Estimation Of Distribution Research Articles

Ocean Wave Directional Distribution from GPS Buoy Observations off the West Coast of Ireland: Assessment of a Wavelet-Based Method

Abstract Knowledge of the directional distribution of a wave field is crucial for a better understanding of complex air–sea interactions. However, the dynamic and unpredictable nature of ocean waves, combined with the limitations of existing measurement technologies and analysis techniques, makes it difficult to obtain precise directional information, leading to a poor understanding of this important quantity. This study investigates the potential use of a wavelet-based method applied to GPS buoy observations as an alternative approach to the conventional methods for estimating the directional distribution of ocean waves. The results indicate that the wavelet-based estimations are consistently good when compared to the framework of widely used parameterizations for the directional distribution. The wavelet-based method presents advantages in comparison with the conventional methods, including being purely data-driven and not requiring any assumptions about the shape of the distribution. In addition, it was found that the wave directional distribution is narrower at the spectral peak and broadens asymmetrically at higher and lower scales, particularly sharply for frequencies below the peak. The directional spreading appears to be independent of the wave age across the entire range of frequencies, implying that the angular width of the directional spectrum is primarily controlled by nonlinear wave–wave interactions rather than by wind forcing. These results support the use of the wavelet-based method as a practical alternative for the estimation of the wave directional distribution. In addition, this study highlights the need for continued innovation in the field of ocean wave measuring technologies and analysis techniques to improve our understanding of air–sea interactions. Significance Statement This study presents a wavelet-based technique for obtaining the directional distribution of ocean waves applied to GPS buoy. This method serves as an alternative to conventional methods and is relatively easy to implement, making it a practical option for researchers and engineers. The study was conducted in a highly energetic environment characterized by high wind speeds and large waves, providing a valuable dataset for understanding the dynamics of marine environment in extreme conditions. This research has implications for improving our understanding of directional characteristics of ocean waves, which is crucial for navigation, offshore engineering, weather forecasting, and coastal hazard mitigation. This study also highlights the challenges associated with understanding wave directionality and emphasizes a need for further observations.

Enhancing subsurface seismic profiling with distributed acoustic sensing and optimization algorithms

The distribution of shear-wave velocities in the subsurface is generally used to assess the potential for seismic liquefaction and soil amplification effects and to classify seismic sites. Newly developed distributed acoustic sensing (DAS) technology enables estimation of the shear-wave distribution as a high-density seismic observation system. This technology is characterized by low maintenance costs, high-resolution outputs, and real-time data transmission capabilities, albeit with the challenge of managing massive data generation. Rapid and efficient interpretation of data is the key to advancing application of the DAS technology. In this study, field tests were carried out to record ambient noise over a short period using DAS technology, from which the surface-wave dispersion curves were extracted. In order to reduce the influence of directional effects on the results, an unsupervised clustering method is used to select appropriate clusters to extract the Green's function. A combination of a genetic algorithm and Monte Carlo (GA-MC) simulation is proposed to invert the subsurface velocity structure. The stratigraphic profiles obtained by the GA-MC method are in agreement with the borehole profiles. Compared to other methods, the proposed optimization method not only improves the solution quality but also reduces the solution time.

The SPAR Model: A New Paradigm for Multivariate Extremes: Application to Joint Distributions of Metocean Variables

Abstract This paper presents the application of a new multivariate extreme value model for the estimation of metocean variables. The model requires fewer assumptions about the forms of the marginal distributions and dependence structure compared to existing approaches, and provides a flexible and rigorous framework for modeling multivariate extremes. The method involves a transformation of variables to polar coordinates. The tail of the radial variable is then modeled using the generalized Pareto distribution, with parameters conditional on angle, providing a natural extension of univariate theory to multivariate problems. The resulting model is referred to as the semi-parametric angular-radial (SPAR) model. We consider the estimation of the joint distributions of (1) wave height and wave period, and (2) wave height and wind speed. We show that the SPAR model provides a good fit to the observations in terms of both the marginal distributions and dependence structures. The use of the SPAR model for estimating long-term extreme responses of offshore structures is discussed, using some simple response functions for floating structures and an offshore wind turbine with monopile foundation. We show that the SPAR model is able to accurately reproduce response distributions, and provides a realistic quantification of uncertainty.

Using joint species distribution modelling to predict distributions of seafloor taxa and identify vulnerable marine ecosystems in New Zealand waters

Effective ecosystem-based management of bottom-contacting fisheries requires understanding of how disturbances from fishing affect seafloor fauna over a wide range of spatial and temporal scales. Spatial predictions of abundance for 67 taxa were developed, using an extensive dataset of faunal abundances collected using a towed camera system and spatially explicit predictor variables including bottom-trawl fishing effort, using a Joint Species Distribution Model (JSDM). The model fit metrics varied by taxon: the mean tenfold cross-validated AUC score was 0.70 ± 0.1 (standard deviation) for presence–absence and an R2 of 0.11 ± 0.1 (standard deviation) for abundance models. Spatial predictions of probability of occurrence and abundance (individuals per km2) varied by taxon, but there were key areas of overlap, with highest predicted taxon richness in areas of the continental shelf break and slope. The resulting joint predictions represent significant advances on previous predictions because they are of abundance, allow the exploration of co-occurrence patterns and provide credible estimates of taxon richness (including for rare species that are often not included in more commonly used single-species distribution modelling). Habitat-forming taxa considered to be Vulnerable Marine Ecosystem (VME) indicators (those taxa that are physically or functionally fragile to anthropogenic impacts) were identified in the dataset. Spatial estimates of likely VME distribution (as well as associated estimates of uncertainty) were predicted for the study area. Identifying areas most likely to represent a VME (rather than simply VME indicator taxa) provides much needed quantitative estimates of vulnerable habitats, and facilitates an evidence-based approach to managing potential impacts of bottom-trawling.

Exploring the Transport Path of Oceanic Microplastics in the Atmosphere.

Microplastics (MP) have been recognized as an emerging atmospheric pollutant, yet uncertainties persist in their emissions and concentrations. With a bottom-up approach, we estimate 6-hourly MP fluxes at the ocean-atmosphere interface, using as an input the monthly ocean surface MP concentrations simulated by the global oceanic model (NEMO/PISCES-PLASTIC, Nucleus for European Modeling of the Ocean, Pelagic Interaction Scheme for Carbon and Ecosystem Studies), a size distribution estimate for the MP in the micrometer range, and a sea salt emission scheme. The atmospheric dispersion is then simulated with the Lagrangian model FLEXPART. We identify hotspot sources in the tropical regions and highlight the seasonal variability of emissions, atmospheric concentrations, and deposition fluxes both on land and ocean surfaces. Due to the variability of MP concentration during the year, the MP flux from the sea surface appears to follow a seasonality opposite to that of sea salt aerosol emissions. The comparison with existing observations of MP in the marine atmosphere suggests an underestimation of one to 2 orders of magnitude in our current knowledge of the MP in the oceans' surface. In addition, we show that the MP in the micrometer range is transported efficiently around the globe and can penetrate and linger in the stratosphere over time scales of months. The interaction of these particles with the chemistry and physics of the atmosphere is still mostly unknown and deserves to be further investigated.

Adaptive minimax estimation of service time distribution in the Mt/G/∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_t/G/\\infty $$\\end{document} queue from departure data

This article deals with the problem of estimating the service time distribution of the Mt/G/∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_t/G/\\infty $$\\end{document} queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure.

Numerical Modeling of Cantilever Retaining Wall Using EPS Geofoam

Earth retaining wall structures are common civil engineering structures. Estimation of magnitude and distribution of earth pressure on retaining structures under different surcharge loading conditions is essential as they influence the design and overall economy of retaining structures. Numerical modeling using finite element code PLAXIS is used static analysis. 7 m height of non-yielding cantilever retaining wall with and without EPS geofoam structure is studied and 20 m backfill width was considered. In the present study backfill was modeled as Mohr-Coulomb yield criteria and EPS geofoam and wall were modeled as Linear-elastic. EPS geofoam densities namely 12 kg/m3 and 15 kg/m3 and two different geofoam thicknesses 0.107H and 0.143H were used for static analysis. Three different surcharge loading namely 10 kPa,30kPa and 50kPa which were kept at a distance of 2.0 m away from the wall face. In the static analysis earth pressure distribution for wall with and without geofoam were analyzed. Approximately 50% isolation efficiency was reported. At lower surcharge loads the effectiveness of EPS is more as compare to higher surcharge load and with increase in surcharge load, isolation efficiency gradually decreases and isolation efficiency decreases with increase in buffer modulus. Apart from these serviceability criteria was also checked. Serviceability criteria comprise of lateral deformation of EPS geofoam at sand-geofoam interface and backfill surface settlement were studied. Lower EPS geofoam density and higher EPS geofoam thickness reduces higher magnitude of earth pressure but in this combination the backfill surface settlement was coming very high.

Efficient Bayesian inference using physics-informed invertible neural networks for inverse problems

This paper presents an innovative approach to tackle Bayesian inverse problems using physics-informed invertible neural networks (PI-INN). Serving as a neural operator model, PI-INN employs an invertible neural network (INN) to elucidate the relationship between the parameter field and the solution function in latent variable spaces. Specifically, the INN decomposes the latent variable of the parameter field into two distinct components: the expansion coefficients that represent the solution to the forward problem, and the noise that captures the inherent uncertainty associated with the inverse problem. Through precise estimation of the forward mapping and preservation of statistical independence between expansion coefficients and latent noise, PI-INN offers an accurate and efficient generative model for resolving Bayesian inverse problems, even in the absence of labeled data. For a given solution function, PI-INN can provide tractable and accurate estimates of the posterior distribution of the underlying parameter field. Moreover, capitalizing on the INN’s characteristics, we propose a novel independent loss function to effectively ensure the independence of the INN’s decomposition results. The efficacy and precision of the proposed PI-INN are demonstrated through a series of numerical experiments.

Estimated distribution of high nature value forest in the Republic of Ireland

High Nature Value (HNV) farmland and forest systems play a vital role in supporting biodiversity and delivery of ecosystem services. Estimates of HNV forest area and distribution in the European Union (EU) are rarely conducted, despite having been a requirement of Rural Development Programmes. This work represents the first attempt to identify and estimate the area of HNV forest in the Republic of Ireland in a repeatable and transparent way. Relevant geo-datasets available for Ireland were collated and analysed. We investigated whether the datasets contained information on the indicators used in a recently-developed Nature Value (NV) index, and explored the potential of proxy indicators to determine the likelihood of a mapped area of forest being HNV. Based on these analyses, a likelihood map of the distribution of forest in different NV categories was produced and an accuracy assessment conducted. Results from this study suggest that HNV forest accounts for approximately 1 % of the Irish land area, or 8 % of the total forest area. Accuracy assessments indicated substantial agreement between the likelihood map classifications and the calculated NV status of National Forest Inventory plots. The methodology presented here could also be applied to existing similar datasets to estimate the extent and distribution of HNV forest in other regions. The mapped output provides a likelihood of a forest area being HNV and can provide evidence to inform the development of forest conservation policies.

Spatial Durbin Model with Expansion Using Casetti’s Approach: A Case Study for Rainfall Prediction in Java Island, Indonesia

Research on rainfall is critically important due to its significant impact on climate change and natural disasters in Indonesia. Various factors influence rainfall variability. Consequently, when examining spatial aspects, it is likely that spatial dependency exists not only in the response variable but also in the exogenous variables. Hence, a model that accounts for spatial dependencies between these variables is required. The integration of the Spatial Durbin Model (SDM) with Casetti’s expansion approach can be utilized to predict spatial patterns of rainfall influenced by exogenous variables. By incorporating spatial effects and relevant independent variables, this model can provide more precise estimates of rainfall distribution across different regions. This modeling technique is particularly effective for accurate rainfall prediction, considering exogenous factors such as air temperature, humidity, solar irradiation, and surface pressure. The SDM with Casetti’s expansion approach was employed to predict rainfall patterns in the Java Island region, utilizing data from the National Aeronautics and Space Administration’s Prediction of Worldwide Energy Resources (NASA POWER) big data website. The application of this model in the context of rainfall prediction highlights its importance in enhancing the understanding of weather dynamics and aiding disaster risk mitigation in Java Island, a highly populated region characterized by a Monsoon rainfall pattern. The rainfall prediction follows a Knowledge Discovery in Databases (KDD) methodology. The results of this study are expected to be valuable to relevant agencies, such as the Meteorology, Climatology, and Geophysics Agency (BMKG), and agribusiness companies, improving agricultural planning and planting seasons. Additionally, the general public can benefit from more accurate climate information, particularly regarding rainfall. The computational framework is developed within an RShiny web application, and the performance of the proposed technique is measured by the Mean Absolute Percentage Error (MAPE), achieving a very accurate prediction rate of 2.78%.

Vehicle Stock Numbers and Survival Functions for On-Road Exhaust Emissions Analysis in India: 1993–2018

Road transport plays a crucial role in sustaining all the personal and freight movement needs of residential, commercial, and industrial activities, and in Indian cities, big and small, vehicle exhaust emissions and dust from vehicle movement on the roads contribute to as much as 50% of particulate matter pollution in a year. Therefore, effective management of vehicle exhaust emissions is vital not only for improving current air quality but also for ensuring the long-term benefits from efforts to reduce air pollution. In the approved clean air action plans for 131 cities under the national clean air program (NCAP), more than 50% of the implementable actions are transport-centric. Having a reliable and replicable vehicle exhaust emissions inventory is essential for effective planning, which can help establish a baseline, support scenario analysis, and allow for tracking progress in the sector. This process begins with accessing accurate vehicle stock numbers, typically obtained from vehicle registration databases, traffic surveys, and other governmental records. Often, in low- and middle-income countries like India, these numbers require extensive data cleaning before they can be used for emissions and pollution analysis. This paper presents a cleaned, open-access vehicle stock database for India and outlines a methodology to build and maintain an in-use vehicle age-mix database for future years. The database covers the years 1993 to 2018 for the entire country and individual states, along with estimates of the age distribution of vehicles using survival functions. By offering a comprehensive and reliable data source, this paper aims to support sustainable national and urban air quality management efforts, helping policymakers and stakeholders make informed decisions to improve air quality and public health.

Copula-based Bayesian estimation of probabilities for two dependent non homogenous compound Poisson processes

Bivariate copulas for two dependent non homogeneous compound Poisson processes (NCPP) are considered. In this scenario, the arrival times of events are assumed to follow two independent non homogeneous Poisson processes (NHPP), but the corresponding renewal variables are dependent through a bivariate copula. The article aims to provide a computational tool for the estimation of the probability that the random sum associated with the first NCPP is less than the other random sum by a truncated time. The proposed ML and Bayesian estimation methods in a general setting can be applied using bivariate copulas such as Gumbel (for upper tail dependency), Clayton (for lower tail dependency), and Frank (for symmetric dependency). Power Law (PL) intensity function for the NHPPs and Inverse-Gaussian as renewal distribution are considered as examples. Bayes estimates of NHPPs parameters use gamma priors, and for Bayes estimates of Inverse-Gaussian distribution, an MCMC algorithm is employed. Our method has a broad range of practical applications, especially in the insurance sector, where the renewal variable may represent the dollar amount associated with a claim. To illustrate our approach, we analyze injury claims in North Carolina and South Carolina over a specific period, using a dataset sourced from docs.databricks.com.

Quantifying Earth's Topography: Steeper and Larger Than Projected in Digital Terrain Models

AbstractGrid‐ or pixel‐based models, used across various scientific disciplines from microscopic to planetary scales, contain an unquantified error that bias our interpretation of the data. The error is produced by projecting 3D data onto a 2D grid. For Digital Terrain Models (DTMs) the projection error affects all slope‐dependent topographic metrics, like surface area or slope angle. Due to the proportionality of the error to the cosine of the slope, we can correct for it. We quantify the error and test the correction using synthetic landscapes for which we have analytical solutions of their metrics. Application to real‐world landscapes in California, reveal the systematic underestimation of surface area by up to a third, and mean slope angles by up to 10° in steep topography in current DTMs. Correcting projection errors allow for true estimates of surface areas and slope distributions enabling physics‐based models of surface processes at any spatial scale.

Estimation of photon number distribution and derivative characteristics of photon-pair sources

The evaluation of a photon-pair source employs characteristic metrics like the photon-pair generation rate, heralding efficiency, and second-order correlation function, all of which are determined by the photon number distribution of the source. The photon number distribution, however, can be altered due to spectral or spatial filtering and optical losses, leading to changes in the above characteristics. This paper theoretically describes the effects of different filterings, losses, and noise counts on the photon number distribution and related characteristics. From the theoretical description, an analytic expression for the effective mode number of the joint spectral density is also derived. Compared with previous methods for estimating the photon number distribution and characteristics, an improved methodology is introduced along with a suitable metric of accuracy for estimating the photon number distribution, focusing on photon-pair sources. We discuss the accuracy of the calculated characteristics from the estimated (or reconstructed) photon number distribution through repeated simulations and bootstrapped experimental data.

Decreasing Trend Bumped Probability Distribution: its Properties, Simulations and Application

In this paper, a probability model is proposed which engaged the mathematical combination of Lindley distribution and a trigonometric component known as haversine function〖 δ〗_s. The one parameter model prototype sustains the capacity to forecast multimodal decreasing trend sinusoidal outcomes. By nomenclature, the proposed probability model is called Modified Lindley Trigonometric Distribution (MLTD). Some statistical properties studied include the hazard function, mean residual life function, moments, conditional moments and moment generating function, Bonferroni and Lorenz curve, entropy, asymptotic distribution, order statistics, and parameter estimation; where the hazard function specially features a cyclic or periodic bathtub and inverted bathtub shape in chain format. The numerical behavior of the estimates of the average bias and mean square error were examined under Monte Carlo simulation approach; and an applicative simulation is experimented to underscore the parametric behavior of MLTD in data modeling. A real life flood data is used to illustrate the essence of the development.

A new sine-inspired probability model: Theoretical features with statistical modeling of the music engineering and reliability scenarios

It is a proven authenticity that probability-schooled methodologies have a cardinal role in making decisions under the vagueness circumstances. Thus, to reach meaningful and fruitful decisions under vagueness circumstances, numerous probability-focused methodologies have been introduced, promoted, and implemented. This paper also contributes to adding another useful probability model to the existing literature for data modeling in engineering-oriented areas. The new model is called the weighted sine exponentiated exponential (WSEE) distribution, which is formed by implementing the exponentiated exponential model together with a sine-adapted method. Certain properties of the WSEE distribution are given. The parameter estimation of the WSEE distribution along with the simulation study is also provided. Last, in order, we apply the WSEE distribution for analyzing three data sets taken from the musical engineering and reliability settings. The optimality of the WSEE distribution is proved by comparing its results with other prominent modifications of the exponentiated exponential distribution. Using 4 statistical criteria as judgment tools, it was shown numerically and pictorially that the WSEE distribution is an optimal and suitable model for the musical engineering reliability data sets.

Identification of illicit discharges in sewer networks by an SWMM-Bayesian coupled approach.

Illicit discharges into sewer systems are a widespread concern within China's urban drainage management. They can result in unforeseen environmental contamination and deterioration in the performance of wastewater treatment plants. Consequently, pinpointing the origin of unauthorized discharges in the sewer network is crucial. This study aims to evaluate an integrative method that employs numerical modeling and statistical analysis to determine the locations and characteristics of illicit discharges. The Storm Water Management Model (SWMM) was employed to track water quality variations within the sewer network and examine the concentration profiles of exogenous pollutants under a range of scenarios. The identification technique employed Bayesian inference fused with the Markov chain Monte Carlo sampling method, enabling the estimation of probability distributions for the position of the suspected source, the discharge magnitude, and the commencement of the event. Specifically, the cases involving continuous release and multiple sources were examined. For single-point source identification, where all three parameters are unknown, concentration profiles from two monitoring sites in the path of pollutant transport and dispersion are necessary and sufficient to characterize the pollution source. For the identification of multiple sources, the proposed SWMM-Bayesian strategy with improved sampling is applied, which significantly improves the accuracy.

Flexible Bayesian estimation of incubation times.

The incubation period is of paramount importance in infectious disease epidemiology as it informs about the transmission potential of a pathogenic organism and helps to plan public health strategies to keep an epidemic outbreak under control. Estimation of the incubation period distribution from reported exposure times and symptom onset times is challenging as the underlying data is coarse. We develop a new Bayesian methodology using Laplacian-P-splines that provides a semi-parametric estimation of the incubation density based on a Langevinized Gibbs sampler. A finite mixture density smoother informs a set of parametric distributions via moment matching and an information criterion arbitrates between competing candidates. Algorithms underlying our method find a natural nest within the EpiLPS package, which has been extended to cover estimation of incubation times. Various simulation scenarios accounting for different levels of data coarseness are considered with encouraging results. Applications to real data on COVID-19, MERS and Mpox reveal results that are in alignment with what has been obtained in recent studies. The proposed flexible approach is an interesting alternative to classic Bayesian parametric methods for estimation of the incubation distribution.

Enhancing Reptile search algorithm with shifted distribution estimation strategy for coverage optimization in wireless sensor networks

The rapid development of the Internet of Things (IoT) has extensively promoted the development of Wireless Sensor Networks (WSNs), an essential technology for series displaying perception and data collected from the physical world. In densely distributed areas, sensor nodes are unevenly distributed, which leads to the network coverage build-up and the consequent efficiency and effectiveness of WSNs. To address this issue, this paper proposes a new method for WSN coverage optimization based on the Reptile Search Algorithm (RSA). In the past, the Reptile Search algorithm has been used to solve optimization problems, which means it can improve different processes. However, the RSA needs to track the trajectory of optimal individuals in each iteration, which will ignore non-optimal individuals' bioeconomic characteristics. Therefore, the paper introduces a distribution estimation strategy into the RSA framework, which can fully mine all the positional information hidden in the entire population. We selected several functions as optimization test benchmark functions to evaluate the feasibility of the proposed method. This paper compares the proposed improved RSA with the standard RSA and some traditional optimization algorithms. The result has been calculated through a series of experiments on network coverage optimization, and the change of parameters also determines the effect of the RSA in the optimization of network coverage. The simulated results of the three similar network coverage optimization experiments show that the improved RSA can be used efficiently within different scenarios.

Determining tissue distribution of the oral antileishmanial agent miltefosine: a physiologically-based pharmacokinetic modeling approach.

Miltefosine (MTS) is the only approved oral drug for treating leishmaniasis caused by intracellular Leishmania parasites that localize in macrophages of the liver, spleen, skin, bone marrow, and lymph nodes. MTS is extensively distributed in tissues and has prolonged elimination half-lives due to its high plasma protein binding, slow metabolic clearance, and minimal urinary excretion. Thus, understanding and predicting the tissue distribution of MTS help assess therapeutic and toxicologic outcomes of MTS, especially in special populations, e.g., pediatrics. In this study, a whole-body physiologically-based pharmacokinetic (PBPK) model of MTS was built on mice and extrapolated to rats and humans. MTS plasma and tissue concentration data obtained by intravenous and oral administration to mice were fitted simultaneously to estimate model parameters. The resulting high tissue-to-plasma partition coefficient values corroborate extensive distribution in all major organs except the bone marrow. Sensitivity analysis suggests that plasma exposure is most susceptible to changes in fraction unbound in plasma. The murine oral-PBPK model was further validated by assessing overlay of simulations with plasma and tissue profiles obtained from an independent study. Subsequently, the murine PBPK model was extrapolated to rats and humans based on species-specific physiological and drug-related parameters, as well as allometrically scaled parameters. Fold errors for pharmacokinetic parameters were within acceptable range in both extrapolated models, except for a slight underprediction in the human plasma exposure. These animal and human PBPK models are expected to provide reliable estimates of MTS tissue distribution and assist dose regimen optimization in special populations.