Accurate Parameter Estimates Research Articles

Pynta─An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics.

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. We present Pynta, a workflow software for automating the calculation of surface and gas-surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

Improving Estimation of Tree Parameters by Fusing ALS and TLS Point Cloud Data Based on Canopy Gap Shape Feature Points

Airborne laser scanning (ALS) and terrestrial laser scanning (TLS) are two ways to obtain forest three-dimensional (3D) spatial information. Due to canopy occlusion and the features of different scanning methods, some of the forest point clouds acquired by a single scanning platform may be missing, resulting in an inaccurate estimation of forest structure parameters. Hence, the registration of ALS and TLS point clouds is an alternative for improving the estimation accuracy of forest structure parameters. Currently, forest point cloud registration is mainly conducted based on individual tree attributes (e.g., location, diameter at breast height, and tree height), but the registration is affected by individual tree segmentation and is inefficient. In this study, we proposed a method to automatically fuse ALS and TLS point clouds by using feature points of canopy gap shapes. First, the ALS and TLS canopy gap boundary vectors were extracted by the canopy point cloud density model, and the turning or feature points were obtained from the canopy gap vectors using the weighted effective area (WEA) algorithm. The feature points were then aligned, the transformation parameters were solved using the coherent point drift (CPD) algorithm, and the TLS point clouds were further aligned using the recovery transformation matrix and refined by utilizing the iterative closest point (ICP) algorithm. Finally, individual tree segmentations were performed to estimate tree parameters using the TLS and fusion point clouds, respectively. The results show that the proposed method achieved more accurate registration of ALS and TLS point clouds in four plots, with the average distance residuals of coarse and fine registration of 194.83 cm and 2.14 cm being much smaller compared with those from the widely used crown feature point-based method. Using the fused point cloud data led to more accurate estimates of tree height than using the TLS point cloud data alone. Thus, the proposed method has the potential to improve the registration of ALS and TLS point cloud data and the accuracy of tree height estimation.

Joint Direction of Arrival-Polarization Parameter Tracking Algorithm Based on Multi-Target Multi-Bernoulli Filter

This paper presents a tracking algorithm for joint estimation of direction of arrival (DOA) and polarization parameters, which exhibit dynamic behavior due to the movement of signal source carriers. The proposed algorithm addresses the challenge of real-time estimation in multi-target scenarios with an unknown number. This algorithm is built upon the Multi-target Multi-Bernoulli (MeMBer) filter algorithm, which makes use of a sensor array called Circular Orthogonal Double-Dipole (CODD). The algorithm begins by constructing a Minimum Description Length (MDL) principle, taking advantage of the characteristics of the polarization-sensitive array. This allows for adaptive estimation of the number of signal sources and facilitates the separation of the noise subspace. Subsequently, the joint parameter Multiple Signal Classification (MUSIC) spatial spectrum function is employed as the pseudo-likelihood function, overcoming the limitations imposed by unknown prior information constraints. To approximate the posterior distribution of MeMBer filters, Sequential Monte Carlo (SMC) method is utilized. The simulation results demonstrate that the proposed algorithm achieves excellent tracking accuracy in joint DOA-polarization parameter estimation, whether in scenarios with known or unknown numbers of signal sources. Moreover, the algorithm demonstrates robust tracking convergence even under low Signal-to-Noise Ratio (SNR) conditions.

Parsimonious item response theory modeling with the negative log-log link: The role of inflection point shift.

In item response theory (IRT) modeling, the magnitude of the lower and upper asymptote parameters determines the degree to which the inflection point shifts above or below P = 0.50. The current study examines the one-parameter negative log-log model (NLLM), which is characterized by a downward shift in the inflection point, among other distinctive psychometric properties. After detailing the statistical foundations of the NLLM, we present a series of simulation studies to establish item and person parameter estimation accuracy and to demonstrate that this parsimonious model addresses the "slipping" effect (i.e., unexpectedly incorrect answers) via an inflection point < 0.50 rather than through computationally difficult estimation of the upper asymptote. We then provide further support for these simulation results through empirical data analysis. Finally, we discuss how the NLLM contributes to recent methodological literature on the utility of asymmetric IRT models.

A temperature-controlled cooling system for accurate quantitative post-mortem MRI.

To develop a temperature-controlled cooling system to facilitate accurate quantitative post-mortem MRI and enable scanning of unfixed tissue. A water cooling system was built and integrated with a 7T scanner to minimize temperature drift during MRI scans. The system was optimized for operational convenience and rapid deployment to ensure efficient workflow, which is critical for scanning unfixed post-mortem samples. The performance of the system was evaluated using a 7-h diffusion MRI protocol at 7T with a porcine tissue sample. Quantitative T1 , T2 , and ADC maps were interspersed with the diffusion scans at seven different time points to investigate the temperature dependence of MRI tissue parameters. The impact of temperature changes on biophysical model fitting of diffusion MRI data was investigated using simulation. Tissue T1 , T2 , and ADC values remained stable throughout the diffusion MRI scan using the developed cooling system, but varied substantially using a conventional scan setup without temperature control. The cooling system enabled accurate estimation of biophysical model parameters by stabilizing the tissue temperature throughout the diffusion scan, while the conventional setup showed evidence of significantly biased estimation. A temperature-controlled cooling system was developed to tackle the challenge of heating in post-mortem imaging, which shows potential to improve the accuracy and reliability of quantitative post-mortem imaging and enables long scans of unfixed tissue.

Deep Q-learning to globally optimize a k-D parameter search for medical imaging.

Estimation of the global optima of multiple model parameters is valuable for precisely extracting parameters that characterize a physical environment. This is especially useful for imaging purposes, to form reliable, meaningful physical images with good reproducibility. However, it is challenging to avoid different local minima when the objective function is nonconvex. The problem of global searching of multiple parameters was formulated to be a k-D move in the parameter space and the parameter updating scheme was converted to be a state-action decision-making problem. We proposed a novel Deep Q-learning of Model Parameters (DQMP) method for global optimization which updated the parameter configurations through actions that maximized the Q-value and employed a Deep Reward Network (DRN) designed to learn global reward values from both visible fitting errors and hidden parameter errors. The DRN was constructed with Long Short-Term Memory (LSTM) layers followed by fully connected layers and a rectified linear unit (ReLU) nonlinearity. The depth of the DRN depended on the number of parameters. Through DQMP, the k-D parameter search in each step resembled the decision-making of action selections from 3k configurations in a k-D board game. The DQMP method was evaluated by widely used general functions that can express a variety of experimental data and further validated on imaging applications. The convergence of the proposed DRN was evaluated, which showed that the loss values of six general functions all converged after 12 epochs. The parameters estimated by the DQMP method had relative errors of less than 4% for all cases, whereas the relative errors achieved by Q-learning (QL) and the Least Squares Method (LSM) were 17% and 21%, respectively. Furthermore, the imaging experiments demonstrated that the imaging of the parameters estimated by the proposed DQMP method were the closest to the ground truth simulation images when compared to other methods. The proposed DQMP method was able to achieve global optima, thus yielding accurate model parameter estimates. DQMP is promising for estimating multiple high-dimensional parameters and can be generalized to global optimization for many other complex nonconvex functions and imaging of physical parameters.

Simplifying asteroseismic analysis of solar-like oscillators

Context. The asteroseismic analysis of stellar power density spectra is often computationally expensive. The models used in the analysis may require several dozen parameters to accurately describe features in the spectra caused by the oscillation modes and surface granulation. Many of these parameters are often highly correlated, making the parameter space difficult to quickly and accurately sample. They are, however, all dependent on a much smaller set of parameters, namely the fundamental stellar properties. Aims. We aim to leverage this to develop a method for simplifying the process of sampling the model parameter space for the asteroseismic analysis of solar-like oscillators, with an emphasis on mode identification. Methods. Using a large set of previous observations, we applied principal component analysis to the sample covariance matrix to select a new basis on which to sample the model parameters. Selecting the subset of basis vectors that explains the majority of the sample variance, we then redefined the model parameter prior probability density distributions in terms of a smaller set of latent parameters. Results. We are able to reduce the dimensionality of the sampled parameter space by a factor of two to three. The number of latent parameters needed to accurately model the stellar oscillation spectra cannot be determined exactly but is likely only between four and six. Using two latent parameters, the method is able to produce models that describe the bulk features of the oscillation spectrum, while including more latent parameters allows for a frequency precision better than ≈10% of the small frequency separation for a given target. Conclusions. We find that sampling a lower-rank latent parameter space still allows for accurate mode identification and parameter estimation on solar-like oscillators over a wide range of evolutionary stages. This allows for the potential to increase the complexity of spectrum models without a corresponding increase in computational expense.

Link-Level Simulator for 5G Localization

Channel-state-information-based localization in 5G networks has been a promising way to obtain highly accurate positions compared to previous communication networks. However, there is no unified and effective platform to support the research on 5G localization algorithms. This paper releases a link-level simulator for 5G localization, which can depict realistic physical behaviors of the 5G positioning signal transmission. Specifically, we first develop a simulation architecture considering more elaborate parameter configuration and physical-layer processing. The architecture supports the link modeling at sub-6GHz and millimeter-wave (mmWave) frequency bands. Subsequently, the critical physical-layer components that determine the localization performance are designed and integrated. In particular, a lightweight new-radio channel model and hardware impairment functions that significantly limit the parameter estimation accuracy are developed. Finally, we present three application cases to evaluate the simulator, i.e. two-dimensional mobile terminal localization, mmWave beam sweeping, and beamforming-based angle estimation. The numerical results in the application cases present the performance diversity of localization algorithms in various impairment conditions.

Motion estimation and system identification of a moored buoy via physics-informed neural network

This paper explores the use of physics-informed neural networks (PINNs) to estimate motion and identify system parameters of a moored buoy under three different sea states. PINNs are a deep learning architecture that incorporates physical information to provide an interpretable and physically-meaningful neural network model, making it well-suited for modeling offshore moored structures with high nonlinearity. The moored buoy is modeled as a nonlinear ordinary differential equation (ODE), and the general formulation of PINN for the system of ODEs is established. Two new metrics for motion estimation and system identification are proposed to evaluate the accuracy and efficiency of the implementation of PINN. The results demonstrate that PINN can accurately estimate motion and identify system parameters by choosing appropriate hyperparameters (HPs). This paper also investigates the effects of the number of layers, nodes, and learning rate on motion estimation and system identification to provide a benchmark for selecting optimal HPs. This study finds that hyperparameter optimization can reduce the relative error of identified parameters by up to two thousand times compared to no optimization. Motion estimation prefers large neural networks for all sea states, while at least three layers of neural networks are needed for accurate parameter identification. The paper also provides a look-up table to investigate further implementing PINN on moored floating offshore structures. Proper selection of HPs is crucial as it can incur up to three orders of magnitude PINN loss and exceedingly-high identification error. Overall, this study highlights the applicability of PINN in modeling complex offshore structures and provides insights into selecting optimal HPs for accurate and efficient estimation of motion and system parameters.

Bayesian regularization in multiple-indicators multiple-causes models.

Integrating regularization methods into structural equation modeling is gaining increasing popularity. The purpose of regularization is to improve variable selection, model estimation, and prediction accuracy. In this study, we aim to: (a) compare Bayesian regularization methods for exploring covariate effects in multiple-indicators multiple-causes models, (b) examine the sensitivity of results to hyperparameter settings of penalty priors, and (c) investigate prediction accuracy through cross-validation. The Bayesian regularization methods examined included: ridge, lasso, adaptive lasso, spike-and-slab prior (SSP) and its variants, and horseshoe and its variants. Sparse solutions were developed for the structural coefficient matrix that contained only a small portion of nonzero path coefficients characterizing the effects of selected covariates on the latent variable. Results from the simulation study showed that compared to diffuse priors, penalty priors were advantageous in handling small sample sizes and collinearity among covariates. Priors with only the global penalty (ridge and lasso) yielded higher model convergence rates and power, whereas priors with both the global and local penalties (horseshoe and SSP) provided more accurate parameter estimates for medium and large covariate effects. The horseshoe and SSP improved accuracy in predicting factor scores, while achieving more parsimonious models. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

An analytical model of multi-layered heat transport to estimate vertical streambed fluxes and sediment thermal properties

Using heat as a tracer to estimate the vertical streambed fluxes (VSFs) and sediment thermal properties, the choice of mathematical models of heat transport is critical for the accuracy of estimated values. In this study, a new analytical model of heat transport in a multi-layered streambed is developed with arbitrary boundary conditions, arbitrary initial conditions, a velocity-dependent effective thermal diffusivity, and time-variant VSFs, which is named the MLT model. A finite-difference solution and field experimental data are employed to test the MLT model. The particle swarm optimization (PSO) algorithm is employed to estimate VSFs and streambed sediment thermal properties. Results show that the MLT model releases the limitation included in the one-layered streambed models in parameter estimation that the observation locations have to be within a sub-layer of the streambed. The MLT model coupled with the PSO method can accurately estimate the VSFs and thermal properties of each layer in a multi-layered streambed system using only one observation point, and the location of the observation point has no impact on the accuracy of parameter estimation when using the MLT model. The Morris global sensitivity analysis reveals that heat transport in the layered streambed system is most sensitive to VSFs, and followed by the effective thermal diffusivity of the upper streambed layer, the effective thermal diffusivity of the lower streambed layer, and the thickness of the upper streambed layer. The field application shows that the MLT model outperforms the previous models in terms of interpreting field data, and the location of interfaces between streambed layers could be estimated by the MLT model.

Methodology for measuring dendrometric parameters in a mediterranean forest with UAVs flying inside forest

Accurate field measurements of tree morphological features are essential for effective forest inventory and the sustainable management of forest resources. Traditional methods involve time-consuming and expensive tree-by-tree measurements conducted by specialized technicians, which can lead to subjective measurement errors. To address these limitations, advanced sensor technologies have garnered attention in recent years. Terrestrial laser scanning (TLS) has been widely employed due to its high precision in deriving tree attributes at the plot level. However, TLS has certain drawbacks, including high acquisition costs, limited portability, and the requirement for specialized software and expertise. As alternatives, aerial photogrammetry and computer vision algorithms have emerged to obtain high-resolution 3D measurements of forest vegetation.This study proposes a novel approach utilizing a small drone under the forest canopy to estimate biometric parameters such as trunk diameter at various heights and circumference. By joining the capabilities of drones with the structure-from-motion approach, this study presents a promising solution for cost-effective and accurate estimation of biometric parameters in forest inventories. Moreover, the results demonstrate superior accuracy compared to those reported in previous studies with improvements up to one order of magnitude.

Cessation time approach incorporating parametric and non-parametric machine-learning algorithms for recovery test data

ABSTRACT In this study we propose a new method called the cessation time approach (CTA) for interpreting recovery tests in confined aquifers, which is based on the Theis solution. The CTA method involves selecting a residual drawdown measurement from the recovery phase and linking it to its dimensionless counterpart through simple algebraic steps. This approach is then incorporated with a regression model to estimate aquifer parameters. The performance of several parametric polynomial and non-parametric machine learning regression models was investigated using various datasets. Results show that CTA with third-order multivariable polynomials produced highly accurate parameter estimates with a normalized root mean squared error (NRMSE) within 0.5% for a field dataset. Among the machine learning algorithms tested, the radial basis function and Gaussian process regression achieved the highest accuracy with NRMSEs of 0.6%. We conclude that CTA can be a viable interpretation tool for recovery tests due to its accuracy and simplicity.

Fast estimation for generalised multivariate joint models using an approximate EM algorithm

Joint models for longitudinal and survival data have become an established tool for optimally handling scenarios when both types of data co-exist. Multivariate extensions to the classic univariate joint model have started to emerge but are typically restricted to the Gaussian case, deployed in a Bayesian framework or focused on dimension reduction. An approximate EM algorithm is utilised which circumvents the oft-lamented curse of dimensionality and offers a likelihood-based implementation which ought to appeal to clinicians and practitioners alike. The proposed method is validated in a pair of simulation studies, which demonstrate both its accuracy in parameter estimation and efficiency in terms of computational cost. Its clinical use is demonstrated via an application to primary billiary cirrhosis data. The proposed methodology for estimation of these joint models is available in R package gmvjoint.

Maximum likelihood based multi‐innovation stochastic gradient identification algorithms for bilinear stochastic systems with ARMA noise

SummaryThis paper considers the parameter estimation problem for bilinear stochastic systems with autoregressive moving average (ARMA) noise using the stochastic gradient method. First, the identification model is derived by eliminating the state variables. Based on the obtained identification model, a multi‐innovation generalized extended stochastic gradient (MI‐GESG) algorithm is proposed using the multi‐innovation identification theory. Furthermore, to enhance the parameter estimation accuracy, a maximum likelihood based MI‐GESG (ML‐MI‐GESG) algorithm is developed by using the maximum likelihood identification principle. Finally, an illustrative simulation example is provided to testify the proposed algorithms. The simulation results show the effectiveness of the proposed algorithms for identifying bilinear systems.

Research on Financial Default Model with Stochastic Intensity Using Filtered Likelihood Method

This paper investigates the financial default model with stochastic intensity by incomplete data. On the strength of the process-designated point process, the likelihood function of the model in the parameter estimation can be decomposed into the factor likelihood term and event likelihood term. The event likelihood term can be successfully estimated by the filtered likelihood method, and the factor likelihood term can be calculated in a standardized manner. The empirical study reveals that, under the filtered likelihood method, the first model outperforms the other in terms of parameter estimation efficiency, convergence speed, and estimation accuracy, and has a better prediction effect on the default data in China’s financial market, which can also be extended to other countries, which is of great significance in the default risk control of financial institutions.

Dynamic parameter estimation of the alkaline electrolysis system combining Bayesian inference and adaptive polynomial surrogate models

Utility-scale hydrogen production via alkaline electrolysis (AEL) is a promising pathway toward the decarbonization of the power, transportation, and chemical industries. The efficiency, load flexibility, and operational safety of the AEL system are subject to electrochemical, thermal, and mass transfer dynamics, and the corresponding parameters, including overvoltage coefficients, heat capacities and resistances of the stack and lye-gas separators, thickness and permeability of the diaphragm, etc. The community has developed many models to depict these dynamic behaviors. However, due to the lack of a comprehensive parameter estimation method, these models are generally tuned manually in industrial applications, which can be inaccurate and cannot fit their time-varying nature. To fill this gap, we present a fast and accurate parameter estimation method for the AEL system. Specifically, to address the difficulties of strong nonlinearity of the dynamic electrolyzer models and correlation between different parameters, a Bayesian inference-based Markov chain Monte Carlo method is proposed. To reduce the computing time for online estimation, data-driven adaptive polynomial surrogate models are established to replace repeated time-domain simulations of the electrolyzer model so that estimation can be finished within a few minutes. Experiments on a 5 Nm3/hr-rated AEL system validate the proposed method. Compared with the existing Kalman filter variants, the estimation error is reduced by at most 71.1% in terms of RMSE and NRMSE. In addition, the proposed method provides approaches to fault diagnosis and global sensitivity analysis for operating and designing AEL systems.

Construction of quantile regression using natural gradient descent

Building mathematical models is an important part of developing digital products in various industries, medicine, geology, construction, finance and other areas. Modeling allows optimizing production processes, identifying patterns, predicting time series, classifying objects, and constructing regressions. Quantile regression models are a generalization of median regression and can be used to examine data in depth. Quantile analysis involves estimating model parameters and determining quantile values of the dependent variable for given values of the independent variable. This is done by minimizing the loss function based on quantile values. In contrast to the method of least squares, quantile regression allows to predict the values of the dependent variable more accurately when the values of the independent variable change. That is, quantile regression is more robust. It can be used to solve many problems in various fields of science and business, where it is necessary to more accurately predict the values of the dependent variable under changing conditions. The natural gradient descent is an effective method for constructing regression and has a higher rate of convergence than the classical algorithm. However, in practice this method is quite complicated from a computational point of view, since it requires the calculation of the second derivative. This problem is especially acute when training neural networks, where the number of parameters is much higher than when building classical regression models. The study of methods of regression construction and application of numerical methods are of practical and scientific interest. This paper will look at quantile regression, natural gradient descent and their combination to build mathematical models. Gradient descent is one of the most popular optimization methods and is widely used in machine learning. The natural gradient descent is the preferred method because it is more efficient and has a high rate of convergence. In addition, this method is less vulnerable to hitting local minima and provides more accurate estimates of model parameters. In practice, however, this method is computationally difficult, as it requires the calculation of the second derivative. The article presents an algorithm for model building using natural gradient descent. The essence of using quantile regression in a natural gradient descent is to use a quantile estimate of the loss function instead of the usual estimate used in the least squares method. This allows not only the mean value of the dependent variable, but also more extreme values (e.g., median, 25th percentile, 95th percentile, etc.) to be considered when constructing the model. The resulting method has also been compared with other popular quantile regression-supported gradient descent methods on open data sets of different dimensionality, both in terms of the number of factors and the number of observations. In addition, the possibilities of further development and optimization of this method will be discussed.

Parameter estimation for Einstein-dilaton-Gauss-Bonnet gravity with ringdown signals* *Supported by the National Key R & D Program of China (2022YFC2204602), and the Natural Science Foundation of China (11925503)

Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band, providing more opportunities to test theories of gravity than ground-based detectors. The study of quasinormal modes (QNMs) and their application in gravity theory testing have been an important aspect in the field of gravitational physics. In this study, we investigate the capability of future space-based gravitational wave detectors, such as LISA, TaiJi, and TianQin, to constrain the dimensionless deviating parameter for Einstein-dilaton-Gauss-Bonnet (EdGB) gravity with ringdown signals from the merger of binary black holes. The ringdown signal is modeled by the two strongest QNMs in EdGB gravity. Considering time-delay interferometry, we calculate the signal-to-noise ratio of different space-based detectors for ringdown signals to analyze their capabilities. The Fisher information matrix is employed to analyze the accuracy of parameter estimation, with particular focus on the dimensionless deviating parameter for EdGB gravity. The impact of the parameters of gravitational wave sources on the estimation accuracy of the dimensionless deviating parameter is also studied. We find that the constraint ability of EdGB gravity is limited because the uncertainty of the dimensionless deviating parameter increases with a decrease in the dimensionless deviating parameter. LISA and TaiJi offer more advantages in constraining the dimensionless deviating parameter to a more accurate level for massive black holes, whereas TianQin is more suited to less massive black holes. The Bayesian inference method is used to perform parameter estimation on simulated data, which verifies the reliability of the conclusion.

Bayesian parameter identification in electrochemical model for lithium-ion batteries

Electrochemical models can characterize the internal behavior of cells and are powerful and effective tools for the design and management of batteries. This study proposes a comprehensive framework of Bayesian parameter identification to determine the parameter distributions in the electrochemical model and to estimate the global sensitivity of the parameters for lithium-ion batteries. Bayesian inference in parameter identification can simultaneously determine accurate parameter estimates and parameter identifiability, given specific voltage measurements. Among the several parameters in the pseudo-two-dimensional model, 15 parameters are selected to estimate the posterior distributions. The reconstructed voltage curves through the estimated parameter distributions are consistent with the reference voltages, with relative errors of less than 0.7% at various discharge rates. Changes in the parameter distributions and identifiability were investigated for different discharge rates through the estimated joint and marginal distributions of the parameters. Moreover, based on variance-based global sensitivity analysis, the identifiability of the electrochemical parameters according to the discharge rates is quantitatively analyzed. We demonstrate that the Bayesian parameter identification simultaneously obtains the parameter distributions and identifiability, considering the correlation between various parameters. The proposed framework can help to analyze the behaviors of batteries according to specific operating conditions and materials.