Parameter Estimation Research Articles

Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems

In models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theoretic approaches designed to address this classical dilemma, focusing on balancing the expected profits and the information needed to be obtained about all of the possible outcomes. Initially utilized in binary outcome scenarios, these methods leverage information measures to harmonize competing objectives efficiently. Building upon the foundations laid by existing research, this methodology is expanded to encompass experiments with multiple outcome categories using Dirichlet processes. The core of our approach is centered around weighted entropy measures, particularly in scenarios dictated by Dirichlet distributions, which have not been extensively explored previously. We innovatively adapt the technique initially applied to binary case to Dirichlet distributions/processes. The primary contribution of our work is the formulation of a sequential minimization strategy for the main term of an asymptotic expansion of differential entropy, which scales with sample size, for non-binary outcomes. This paper provides a theoretical grounding, extended empirical applications, and comprehensive proofs, setting a robust framework for further interdisciplinary applications of information-theoretic paradigms in sequential decision-making.

Bayesian grouping-Gibbs sampling estimation of high-dimensional linear model with non-sparsity

In high-dimensional linear regression models, common assumptions typically entail sparsity of regression coefficients β∈Rp. However, these assumptions may not hold when the majority, if not all, of regression coefficients are non-zeros. Statistical methods designed for sparse models may lead to substantial bias in model estimation. Therefore, this article proposes a novel Bayesian Grouping-Gibbs Sampling (BGGS) method, which departs from the common sparse assumptions in high-dimensional problems. The BGGS method leverages a grouping strategy that partitions β into distinct groups, facilitating rapid sampling in high-dimensional space. The grouping number (k) can be determined using the ‘Elbow plot’, which operates efficiently and is robust against the initial value. Theoretical analysis, under some regular conditions, guarantees model selection and parameter estimation consistency, and bound for the prediction error. Furthermore, three finite simulations are conducted to assess the competitive advantages of the proposed method in terms of parameter estimation and prediction accuracy. Finally, the BGGS method is applied to a financial dataset to explore its practical utility.

A Joint Estimation Method of Distribution Network Topology and Line Parameters Based on Power Flow Graph Convolutional Networks

Accurate identification of network topology and line parameters is essential for effective management of distribution systems. An innovative joint estimation method for distribution network topology and line parameters is presented, utilizing a power flow graph convolutional network (PFGCN). This approach addresses the limitations of traditional methods that rely on costly voltage phase angle measurements. The node correlation principle is applied to construct a node correlation matrix, and a minimum distance iteration algorithm is proposed to generate candidate topologies, which serve as graph inputs for the parameter estimation model. Based on the topological dependencies and convolutional properties of AC power flow equations, a PFGCN model is designed for line parameter estimation. Parameter refinement is achieved through an alternating iterative process of pseudo-trend calculation and neural network training. Training convergence and loss function values are used as feedback to filter and validate candidate topologies, enabling precise joint estimation of both topologies and parameters. The proposed method’s accuracy, transferability, and robustness are demonstrated through experiments on the IEEE-33 and modified IEEE-69 distribution systems. Multiple metrics, including MAPE, IAE, MAE, and R2, highlight the proposed method’s advantages over Adaptive Ridge Regression (ARR). In the C33 scenario, the proposed method achieves MAPEs of 4.6% for g and 5.7% for b, outperforming the ARR method with MAPEs of 7.1% and 7.9%, respectively. Similarly, in the IC69 scenario, the proposed method records MAPEs of 3.0% for g and 5.9% for b, surpassing the ARR method’s 5.1% and 8.3%.

Uniformization and bounded Taylor series in Newton-Raphsonmethod improves computational performance for a multistate transition model estimation and inference.

Multistate transition models (MSTMs) are valuable tools depicting disease progression. However, due to the complexity of MSTMs, larger sample size and longer follow-up time in real-world data, the computation of statistical estimation and inference for MSTMs becomes challenging. A bounded Taylor series in Newton-Raphson procedure is proposed which leverages the uniformization technique to derive maximum likelihood estimates and corresponding covariance matrix. The proposed method, namely uniformization Taylor-bounded Newton-Raphson, is validated in three simulation studies, which demonstrate the accuracy in parameter estimation, the efficiency in computation time and robustness in terms of different situations. This method is also illustrated using a large electronic medical record data related to statin-induced side effects and discontinuation.

Improving the accuracy of dynamic inclination measurement by machine learning

With the diminishing availability of oil and gas resources, the Rotary Steerable System has become increasingly important. However, the vibrations and shocks during the drilling process pose challenges to the Measurement While Drilling. In recent years, the application of machine learning in the field of petroleum exploration has gradually expanded, especially in the estimation of geological parameters and lithology discrimination. However, there is still limited research on drilling tool attitude measurement. To address the above-mentioned issues, this study proposes a method that combines drilling tool attitude sensor data with artificial neural networks to improve the accuracy of dynamic inclination measurement. This method utilizes machine learning techniques, combining real-time z-axis acceleration signals and magnetic induction signals, and employs a deep learning model to invert the x and y-axis acceleration signals, thereby achieving high-precision measurement of dynamic inclination angles. Experimental results show that Long Short-Term Memory model, under simulated measurement conditions with different rotational speeds, yields dynamic inclination curve errors ranging from 0.4° to 0.7°, significantly reducing the errors compared to the original measurements. This method not only improves the accuracy of inclination angle measurement but also demonstrates strong adaptability to different rotational speeds, providing more accurate data support for drilling operations.

Order-restricted statistical inference and optimal censoring scheme for Gompertz distribution based on joint type-II progressive censored data

This paper considers the order-restricted statistical inference for two populations based on the joint type-II progressive censoring scheme. The lifetime distributions of the two populations are supposed to follow the Gompertz distribution with the same shape parameter but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived by employing the Newton-Raphson algorithm and the expectation-maximization algorithm, respectively. The Fisher information matrix is then employed to construct asymptotic confidence intervals. For Bayes estimation, we assume an ordered Beta-Gamma prior for the scale parameters and a Gamma prior for the common shape parameter. Bayes estimations and the highest posterior density credible intervals for unknown parameters under two different loss functions are obtained with the importance sampling technique. To evaluate the performance of order-restricted inference, extensive Monte Carlo simulations are performed and two air-conditioning systems datasets are used to illustrate the proposed inference methods. In addition, the results are compared with the case when there is no order restriction on the parameters. Finally, the optimal censoring scheme is obtained by four optimality criteria.

Unified rules of renewable weighted sums for various online updating estimations

This paper establishes unified frameworks of renewable weighted sums (RWS) for various online updating estimations in the models with streaming data sets. The newly defined RWS lays the foundation of online updating likelihood, online updating loss function, online updating estimating equation and so on. The idea of RWS is intuitive and heuristic, and the algorithm is computationally simple. The RWS applies to various types of parametric, nonparametric and semiparametric estimators from likelihood, quasi-likelihood and least squares. The consistency and asymptotic normality of the proposed renewable estimator are established, and the oracle property is obtained. Moreover, these properties are always satisfied, without the familiar constraints on the number of data batches, which means that the new method is adaptive to the situation where streaming data sets arrive perpetually. The performance of the method is further illustrated by various numerical examples from simulation experiments and real data analysis.

Black hole spectroscopy with ground-based atom interferometer and space-based laser interferometer gravitational wave detectors

Gravitational wave (GW) detection allows us to test general relativity in entirely new regimes. A prominent role takes the detection of quasi-normal modes (QNMs), which are emitted after the merger of a binary black hole (BBH) when the highly distorted remnant emits GWs to become a regular Kerr black hole (BH). The BH uniqueness theorems of Kerr black hole solutions in general relativity imply that the frequencies and damping times of QNMs are determined solely by the mass and spin of the remnant BH. Therefore, detecting QNMs offers a unique way to probe the nature of the remnant BH and to test general relativity. We study the detection of a merging BBH in the intermediate-mass range, where the inspiral–merger phase is detected by space-based laser interferometer detectors TianQin and LISA, while the ringdown is detected by the ground-based atom interferometer (AI) observatory AION. The analysis of the ringdown is done using the regular broadband mode of AI detectors as well as the resonant mode optimizing it to the frequencies of the QNMs predicted from the inspiral–merger phase. We find that the regular broadband mode allows constraining the parameters of the BBH with relative errors of the order 10−1 and below from the ringdown. Moreover, for a variety of systems considered, the frequencies and the damping times of the QNMs can be determined with relative errors below 0.1 and 0.2, respectively. We further find that using the resonant mode can improve the parameter estimation for the BBH from the ringdown by a factor of up to three. Utilizing the resonant mode significantly limits the detection of the frequency of the QNMs but improves the detection error of the damping times by around two orders of magnitude.

Energy Efficiency of Plasma Jets: Electrical Modeling Based on Experimental Results

This paper focuses on the determination of and improvement in the energy efficiency of plasma jets. To achieve this goal, an equivalent electrical model of a discharge reactor was developed, incorporating variable electrical parameters. The evolution of these parameters was determined by a mathematical identification method based on the recursive least squares algorithm (RLSA). The good agreement between the measured currents and those calculated using our electrical circuit, as well as the significant shapes of the estimated parameters, confirmed the accuracy of the parameter estimation method. This allowed us to use these parameters to determine the energy delivered to the reactor and that used during the discharge. This made our reactor controllable at the energy level. Thus, the ratio between these two energies allowed us to calculate the energy efficiency of plasma jets at each discharge instant. We also studied the effect of the applied voltage on efficiency. We found that efficiency was increased from 75% to 90% by increasing the voltage from 6 kV to 8 kV. All the results found in this work were interpreted and compared with the discharge behavior. This proposed model will help us to choose the right operating conditions to reach the maximum efficiency.

A fault location method for DC transmission line based on the distributed parameter model considering line parameter uncertainty

Addressing the impact of whether line parameters can be accurately obtained and the errors due to environmental influences on the accuracy of fault location for DC transmission line, this paper proposes a fault location method based on the distributed parameter model that accounts for uncertainty in line parameter. To address the challenge of accurately obtaining DC transmission line parameters, a high-order derivative-based parameter estimation method is introduced to determine unknown equivalent parameters of the DC transmission line. Additionally, an optimization algorithm is incorporated to dynamically correct parameter errors, thereby enhancing parameter stability and constructing an accurate line model. Based on this, theoretical derivations confirm the applicability of the Tellegen's quasi-power theorem in the normal operation and internal fault equivalent models of DC transmission line. A fault location function is established based on the relationship between the line's Tellegen quasi-power characteristic and fault distance. The proposed method's effectiveness and accuracy are validated using a DC system model built on the PSCAD/EMTDC simulation platform. Simulation results indicate that the proposed method can locate faults under different fault conditions.

Noise aware parameter estimation in bioprocesses: Using neural network surrogate models with nonuniform data sampling

AbstractThis article demonstrates a parameter estimation technique for bioprocesses that utilizes measurement noise in experimental data to determine credible intervals on parameter estimates, with this information of potential use in prediction, robust control, and optimization. To determine these estimates, the work implements Bayesian inference using nested sampling, presenting an approach to develop neural network‐ (NN) based surrogate models. To address challenges associated with nonuniform sampling of experimental measurements, an NN structure is proposed. The resultant surrogate model is utilized within a Nested Sampling Algorithm that samples possible parameter values from the parameter space and uses the NN to calculate model output for use in the likelihood function based on the joint probability distribution of the noise of output variables. This method is illustrated against simulated data, then with experimental data from a Sartorius fed‐batch bioprocess. Results demonstrate the feasibility of the proposed technique to enable rapid parameter estimation for bioprocesses.

Advanced parameter estimation for lithium-ion battery model using the information sharing group teaching optimization algorithm

Accurate battery modeling is crucial for optimizing the performance and safety of Lithium-ion batteries (LiBs), particularly in applications such as electric vehicles and smart grids. This paper introduces the Information Sharing Group Teaching Optimization Algorithm (ISGTOA), a novel human-based metaheuristic algorithm designed to estimate the 21 parameters of third-order Equivalent Circuit Model (ECM) for LiBs. Unlike existing methods, ISGTOA effectively manages the increased complexity of a model through advanced group teaching strategies and sophisticated information-sharing mechanisms inspired by classroom dynamics. We validated the effectiveness of ISGTOA using two distinct datasets—High Dynamic Profile (HDP) and Urban Dynamometer Driving Schedule (UDDS)—across various LiB chemistries (NCA and NMC) and temperature conditions (−5 °C, 25 °C and 45 °C). The results demonstrate that ISGTOA achieves superior parameter estimation accuracy and convergence speed compared to established and recent optimization methods such as TLBO, TLSBO, AISA, MTBO, and DTBO. Specifically, ISGTOA attained a minimum RMSE of 8.357 mV with rapid convergence and high stability in the HDP dataset and minimized RMSE to 10 mV within ten iterations at both 25 °C and 45 °C in the UDDS dataset. Additionally, ISGTOA exhibited high efficiency (up to 97.75 %) under varying thermal environments. This work not only introduces a novel algorithm for complex battery modeling but also sets the stage for future advancements in real-time battery management systems, emphasizing the importance of robust, versatile, and efficient parameter estimation techniques.

Model-Centric Integration of Uncertain Expert Knowledge into Importance Sampling-Based Parameter Estimation

This study presents a model-based parameter estimation method for integrating and validating uncertainty in expert knowledge and simulation models. The parameters of the models of complex systems are often unknown due to a lack of measurement data. The experience-based knowledge of experts can substitute missing information, which is usually imprecise. The novelty of the present paper is a method based on Monte Carlo (MC) simulation and importance sampling (IS) techniques for integrating uncertain expert knowledge into the system model. Uncertain knowledge about the model parameters is propagated through the system model by MC simulation in the form of a discrete sample, while IS helps to weight the sample elements regarding imprecise knowledge about the outputs in an iterative circle. Thereby, the consistency of expert judgments can be investigated as well. The contributions of this paper include an expert knowledge-based parameter estimation technique and a method for the evaluation of expert judgments according to the estimation results to eliminate incorrect ones. The applicability of the proposed method is introduced through a case study of a Hungarian operating waste separation system. The results verify that the assessments of experts can be efficiently integrated into system models, and their consistency can be evaluated.

Improved modelling of low-pressure rotor speed in commercial turbofan engines: A comprehensive analysis of machine learning approaches

Accurate engine thrust modelling offers notable opportunities for reducing fuel consumption, mitigating emission effects, managing air traffic, and optimizing the preliminary design of aircraft. This study focuses on the development of machine learning models to predict the low-pressure rotor speed (N1) parameter, which is closely related to the thrust of turbofan engines, for commercial aircraft during the cruise phase. The analysis utilizes a Flight Data Recorder (FDR) dataset from 1086 actual flights involving twin-engine, narrow-body, short-to-medium haul commercial aircraft equipped with CFM56-7B turbofan engines. To achieve accurate N1 parameter predictions, the study employs machine learning models, including Deep Learning (DL), Random Forest (RF), Gradient Boosted Machines (GBM), and Artificial Neural Networks (ANN). These models are evaluated using statistically significant indicators, demonstrating that machine learning models yield highly accurate results. Among the models tested, the DL model provides the most precise estimates of the N1 parameter. This study not only advances the understanding of engine thrust modelling through machine learning but also provides practical insights for the aerospace industry. The findings underline the potential of machine learning techniques in delivering superior prediction accuracy, which can be integrated into real-time flight management systems, ultimately contributing to more sustainable and efficient aviation operations.

Estimation Network for Multiple Chemical Parameters of Astragalus Leaves Based on Attention Mechanism and Multivariate Hyperspectral Features

In the context of smart agriculture, accurately estimating plant leaf chemical parameters is crucial for optimizing crop management and improving agricultural yield. Hyperspectral imaging, with its ability to capture detailed spectral information across various wavelengths, has emerged as a powerful tool in this regard. However, the complex and high-dimensional nature of hyperspectral data poses significant challenges in extracting meaningful features for precise estimation. To address this challenge, this study proposes an end-to-end estimation network for multiple chemical parameters of Astragalus leaves based on attention mechanism (AM) and multivariate hyperspectral features (AM-MHENet). We leverage HybridSN and multilayer perceptron (MLP) to extract prominent features from the hyperspectral data of Astragalus membranaceus var. mongholicus (AMM) leaves and stems, as well as the surface and deep soil surrounding AMM roots. This methodology allows us to capture the most significant characteristics present in these hyperspectral data with high precision. The AM is subsequently used to assign weights and integrate the hyperspectral features extracted from different parts of the AMM. The MLP is then employed to simultaneously estimate the chlorophyll content (CC) and nitrogen content (NC) of AMM leaves. Compared with estimation networks that utilize only hyperspectral data from AMM leaves as input, our proposed end-to-end AM-MHENet demonstrates superior estimation performance. Specifically, AM-MHENet achieves an R2 of 0.983, an RMSE of 0.73, an MAE of 0.49, and an RPD of 7.63 for the estimation of CC in AMM leaves. For NC estimation, AM-MHENet achieves an R2 value of 0.977, an RMSE of 0.27, an MAE of 0.16, and an RPD of 6.62. These results underscore AM-MHENet’s effectiveness in significantly enhancing the accuracy of both CC and NC estimation in AMM leaves. Moreover, these findings indirectly suggest a strong correlation between the development of AMM leaves and stems, as well as the surface and deep soil surrounding the roots of AMM, and directly highlight the ability of AM to effectively focus on the relevant spectral features within the hyperspectral data. The findings from this study could offer valuable insights into the simultaneous estimation of multiple chemical parameters in plants, thereby making a contribution to the existing body of research in this field.

The Representative Points of Generalized Alpha Skew-t Distribution and Applications

Assuming the underlying statistical distribution of data is critical in information theory, as it impacts the accuracy and efficiency of communication and the definition of entropy. The real-world data are widely assumed to follow the normal distribution. To better comprehend the skewness of the data, many models more flexible than the normal distribution have been proposed, such as the generalized alpha skew-t (GAST) distribution. This paper studies some properties of the GAST distribution, including the calculation of the moments, and the relationship between the number of peaks and the GAST parameters with some proofs. For complex probability distributions, representative points (RPs) are useful due to the convenience of manipulation, computation and analysis. The relative entropy of two probability distributions could have been a good criterion for the purpose of generating RPs of a specific distribution but is not popularly used due to computational complexity. Hence, this paper only provides three ways to obtain RPs of the GAST distribution, Monte Carlo (MC), quasi-Monte Carlo (QMC), and mean square error (MSE). The three types of RPs are utilized in estimating moments and densities of the GAST distribution with known and unknown parameters. The MSE representative points perform the best among all case studies. For unknown parameter cases, a revised maximum likelihood estimation (MLE) method of parameter estimation is compared with the plain MLE method. It indicates that the revised MLE method is suitable for the GAST distribution having a unimodal or unobvious bimodal pattern. This paper includes two real-data applications in which the GAST model appears adaptable to various types of data.

Rethinking Porosity-Based Diffusivity Estimates for Sorptive Gas Transport at Variable Temperatures.

The detection of noble gas radioisotopes following a suspected underground nuclear explosion is the surest indicator that nuclear detonation has occurred. However, the accurate interpretation and attribution of radioisotopic signatures is only possible with a complete understanding of transport processes occurring between the nuclear cavity and surface. In the far-field, diffusive forces contributing to gas transport are impacted by temperature gradients and subsurface lithology. In the current study, we investigate diffusive transport of xenon (Xe), krypton (Kr), and sulfur hexafluoride (SF6) through intact Bandelier tuff at elevated temperatures using a newly developed high temperature diffusion cell. Diffusion coefficients determined using Finite Element Heat and Mass transfer code simulations and the Parameter ESTimation tool range from 2.6-3.1 × 10-6 m2/s at 20 °C, 3.4-5.1 × 10-6 m2/s at 40 °C, and 4.3-7.0 × 10-6 m2/s at 70 °C. Sorption was found to be an important transport mechanism at ambient temperatures (20 °C). Most critically, our study shows that empirical porosity-based diffusion estimates for these gases through tuff captured neither the magnitude nor trends relative to a nonsorbing sandstone. These new insights highlight the importance of experimental transport investigations and will be used to improve models for subsurface gas propagation relevant to proliferation detection and environmental contamination.

Thinking beyond the closure assumption: Designing surveys for estimating biological truth with occupancy models

Abstract Occupancy models estimate distributions of imperfectly detected species, but violations of the closure assumption can bias results. However, researchers working with mobile animals may find it impossible to eliminate such violations. Here, we tested the hypothesis that occupancy models fit to realistic sampling data can generate unbiased occupancy estimates for an itinerant Wood Thrush (Hylocichla mustelina) population. In 2013 and 2014, we tracked movements of 41 breeding Wood Thrush males. We modelled territory shift probabilities using logistic exposure models and within‐territory movements using continuous‐time stochastic process models. We then constructed an individual‐based model, simulated (1000 iterations) spatiotemporal locations for individuals and simulated sampling these populations using 162 different point count protocols with variable spatial (sampling radius and point placement method), and temporal (survey length, between‐survey intervals and number of surveys) characteristics. We compared occupancy estimates with true values of instantaneous, daily and seasonal occupancy from the simulations. We parameterized continuous time stochastic process models based on movements within 34 unique territories and estimated a daily territory shift probability of 0.0099 (95% CI: 0.0060, 0.0152). Simulated data indicated that estimates of occupancy ranged from 0.18 (0.06, 1.00) to 0.80 (0.71, 0.89) depending on protocol characteristics. Occupancy estimates increased with increasing survey radius, survey length and between‐survey interval. Protocols using shorter surveys and between‐survey intervals were good estimators for instantaneous occupancy (low bias and mean‐squared error) but poor estimators for daily and seasonal occupancy; longer surveys and intervals generated unbiased estimators of daily occupancy but underestimated seasonal occupancy. Logistic regression models that ignored imperfect detection outperformed occupancy models for estimating instantaneous occupancy but not daily or seasonal occupancy. For mobile animals, occupancy of sampling sites changes in space and time. Consequently, the spatial and temporal aspects of a sampling protocol have strong, but predictable, effects on occupancy model parameter estimates. Our results demonstrate that how these factors interact is critical for designing surveys that produce occupancy estimates representative of the biological process of interest to a researcher.

Quantifying interstellar extinction at high galactic latitudes

Abstract A detailed map of the distribution of dust at high Galactic latitudes is essential for future cosmic microwave background (CMB) polarization experiments because the dust, while diffuse, remains a significant foreground in these regions. We develop a Bayesian model to identify a region of the Hertzsprung-Russell (HR) diagram suited to constrain the single-star extinction accurately at high Galactic latitudes. Using photometry from Gaia, 2MASS and ALLWISE, and parallax from Gaia, we employ nested sampling to fit the model to the data and analyse the posterior over stellar parameters for both synthetic and real data. Charting low variations in extinction is complex due to systematic errors and degeneracies between extinction and other stellar parameters. The systematic errors can be minimised by restricting our data to a region of the HR diagram where the stellar models are most accurate. Moreover, the degeneracies can be reduced by including astrophysical priors and spectroscopic constraints. We show that accounting for the measurement error of the data and the assumed inaccuracies of the stellar models are critical in accurately recovering small variations in extinction. We compare the posterior distribution for individual stars with spectroscopic stellar parameter estimates from LAMOST and Gaia ESO and illustrate the importance of estimating extinction and effective temperature as a joint solution.

Uncertainty propagation of initial conditions in thermal models

The operation of machine tools often demands a highly accurate knowledge of the tool center point’s (TCP) position. The displacement of the TCP over time can be inferred from coupled thermal models, which comprise a set of geometrically coupled heat equations. Each of these equations represents the temperature in part of the machine, and they are often formulated on complicated geometries. The accuracy of the TCP prediction depends highly on the accuracy of the model parameters, such as heat exchange parameters, and the initial temperature. Thus it is of utmost interest to determine the influence of these parameters on the TCP displacement prediction. In turn, the accuracy of the parameter estimate is essentially determined by the measurement accuracy and the sensor placement. Determining the accuracy of a given sensor configuration is a key prerequisite of optimal sensor placement. In this paper, we develop a thermal model for the discretization of realistic machine tool. On top of this model we propose two numerical algorithms to evaluate any given thermal sensor configuration with respect to its accuracy. We compute the posterior variances from the posterior covariance matrix with respect to an uncertain initial temperature field. The full matrix is dense and potentially very large, depending on the size of the discretized model. We first present a way to compute this approximation, which relies on the computation of the model sensitivities with respect to the initial values. Additionally, we present a low-rank tensor method which exploits the underlying system structure. We compare the efficiency of both algorithms with respect to runtime and memory requirements and discuss their respective advantages with regard to optimal sensor placement problems.