field in audio rooms. This is a real breakthrough in the search for a statistical derivation of Sabines' imperial theory which has never been rigorously proven since 1898. Additionally, we provide proper design and calculations of sound wave energy density in audio rooms via two cuboid room examples. We provide proper design and calculations of sound wave energy density in audio rooms via two cuboid room examples. We also propose some general statistical rules that can be applied to statistical problems of physical phenomena in general, such as the thermal diffusion equation and the theory of sound waves in audio rooms. We also give a description of the theory and design of what we call comfortable sound rooms based on the purpose of their use via well-defined measurables. Finally, we provide a consistent derivation of Sabines' theory without using Ls=4V/A or any other statistical assumptions.

493 Predicting pellet quality using multiple linear regression with Principal Component Analysis (PCA)

Abstract Pellet quality is a crucial key performance indicator (KPI) for commercial feed manufacturing, which influences both the efficiency of the feed mill and downstream performance of animals fed these diets. However, due to the complexity of feed manufacturing and the large number of factors involved in the manufacturing process, controlling pellet quality is an ongoing challenge for the feed industry. Previous studies have mainly explored the impact of a few factors on pellet quality under experimental settings, and empirical equations have been seldomly developed to reflect the relationship between the factors and pellet quality under the commercial feed mill settings. This study aimed to establish a relationship between pellet quality and factors collected under the settings of a commercial feed mill. The data were collected from Trouw Nutrition Canada’s feed mill located in St. Marys, Ontario (Plant 2), between December 15, 2021, and December 6, 2022. During this period, 2,691 observations were collected, with each observation representing an individual batch of pelleted feed. A total of 75 factors were recorded, including 4 factors associated with the general information of each batch, 10 manufacturing parameters, 41 feed ingredients, 8 factors regarding the nutrient composition of each diet, and 12 environmental factors. Pellet Durability Index (PDI), which was the response variable, was determined for each batch using the Holmen method. The data were randomly split into an 80% subset for training and a 20% subset for testing. The training subset was used to construct the model via a 5-fold cross-validation, while the testing subset was withheld as an independent dataset to evaluate the generalization performance of the model. The response variable (PDI) was transformed (tPDI) using the Box-Cox method to meet a normal distribution assumption. To avoid multicollinearity, Principal Component Analysis (PCA) was used to reduce the dimensionality of the numeric factors before building the multiple linear regression model. The model prediction performance was evaluated on both the training subset (using 5-fold cross-validation) and the testing subset, and the prediction performance metrics were consistent between the two subsets (Mean Absolute Error = 1.94 ± 0.102 vs. 2.02; Root Mean Square Prediction Error = 2.47 ± 0.111 vs. 2.58; Mean Square Prediction Error = 6.12 ± 0.538 vs. 6.68; Concordance Correlation Coefficient = 0.538 ± 0.0231 vs. 0.490; Pearson Correlation Coefficient = 0.606 ± 0.0247 vs. 0.553, respectively). Most feed ingredients and nutrient compositions showed either positive or negative loadings on Component 1 (17.87% of total variance), and outdoor/indoor environmental factors were positively loaded on Component 2 (14.21% of total variance). The model developed in this study could help commercial feed mills better understand how various factors impact pellet quality and optimize the manufacturing processes of pelleted feeds.

Identification and estimation of entry games under symmetry of unobservables

Abstract This paper provides a new point identification and estimation method for two-player entry games with complete information, based on symmetry of unobservables. Neither equilibrium selection nor parametric distributional assumptions are required. In addition, a weaker support condition is used relative to the existing literature. Unlike other semiparametric estimators, the estimator proposed here is $\sqrt{n}$-consistent. A test of the required symmetry condition is provided. Monte Carlo evidence shows that the estimator performs well with moderate sample sizes, and is robust to unimodal and multimodal error distributions. The estimator is applied to an entry game of discount retailers in Jia (2008). Our results suggest that researchers should apply the normality assumption with caution.

Diffusion random Fourier adaptive filtering algorithm based on logistic distance metric for distributed estimation

Distributed adaptive filtering over networks can improve filtering performance by fusing information from nodes within the same neighbor. In nonlinear estimation, adaptive filters derived from a linear framework usually suffer from large misalignment. To solve the above problem, this work develops a diffusion kernel filtering algorithm based on the random Fourier approximation method. To promote robustness to impulsive noise, the minimum logistic distance metric (LDM) is employed as a loss function. Compared to traditional kernel algorithms, the presented algorithm uses a fixed-length filter and is suitable for online distributed adaptive filtering tasks. In addition, this work also conducts a performance analysis based on Isserlis' and Price's theorems with several statistical assumptions. Simulations are conducted to exhibit the robustness of the proposed method to impulsive noise and to examine the accuracy of the theory on performance analysis.

Conditional symmetry test based on empirical characteristic function

In this paper, we propose a method for testing the conditional symmetry of multivariate random variables, specifically testing whether or not the conditional distribution of one random variable is symmetric around zero given another. Both the conditional symmetry test for observable data and unobserved error terms in parametric models are considered. The proposed test statistics are built on the weighted L 2 -distance between empirical characteristic functions and require no distributional assumption about the data distribution. The asymptotic properties of the test statistics under the null and alternative hypotheses are investigated. Since the limiting null distributions are intractable, a nonparametric Monte Carlo resampling method is used to determine critical values. Simulation results show the good performance of the proposed method in various scenarios. Two real datasets are analysed to illustrate the practical usefulness of the proposed tests.

Enhanced Parameter Estimation of DENsity CLUstEring (DENCLUE) Using Differential Evolution

The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For instance, DENsity CLUstEring (DENCLUE)—a density-based clustering algorithm—requires a trial-and-error approach to find suitable parameters for optimal clusters. Earlier attempts to automate the parameter estimation of DENCLUE have been highly dependent either on the choice of prior data distribution (which could vary across datasets) or by fixing one parameter (which might not be optimal) and learning other parameters. This article addresses this challenge by learning the parameters of DENCLUE through the differential evolution optimisation technique without prior data distribution assumptions. Experimental evaluation of the proposed approach demonstrated consistent performance across datasets (synthetic and real datasets) containing clusters of arbitrary shapes. The clustering performance was evaluated using clustering validation metrics (e.g., Silhouette Score, Davies–Bouldin Index and Adjusted Rand Index) as well as qualitative visual analysis when compared with other density-based clustering algorithms, such as DPC, which is based on weighted local density sequences and nearest neighbour assignments (DPCSA) and Variable KDE-based DENCLUE (VDENCLUE).

A structurally informed data assimilation approach for nonlinear partial differential equations

Ensemble-based Kalman filtering data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is well known that the commonly used Gaussian distribution assumption introduces biases for state variables that admit discontinuous profiles, which are prevalent in nonlinear partial differential equations. This investigation designs a new structurally informed prior that exploits statistical information from the simulated state variables. In particular, based on the second moment information of the state variable gradient, we construct a new weighting matrix for the numerical simulation contribution in the data assimilation objective function. This replaces the typical prior covariance matrix used for this purpose. We further adapt our weighting matrix to include information in discontinuity regions via a clustering technique. Our numerical experiments demonstrate that this new approach yields more accurate estimates than those obtained using standard ensemble-based Kalman filtering on shallow water equations, even when it is enhanced with inflation and localization techniques.

Characterizing patterns of diffusion tensor imaging variance in aging brains.

As large analyses merge data across sites, a deeper understanding of variance in statistical assessment across the sources of data becomes critical for valid analyses. Diffusion tensor imaging (DTI) exhibits spatially varying and correlated noise, so care must be taken with distributional assumptions. Here we characterize the role of physiology, subject compliance, and the interaction of subject with the scanner in the understanding of DTI variability, as modeled in spatial variance of derived metrics in homogeneous regions. We analyze DTI data from 1035 subjects in the Baltimore Longitudinal Study of Aging (BLSA), with ages ranging from 22.4 to 103 years old. For each subject, up to 12 longitudinal sessions were conducted. We assess variance of DTI scalars within regions of interest (ROIs) defined by four segmentation methods and investigate the relationships between the variance and covariates, including baseline age, time from the baseline (referred to as "interval"), motion, sex, and whether it is the first scan or the second scan in the session. Covariate effects are heterogeneous and bilaterally symmetric across ROIs. Inter-session interval is positively related ( ) to FA variance in the cuneus and occipital gyrus, but negatively ( ) in the caudate nucleus. Males show significantly ( ) higher FA variance in the right putamen, thalamus, body of the corpus callosum, and cingulate gyrus. In 62 out of 176 ROIs defined by the Eve type-1 atlas, an increase in motion is associated ( ) with a decrease in FA variance. Head motion increases during the rescan of DTI ( millimeters per volume). The effects of each covariate on DTI variance, and their relationships across ROIs are complex. Ultimately, we encourage researchers to include estimates of variance when sharing data and consider models of heteroscedasticity in analysis. This work provides a foundation for study planning to account for regional variations in metric variance.

Rationale and Design of the COPERNIC Trial: A Study of On-treatment ctDNA Changes in Chemo-refractory Colorectal Cancer Patients

BackgroundEvidence suggests that ctDNA may be a reliable biomarker to monitor metastatic colorectal cancer (CRC) evolution. Nevertheless, evidence on the potential of liquid biopsy in this setting is still low quality, mostly consisting of retrospective studies. MethodsCOPERNIC is an international, multicenter clinical trial. The pilot study aims to confirm the predictive potential of early on-treatment ctDNA dynamics, and inform the design of a larger ctDNA-driven trial. Advanced CRC patients who are candidates for ≥3rd lines of systemic therapy undergo longitudinal blood sample collection during treatment (day 1, 15 and 29 for 2- or 4-weekly treatment regimens; day 1, 22 and 43 for 3-weekly treatment regimens) and at each imaging assessment. ctDNA analyses are carried out with the FoundationOne Liquid CDx and FoundationOneMonitor assays, and ctDNA changes during treatment are correlated with radiologic response (as assessed every 8-12 weeks by RECIST v1.1). The primary objective is to select the optimal timepoint and cut-off value for early ctDNA changes (at day 15/22) to predict progressive disease as best radiological response with a high positive predictive value. The cut-off value for ctDNA will be defined based on nonparametric ROC-curves with bootstrapping. Based on the expected rate of progressive disease and statistical assumptions, 109 patients are needed to be screened to have 87 assessable patients. COPERNIC is sponsored by the Institut Jules Bordet, and supported by Roche and Foundation Medicine. Recruitment is open in 13 centres across Belgium and France. The study is registered with clinicaltrials.gov (NCT05487248).