Estimation Of Distribution Research Articles

Bayes estimation of a two-parameter exponential distribution and its implementation

Bayes estimation of a two-parameter exponential distribution and its implementation

Optimizing Group Size using Percentile Based Group Acceptance Sampling Plans with Application

The present paper focuses on optimizing the sample size and the acceptance number which are commonly known as design parameters for the group acceptance sampling plan (GASP). Design parameters are analyzed under the assumption that the characteristic of interest for the product follows Another Generalized Transmuted-Exponential (AGTransmuted-Exponential) distribution. Using different values of the quality levels (median lifetime), the values of the Operating Characteristic function is determined. The proposed plan satisfies two types of risks based on producer's point of view and consumer’s point of view at varied stipulated quality levels. Optimization of the sample size, group size and acceptance numbers is obtained through Monte Carlo simulation, for which relevant R codes were developed. Specific R codes are appended for future usage by academia and practitioners from various fields of life. The simulated results of the study are exhibited in the form of tables and explained with relevant examples. Results of the proposed GASP are compared with plan parameters obtained using MLE estimates of AGTransmuted-Exponential distribution and also by design parameters obtained using mean as quality level. Results of the study exhibited that Median as a quality parameter resulted in the decrease of group size and acceptance number simultaneously at all quality levels. Easy to follow the methodology of the current paper will open new vistas for applying the proposed GASP to a family of transmuted probability distributions. For illustration purposes, a real data set for fatigue fracture stress is analyzed using MLE estimates of AGTransmuted-Exponential distribution to demonstrate the implementation of the proposed sampling plan.

Toward Modeling Continental‐Scale Inland Water Carbon Dioxide Emissions

AbstractInland waters emit significant amounts of carbon dioxide (CO2) to the atmosphere; however, the global magnitude and source distribution of inland water CO2 emissions remain uncertain. These fluxes have previously been “statistically upscaled” by independently estimating dissolved CO2 concentrations and gas exchange velocities to calculate fluxes. This scaling, while robust and defensible, has known limitations in representing carbon source limitations and spatial variability. Here, we develop and calibrate a CO2 transport model for the continental United States, simulating carbon transport and transformation in >22 million hydraulically connected rivers, lakes, and reservoirs. We estimate 25% lower CO2 fluxes compared to upscaling estimates forced by the same observational calibration data. While precise CO2 source distribution estimates are limited by the resolution of model parameterizations, our model suggests that stream corridor CO2 production dominates over groundwater inputs at the continental scale. Our results further suggest that the lack of observational networks for groundwater CO2 and scalable metabolic models of aquatic CO2 production remain the most salient barriers to further coupling of our model with other Earth system components.

The Use of Image‐Based Data and Abundance Modelling Approaches for Predicting the Location of Vulnerable Marine Ecosystems in the South Pacific Ocean

ABSTRACTVulnerable marine ecosystems (VMEs) are typically fragile and slow to recover, thereby making them susceptible to disturbance, including fishing. In the high seas, the United Nations General Assembly (UNGA) requested regional fishery management organisations (RFMOs) to implement measures to prevent significant adverse impacts on VMEs. Here, we predict spatial abundances of 15 taxa, 13 VME indicator taxa, in the South Pacific RFMO (SPRFMO) area. Models used seafloor imagery data, an important advance on previously developed presence‐only predictions, to provide information on spatial variation in taxa abundance that is crucial for better inferring likely location of VMEs, rather than just distribution of VME indicator taxa. Abundance models varied in predictive power (mean R2 ranged 0.02–0.40). Uncertainty estimates of model predictions were developed to inform future spatial planning processes for conservation and management of VMEs. Using the VME index concept, abundance model outputs and previously published presence‐only model predictions were weighted using vulnerability scores, to explore how modelled outputs could provide spatial estimates of likely VME distribution. Spatial predictions of abundance improved on previous modelling to provide an almost complete suite of abundance models for VME indicator taxa in the western portion of the SPRFMO Convention area. Nevertheless, to improve utility of modelled outputs, we recommend more high‐quality seafloor imagery data be gathered within the SPRFMO Convention area to (1) validate abundance models developed here with independent data from the model area, (2) update models, if necessary, (3) link abundance information to ecosystem function and (4) explore validity of the adapted VME index approach used here.

Technical note: A GPU-based shared Monte Carlo method for fast photon transport in multi-energy x-ray exposures.

The Monte Carlo (MC) method is an accurate technique for particle transport calculation due to the precise modeling of physical interactions. Nevertheless, the MC method still suffers from the problem of expensive computational cost, even with graphics processing unit (GPU) acceleration. Our previous works have investigated the acceleration strategies of photon transport simulation for single-energy CT. But for multi-energy CT, conventional individual simulation leads to unnecessary redundant calculation, consuming more time. This work proposes a novel GPU-based shared MC scheme (gSMC) to reduce unnecessary repeated simulations of similar photons between different spectra, thereby enhancing the efficiency of scatter estimation in multi-energy x-ray exposures. The shared MC method selects shared photons between different spectra using two strategies. Specifically, we introduce spectral region classification strategy to select photons with the same initial energy from different spectra, thus generating energy-shared photon groups. Subsequently, the multi-directional sampling strategy is utilized to select energy-and-direction-shared photons, which have the same initial direction, from energy-shared photon groups. Energy-and-direction-shared photons perform shared simulations, while others are simulated individually. Finally, all results are integrated to obtain scatter distribution estimations for different spectral cases. The efficiency and accuracy of the proposed gSMC are evaluated on the digital phantom and clinical case. The experimental results demonstrate that gSMC can speed up the simulation in the digital case by ∼37.8% and the one in the clinical case by ∼20.6%, while keeping the differences in total scatter results within 0.09%, compared to the conventional MC package, which performs an individual simulation. The proposed GPU-based shared MC simulation method can achieve fast photon transport calculation for multi-energy x-ray exposures.

Applications and Advances of UCB Algorithms in Dynamic and Contaminated Environments

The Upper Confidence Bound (UCB) algorithm is a widely used approach in the Multi-Armed Bandit (MAB) problem, where the goal is to maximize cumulative rewards over time by selecting the best possible action among several options. The UCB algorithm uses confidence bounds to balance exploration and exploitation, guiding its decision-making. In recent years, researchers have identified significant challenges in applying the UCB algorithm to dynamic and contaminated environments. In such scenarios, the underlying conditions may change over time, making it difficult for standard UCB to adapt, or the data may be polluted by noise and outliers, leading to incorrect estimations of reward distributions. To address these challenges, several variants of the UCB algorithm have been developed. These new approaches are designed to better handle the complexities of changing environments and data contamination, ensuring more robust and reliable performance in these difficult settings. This paper aims to provide a comprehensive review of Robust-UCB (cr-UCB), Sliding Window UCB (SW-UCB) and bandit-over-bandit UCB (BOB-UCB). Focusing on their theoretical foundations, practical applications, and empirical performance. By examining how these algorithms have been adapted to handle the complexities of dynamic and contaminated environments, we found that the adaptability of these algorithms in dynamic environments is significantly improved, and they can effectively reduce decision-making errors caused by data pollution, thus providing a more reliable solution to the multi-armed bandit problem.

Semi-supervised distribution learning

Abstract This study addresses the challenge of distribution estimation and inference in a semi-supervised setting. In contrast to prior research focusing on parameter inference, this work explores the complexities of semi-supervised distribution estimation, particularly the uniformity problem inherent in functional processes. To tackle this issue, we introduce a versatile framework designed to extract valuable information from unlabelled data by approximating a conditional distribution on covariates. The proposed estimator is derived from the K-fold cross-fitting strategy, exhibiting both consistency and asymptotic Gaussian process properties. Under mild conditions, the proposed estimator outperforms the empirical cumulative distribution function in terms of asymptotic efficiency. Several applications of the methodology are given, including parameter inference and goodness-of-fit tests.

An Adaptive Kernel-Based Structural Change Test for Copulas

This paper proposes a structural change test for copula models based on the kernel smoothing method. The proposed approach enables adaptable estimation of the dynamic marginal distributions, either parametrically or semi-parametrically. The test statistic is formulated via the weighted quadratic distance between the local smoothing copula and the empirical copula function, utilizing pseudo-observations of marginal distributions. The test statistic is pivotal with an asymptotic standard Normal distribution, irrespective of the marginal distributions, parameters, and estimations, and is consistent against a wide range of smoothly transitioning structural changes as well as abrupt structural breaks for copula models. Monte Carlo simulations show that the test performs well in finite samples and outperforms existing tests in the case of periodic changes.

6.G. Scientific session: The importance of using country-specific severity distributions in burden of disease indicators

Abstract One of the most commonly used health gap summary measures in the field of public health is the Disability-adjusted life year (DALY). It has become the key metric for quantifying the burden of disease (BoD) and is used as an information source for setting priorities for health care and health service planning. The DALY metric quantifies gaps between a theoretical population in perfect health and the current health status related to both morbidity and mortality. It is the sum of the number of healthy life years lost due to disability (YLD) and death (YLL). The YLD summarises the loss of healthy life time using the frequency of diseases differentiated by severities or related health states (including sequelae). Depending on each health state, it converts the time spent with diseases into YLD by weighting each year with health limitation with so-called disability weights. This allows the two indicators YLL and YLD to be added to the DALY. Consequently, severity distributions are a means of describing the range of health loss along specific health states, which enables an accurate mapping with disability weights. For most of the diseases, these distributions are usually categorised as mild, moderate, severe, or no health loss (asymptomatic). Conditions with higher severity levels contribute more to the YLD and thus, to the overall disease specific BoD. The severity distributions are highly dependent on utilization at the individual level, but also on available health care services at the society level, which indicates that differences by settings are to be expected. Changes over time in the share of severe cases, for instance, may reflect the effectiveness of health interventions and policies. This underlines the importance of severity distributions, as they also reflect information about the quality of healthcare for those affected. The Global Burden of Disease (GBD) study applies for a significant proportion of their considered diseases uniform severity distributions across countries and broader regions. They acknowledge concerns over applying estimates of severity distributions based on limited data, noting that it is the only available information that they were able to use. As the YLD estimates are often utilized to develop and prioritize health policy interventions, there is a necessity for country-specific estimates that are evidence based and less susceptible to model assumptions. In most cases, the estimation of severity distributions involves complex methodology as data for such assessments are very limited or hardly reliable. In the following workshop, general concepts and country cases from Germany, Scotland, and Belgium will be presented covering a variety of diseases. The examples underline the importance of estimating national and even regional severity distributions when identifying the importance of diseases or comparing the health conditions of populations across time. Key messages • As the Burden of disease indicators are predominantly used to prioritize health interventions and allocate resources, it is crucial to use accurate information in the severity levels of disease. • Severity distributions reflect the health care services and vary across different settings. Utilising country-specific severity distributions when estimating Burden of Disease indicators is essential.

Presence-only fisheries bycatch data produce biased species distribution predictions for Alcyonacean corals on British Columbia’s continental shelf and slope

Sedentary benthic species such as Alcyonacea corals form critical habitat for fishes and invertebrates. Assessing anthropogenic risks to these organisms requires unbiased, species distribution models (SDMs) that attempt to map probabilities of coral presence in relation to bio-physical ocean characteristics; however, in deep-water settings, the accuracy of SDMs is highly variable and dependent on spatial and taxonomic resolution. Here we investigated how data and model types affect SDM predictions of Alcyonacea probability of presence. We compared predictions from generalized additive models (GAMs) fitted to presence-absence observations over a stratified-random survey design with predictions from maximum entropy models (Maxent) fitted to presence-only bycatch records from commercial fisheries. We use a simulation analysis to show that both model types (i.e., GAM or Maxent) using presence-only bycatch data produced biased estimates of species distribution. Additionally, the maxent model fit using presence-only bycatch data produced biased estimates of performance metrics (AUC, TSS) that were overly optimistic. This study demonstrates a need for presence-absence data collected using a robust survey sampling design to fit SDMs that will better inform marine protected area placement while minimizing unnecessary economic losses, such as forgone fishing yield, due to sub-optimal placement.

MEFDPN: Mixture exponential family distribution posterior networks for evaluating data uncertainty

The computation of uncertainty are crucial for developing a reliable machine learning model. The natural posterior network (NatPN) provides uncertainty estimation for any single exponential family distribution, but real-world data is often complex. Therefore, we introduce a mixture exponential family posterior network (MEFDPN), which extends the prior distribution to a mixture of exponential family distributions, aiming to fit complex distributions that better represent real data. During network training, MEFDPN independently updates the posterior Bayesian estimates for each prior distribution, and the weights of these distributions are updated based on the forward propagation results. Furthermore, MEFDPN calculates two types of uncertainty (aleatoric and epistemic) and combines them using entropy weighting to obtain a comprehensive confidence measure for each data point. Theoretically, MEFDPN achieves higher prediction accuracy, and experimental results demonstrate its capability to compute high-quality data comprehensive confidence. Moreover, it shows encouraging accuracy in Out-of-Distribution(OOD) detection and validation experiments. Finally, we apply MEFDPN to a materials dataset, efficiently filtering out OOD data. This results in a significant enhancement of prediction accuracy for machine learning models. Specifically, removing only 5% of outlier data leads to a 2%–5% improvement in accuracy.

A novel method to estimate the 3D chlorophyll a distribution in the South China Sea surface waters using hydrometeorological parameters

Chlorophyll a (Chl-a) is a key indicator of marine ecosystems, and certain hydro-meteorological parameters (HMPs) are highly correlated with its fluctuations. Here, relevant and accessible HMPs were used as inputs, combined with machine learning (ML) algorithms for estimating 3D Chl-a in the South China Sea (SCS). With the inputs of temperature, salinity, depth, wind speed, wind direction, sea surface pressure, and relative humidity, the LightGBM-based model performed well, achieving high R2 values of 0.985 and 0.789 in validation and testing sets, respectively. Based on a large number of in situ measurements, this model enables the estimation of the 3D distribution of summer Chl-a in the SCS over the past fifteen years using a 3D hydrographic dataset combined with surface meteorological parameters. The results show that the 3D distribution of the model estimated Chl-a is characterized similarly to the previous studies and can capture the effect of hydro-meteorological conditions on Chl-a distribution. The environmental variables affecting Chl-a were considered more comprehensively in this study, and the methodological framework has the potential to be applied to the low-cost monitoring of the remaining water quality parameters.

Estimation of Free-Product PCE Distribution in Thick Multilayered Aquifers as Possible Long-Term Pollution Sources for Shallow and Deep Groundwaters, Using High-Precision Numerical Simulations

Estimation of Free-Product PCE Distribution in Thick Multilayered Aquifers as Possible Long-Term Pollution Sources for Shallow and Deep Groundwaters, Using High-Precision Numerical Simulations

Core Concepts in Pharmacoepidemiology: Time-To-Event Analysis Approaches in Pharmacoepidemiology.

This article provides an overview of time-to-event (TTE) analysis in pharmacoepidemiology. The key concept of censoring is reviewed, including right-, left-, interval- and informative censoring. Simple descriptive statistics are explained, including the nonparametric estimation of the TTE distribution as per Kaplan-Meier method, as well as more complex TTE regression approaches, including the parametric Accelerated Failure Time (AFT) model and the semi-parametric Cox Proportional Hazards and Restricted Mean Survival Time (RMST) models. Additional approaches and various TTE model extensions are presented as well. Finally, causal inference for TTE outcomes is addressed. A thorough review of the available concepts and methods outlines the immense variety of available and useful TTE models. There may be underused TTE concepts and methods, which are highlighted to raise awareness for researchers who aim to apply the most appropriate TTE approach for their study. This paper constitutes a modern summary of TTE analysis concepts and methods. A curated list of references is provided.

On fractional moment estimation from polynomial chaos expansion

Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by statistical sampling is challenging since it is typically not possible to create a large experimental design due to limitations in computing capacity. This paper presents a novel approach for the analytical estimation of fractional moments, directly from polynomial chaos expansions. Specifically, the first four statistical moments obtained from the deterministic coefficients of polynomial chaos expansion are used for an estimation of arbitrary fractional moments via Hölder’s inequality. The proposed approach is utilized for an estimation of statistical moments and probability distributions in four numerical examples of increasing complexity. Obtained results show that the proposed approach achieves a superior performance in estimating the distribution of the response, in comparison to a standard Latin hypercube sampling in the presented examples.

A novel generalised extreme value gradient boosting decision tree for the class imbalanced problem in credit scoring

The performance of credit scoring models can be compromised when dealing with imbalanced datasets, where the number of defaulted borrowers is significantly lower than that of non-defaulters. To address this challenge, we propose a gradient boosting decision tree with the generalised extreme value distribution model (GEV-GBDT). Our approach replaces the conventional symmetric logistic sigmoid function with the asymmetric cumulative distribution function of the GEV distribution as the activation function. We derive a novel loss function based on the maximum likelihood estimation of the GEV distribution within the boosting framework. This modification allows the model to focus more on the minority class by emphasising the tail of the response curve, and the shape parameter of the GEV distribution offers flexibility in controlling the model’s emphasis on minority samples. We examine the performance of this approach using four real-life loan datasets. The empirical results show that the GEV-GBDT model achieves superior classification performance compared to other commonly used imbalanced learning methods, including the synthetic minority oversampling technique and the cost-sensitive framework. Furthermore, we conduct performance tests on several datasets with varying imbalance ratios and find that GEV-GBDT performs better on extremely imbalanced datasets.

Development of electromagnetic pollution maps utilizing Gaussian process spatial models

The rapid proliferation of wireless technologies in everyday environments demands the quick and precise estimation of electromagnetic field distribution. This distribution is commonly depicted through the electric field strength across various geographical areas. The objective of this research is to determine the most effective geospatial model for generating a national-level electric field strength map within the 30 MHz–6 GHz frequency range. To achieve this, we employed five different methodologies for constructing the electric field strength map. Four of these methodologies are based on Gaussian process regression, while the fifth utilizes the classical weighted-average method of the nearest neighbor. Our study focused on a country with a total area of 9251 km2, using a dataset comprising 3621 measurements. The findings reveal that Gaussian process spatial models, also known as Kriging models, generally outperform other methods when applied to spatial data. However, it was observed that, after excluding some outlier data points, the performance of the classical nearest neighbor models becomes comparable to that of the Gaussian process models. This indicates the potential for both approaches to be effective, depending on the data quality and the presence of outliers.

Ridge-type covariance and precision matrix estimators of the multivariate normal distribution

AbstractWe consider ridge-type estimation of the multivariate normal distribution’s covariance matrix and its inverse, the precision matrix. While several ridge-type covariance and precision matrix estimators have been presented in the literature, their respective inverses are often not considered as precision and covariance matrix estimators even though their estimands are one-to-one related through the matrix inverse. We study which estimator is to be preferred in what case. Hereto we compare the ridge-type covariance matrix estimators and their properties to that of the inverse of the ridge-type precision matrix estimators, and vice versa. The comparison, in which we take all ridge-type estimators along, is limited to a specific case that is illustrative of the difference between the covariance and precision matrix estimators. The comparison addresses the estimators’ estimating equation, analytic expression, analytic properties like positive definiteness and penalization limit, mean squared error, consistency, Bayesian formulation, and their loss and potential for marginal and partial correlation screening.

Integrating Surface-related Indicators of Coverage, Distance and Distribution for Quantifying Scan-to-BIM Confidence Level

Abstract. Scan-to-BIM is a widely-used approach to generate Building Information Modelling and by extension Digital Twin models in the architecture, engineering, and construction sector. The resulting models need to be as accurate as possible to ensure subsequent activities that make use of them can do so effectively. Quality assessment of point clouds and occlusion assessment of BIM outputted from Scan-to-BIM has been investigated. However, Scan-to-BIM systems currently do not provide proper metrics as to the confidence the user can have in the quality, in particular geometric quality of the outputted model. This paper addresses this gap by introducing a confidence index, for analysing the reliability of the generated 3D models and thereby quantifying the confidence the user can have in them. Index of confidence is itself derived from three more specific indices: index of coverage estimates the portion of the surface of the modelled element that is explained by the input point cloud. Index of distribution estimates how well the points explaining the modelled surfaces are distributed around the overall object’s surface. Index of distance defines the closeness of the generated element models to the input point cloud. The proposed indices are assessed using three real examples, demonstrating their adequacy.

Computationally cost-efficient analysis of the flow behavior of twin-fluid atomizers using computational fluid dynamics

In industrial-scale operations, wet electrostatic precipitators (WESPs) are used to minimize particulate matter, employing atomizers such as single-fluid and twin-fluid atomizers (TFAs). While TFAs provide several benefits over single-fluid atomizers, quantifying their spray characteristics is more complex, necessitating comprehensive case studies to design the internal structure of the spray and achieve desired properties. This study employed computational fluid dynamics (CFD) to simulate the internal and external flow phenomena of TFAs in industrial-scale WESPs, aiming to facilitate various parametric studies by reducing the high computational costs associated with analyzing high-speed internal flows and particle dynamics within the spray system. To decrease computational costs, the simulation was divided into two parts using stepwise segregated scenarios: Part I focused on the high-cost internal flow analysis, examining the spatiotemporal evolution of internal flow until it is fully developed, followed by droplet size distribution estimation at the nozzle. Part II computed the external flow of the spray, assessed potential cost reductions by examining the interactions between dispersed droplets, and validated the spray angle, penetration, and coverage against experimental data. The segregated strategy employed mapping techniques to integrate the two parts seamlessly. The simulation results closely matched the experimental benchmarks for spray angle, penetration, and coverage within a minimal error margin (< 5 %), demonstrating the model’s accuracy in capturing actual spray phenomena in TFAs. This approach significantly reduced the computational cost by more than twentyfold compared to conventional one-step solvers, offering a viable method for conducting various case studies in spray CFD simulations.