Parameter Estimation Research Articles

Introduction of a Framework for the Integration of a Kinematic Robot Arm Model in an Artificial Neural Network - Extended Kalman Filter Approach

The aim of this paper is to introduce a model in which systematic effects can be assigned according to their origin or mode of action. The approach intends to improve the positional accuracy of a robot arm. We show the impact of unaccounted model biases on estimated parameters when applying sequential approaches and conclude the necessity of jointly determining all influencing variables. Therefore, we propose a simultaneous estimation of transformation parameters, robot’s kinematic parameters and non-geometric parameters modelled by an artificial neural network (ANN) in further consequence. Thus, the main contribution of this paper is a new approach of the simultaneous estimation of the geometric and non-geometric components of a robot arm model. The integration of the geometric model (transformations, kinematic robot model) with the non-geometric one (ANN) is realised in the extended Kalman filter. The functionality of the algorithm has been proven on simulated data. The adaptive behaviour of machine learning approaches is made possible by an additional iteration of the ANN. The initialisation of the ANN parameters must not deviate from the nominal parameters by more than 10% so that the ANN can learn the non-geometric part. In this setup, the robot arm position corrections are reduced by 32.5%. A final sensitivity analysis proves the estimability of most kinematic parameters in the course of a future adaptive extension of the approach.

Inference for depending competing risks from Marshall–Olikin bivariate Kies distribution under generalized progressive hybrid censoring

This paper explores inferences for a competing risk model with dependent causes of failure. When the lifetimes of competing risks are modelled by a Marshall–Olikin bivariate Kies distribution, classical and Bayesian estimations are studied under generalized progressive hybrid censoring. The existence and uniqueness results for maximum likelihood estimators of unknown parameters are established, whereas approximate confidence intervals are constructed using the observed Fisher information matrix. In addition, Bayes estimates are explored based on a flexible Gamma-Dirichlet prior information. Furthermore, when there is a priori order information on competing risk parameters being available, traditional classical likelihood and Bayesian estimates are also established under restricted parameter case. The behavior of the proposed estimators is evaluated through extensive simulation studies, and a real data study is presented for illustrative purposes.

Multi-scale hybrid modeling of plant growth in response to environmental conditions and soil nutrients availability

Crop modeling plays a crucial role in agriculture, aiding our understanding and prediction of crop growth and yield in diverse environmental conditions. This study aims to develop a comprehensive mathematical model describing plant growth in response to environmental conditions and soil nutrient availability. To achieve this, we relied on a field experiment with lettuce plants under varying environmental conditions. Employing growth models such as logistic, Gompertz, Aikman & Scaife, and Scaife, Cox & Morris, we assessed the influence of time, day-degrees, and effective-day-degrees across different plant densities and during distinct periods throughout the year. In general, describing plant growth in terms of day-degrees or effective-day-degrees yielded an improved model fit and more precise estimations of growth parameters. As a result, we described the growth of plant length in terms of effective-day-degrees instead of time in the equations of the Bessonov-Volpert system. Additionally, we modified the equation describing plant length growth using previously fitted functions. By incorporating these adjustments, we characterized the one-dimensional growth of plant weight under varying environmental conditions without branching, using the Bessonov-Volpert model. This study contributes valuable insights into crop modeling techniques, refining our understanding of optimizing plant growth under different environmental conditions.

Association between serum uric acid levels and cardio-ankle vascular index stratified by circulating level of CD34-positive cells among elderly Japanese men: a cross-sectional study

Although serum uric acid (UA) has been reported to be positively associated with increased arterial stiffness as evaluated by cardio-ankle vascular index (CAVI), UA also has an antioxidative effect that prevents endothelial damage. Therefore, the status of endothelial repair induced by endothelial damage might affect the correlation between UA and CAVI. To clarify the correlation between UA and CAVI in relation to endothelial repair activity, we performed a cross-sectional study with 246 Japanese men aged 60–69 years undergoing a general health check-up. The analysis was stratified by the median circulating level of CD34-positive cells because circulating levels of CD34-positive cells could indicate the degree of endothelial repair activity. Independent of known cardiovascular risk factors, among participants with high circulating levels of CD34-positive cells (0.95 cells/μL ≤), UA was significantly positively correlated with CAVI (standardized parameter estimate β = 0.23, p = 0.009), but not among participants with low circulating levels of CD34-positive cells (< 0.95 cells/μL) (β = 0.07, p = 0.445). Independent of established cardiovascular risk factors, UA levels were significantly positively correlated with increased arterial stiffness only among participants with aggressive endothelial repair as evaluated by circulating levels of CD34-positive cells. These results might help clarify some background mechanisms related to endothelial activity.

Intraday Variations in Skin Water Parameters

Introduction: Three interrelated skin water assessments include stratum corneum hydration (SCH) via electrical measurements, skin water using tissue dielectric constant (TDC) measurements and transepidermal water loss (TEWL). These are differentially used for skin physiology research, clinical assessments of dermatological conditions and to assess skin water in diabetes and lymphedema. Often volar forearm skin is used for assessments done at various times of day (TOD). The present goal was to assess the extent of intraday variability in SCH, TDC and TEWL. Methods: Twelve medical students self-measured SCH, TDC and TEWL on their forearm every two hours from 0800 to 2400 hours on two consecutive days. All participants were well-trained and pre-certified in all procedures. Tests for parameter differences among TOD were via the nonparametric Friedman test. Results: No significant differences in SCH or TEWL were found among TOD over the 16-hour interval for either day or combined. Contrastingly TDC decreased slightly but significantly from morning through evening. There was no evidence of a diurnal pattern. Interestingly, a significant nonlinear relationship between TEWL and SCH was detected. Conclusion: Findings indicate only minor intra-day variations with TOD trend except for TDC that decreases slightly from morning through evening. The clinical relevance relates to the confidence now gained associated with the parameter estimates when measured at different TOD during normal clinic hours or beyond. This should help in estimating the potential importance of small differences if measured at a different TOD. From a physiological viewpoint, the findings uncover and describe an interesting nonlinear relationship between TEWL and SCH which may serve to propel further investigations that might better characterize this process.

A Bhattacharyya-type Conditional Error Bound for Quadratic Discriminant Analysis

We give an upper bound on the conditional error of Quadratic Discriminant Analysis (QDA), conditioned on parameter estimates. In the case of maximum likelihood estimation (MLE), our bound recovers the well-known Chernoff and Bhattacharyya bounds in the infinite sample limit. We perform an empirical assessment of the behaviour of our bound in a finite sample MLE setting, demonstrating good agreement with the out-of-sample error, in contrast with the simpler but uninformative estimated error, which exhibits unnatural behaviour with respect to the sample size. Furthermore, our conditional error bound is applicable whenever the QDA decision function employs parameter estimates that differ from the true parameters, including regularised QDA.

The estimation of pubertal growth spurt parameters using the superimposition by translation and rotation model in Korean children and adolescents: a longitudinal cohort study

ObjectivesUnderstanding the characteristics of the pubertal growth spurt in Korean children and adolescents can serve as crucial foundational data for researching puberty and growth-related disorders. This study aims to estimate the key parameters of pubertal growth, specifically the age and magnitude of the pubertal growth spurt, utilizing longitudinal data from a cohort of Korean children and adolescents.MethodsThis study used mixed longitudinal height data from a cohort of Korean elementary, middle, and high school students aged 7–18 years. The Superimposition by Translation and Rotation (SITAR) model, a shape-invariant growth curve model, was utilized to estimate a reference height velocity curve for the entire dataset and individual curves via random effects to evaluate pubertal growth parameters. Altogether, 3,339 height measurements (1,519 for boys and 1,820 for girls) from 270 individuals (123 boys and 147 girls) were analyzed.ResultsThe average age of growth spurt onset in Korean boys was 10.17 ± 0.61 years (mean ± SE), with peak height velocity occurring at 12.46 ± 0.69 years of age (9.61 ± 1.26 cm/year). Korean girls, contrarily, experience their growth spurt at an earlier age (8.57 ± 0.68 years), with peak height velocity occurring at 10.99 ± 0.74 years of age (8.32 ± 1.09 cm/year). An earlier onset of puberty in both sexes is associated with a shorter growth spurt duration (0.63 years for boys and 0.58 years for girls) and a higher peak height velocity (1.82 cm/year for boys and 1.39 cm/year for girls). These associations were statistically significant for both sexes (all p &amp;lt; 0.0001).ConclusionThis study is the first to use the height velocity curve from the SITAR model to examine the pubertal growth spurt of Korean children and adolescents. The estimated timing and magnitude of the pubertal growth spurt, and their relationships can be useful data for clinicians and researchers.

A High-Resolution and Robust Microwave Correlation Imaging Method Based on URRF Using MC-AAMPE Algorithm

This manuscript presents a novel framework for high-resolution and robust microwave correlation imaging. In order to generate a more diverse random radiation field distribution, the unified random radiation field (URRF) model is proposed. The URRF model can accurately characterize the joint random modulation in the signals’ phase, amplitude, and frequency. Furthermore, we build a parametric imaging model based on URRF which clearly describes the relationship between the image to be reconstructed and the signals by the URRF model. By using this imaging model, the reconstruction of an image is converted into solving a multi-parameter optimization problem with multiple constraints. To solve this optimization problem with high efficiency and accuracy, the model-constrained adaptive alternating multiple parameter estimation (MC-AAMPE) algorithm is proposed. This algorithm decomposes the high-dimensional multi-parameter optimization problem into several sub-optimization problems. The renewing solutions to these sub-optimization problems make the multi-parameter optimization converge to the image of the target and the parameters of clutter and noise, which are all unknown before the solution. In comparison with the existing methods, the proposed scheme generates images with higher resolution and is more robust under noise conditions. Extensive simulation experiments confirmed the effectiveness and robustness of the proposed method.

New alpha power transformed beta distribution with its properties and applications

The main purpose of this paper is to introduce a new alpha power transformed beta probability distribution that reveals interesting properties. The studuy provide a comprehensive explanation of the statistical characteristics of this innovative model. Various properties of the new distribution were derived, using the baseline beta distribution, statistical techniques, and probabilistic axioms. These include the probability density, cumulative distribution, survival function, hazard function, moments about the origin, moment generating function, and order statistics. For parameter estimation, the maximum likelihood estimation method using Newton Raphson numerical technique is employed. To evaluate the performance of our estimation method, the mean squared errors of the estimated parameters for different simulated sample sizes are used. In addition simulation studies of the new distribution are conducted to demonstrate the behavior of the probability model. To demonstrate the practical utility and flexibility of the alpha power transformed beta distribution, it is fitted to two real-life datasets and compared to commonly known probability distributions such as the Weibull, exponential Weibull, Beta, and Kumaraswamy beta distributions. It offers a superior fit to the data considered. The distribution reviales of the microbes reveald a wide range of shapes of probability density functions and flexible hazard rates. The distribution is a new contribution to the field of statistical and probability theory. The findings of the study can be used as a basis for future research in the area of statistical science and health.

A marker-based method for visual-inertial initialization

Accurate and robust initialization is significant for visual-inertial simultaneous localization and mapping (VI-SLAM). Existing methods solve VI-SLAM initialization based on visual information. However inertial measurement unit (IMU) parameter estimation performed underwater is subject to two major limitations. First, IMU preintegration error accumulates over time, resulting in reduced accuracy. Second, it is difficult for robots to achieve sufficient movement underwater, which affects the reliability of initialization results. For a better balance between the efficiency and accuracy of VI-SLAM initialization, this study proposes a VI-SLAM initialization method using a designed marker calibration device. First, we utilize both marker points and ORB feature points for a fast and robust visual trajectory estimation with real motion scale, and we estimate the gravity direction using the marker calibration device. Second, the IMU trajectory is aligned with the trajectory, and the IMU parameters are solved using the initial gravity direction. Experiments verify the effectiveness of our developed method for improving the accuracy and efficiency of the VI-SLAM initialization. The code is available at https://gitee.com/litseaak/mmorb.

Kinetics of Viral Shedding for Outbreak Surveillance of Emerging Infectious Diseases: Modeling Approach to SARS-CoV-2 Alpha and Omicron Infection

Background Previous studies have highlighted the importance of viral shedding using cycle threshold (Ct) values obtained via reverse transcription polymerase chain reaction to understand the epidemic trajectories of SARS-CoV-2 infections. However, it is rare to elucidate the transition kinetics of Ct values from the asymptomatic or presymptomatic phase to the symptomatic phase before recovery using individual repeated Ct values. Objective This study proposes a novel Ct-enshrined compartment model to provide a series of quantitative measures for delineating the full trajectories of the dynamics of viral load from infection until recovery. Methods This Ct-enshrined compartment model was constructed by leveraging Ct-classified states within and between presymptomatic and symptomatic compartments before recovery or death among people with infections. A series of recovery indices were developed to assess the net kinetic movement of Ct-up toward and Ct-down off recovery. The model was applied to (1) a small-scale community-acquired Alpha variant outbreak under the “zero-COVID-19” policy without vaccines in May 2021 and (2) a large-scale community-acquired Omicron variant outbreak with high booster vaccination rates following the lifting of the “zero-COVID-19” policy in April 2022 in Taiwan. The model used Bayesian Markov chain Monte Carlo methods with the Metropolis-Hastings algorithm for parameter estimation. Sensitivity analyses were conducted by varying Ct cutoff values to assess the robustness of the model. Results The kinetic indicators revealed a marked difference in viral shedding dynamics between the Alpha and Omicron variants. The Alpha variant exhibited slower viral shedding and lower recovery rates, but the Omicron variant demonstrated swifter viral shedding and higher recovery rates. Specifically, the Alpha variant showed gradual Ct-up transitions and moderate recovery rates, yielding a presymptomatic recovery index slightly higher than 1 (1.10), whereas the Omicron variant had remarkable Ct-up transitions and significantly higher asymptomatic recovery rates, resulting in a presymptomatic recovery index much higher than 1 (152.5). Sensitivity analysis confirmed the robustness of the chosen Ct values of 18 and 25 across different recovery phases. Regarding the impact of vaccination, individuals without booster vaccination had a 19% higher presymptomatic incidence rate compared to those with booster vaccination. Breakthrough infections in boosted individuals initially showed similar Ct-up transition rates but higher rates in later stages compared to nonboosted individuals. Overall, booster vaccination improved recovery rates, particularly during the symptomatic phase, although recovery rates for persistent asymptomatic infection were similar regardless of vaccination status once the Ct level exceeded 25. Conclusions The study provides new insights into dynamic Ct transitions, with the notable finding that Ct-up transitions toward recovery outpaced Ct-down and symptom-surfacing transitions during the presymptomatic phase. The Ct-up against Ct-down transition varies with variants and vaccination status. The proposed Ct-enshrined compartment model is useful for the surveillance of emerging infectious diseases in the future to prevent community-acquired outbreaks.

High-resolution multicomponent LFM parameter estimation based on deep learning

This paper addresses the complex challenge of parameter estimation in multi-component Linear Frequency Modulation (LFM) signals by introducing an innovative approach to high-resolution Fractional Fourier Transform (FrFT) parameter estimation, facilitated by convolutional neural networks. Initially, it analyzes the issues of peak shifts and the masking of weaker components due to spectral overlap in the FrFT domain of multi-component LFM signals. Convolutional neural networks are then employed to train and achieve high-resolution representations of FrFT parameters. Specifically, convolutional modules with residual structures are utilized to learn coarse features, while a weighted attention mechanism refines independent features across both channel and spatial dimensions. This approach effectively addresses the challenges posed by spectral peak overlap and frequency shifts in multi-component LFM signals, thereby enhancing the quality of high-resolution parameter estimation. Experimental results demonstrate that the proposed method significantly outperforms traditional methods in processing multi-component LFM signals. Moreover, it exhibits robust detection capabilities for both weak and compact components, thereby underscoring its potential applicability in the field of complex signal processing.

Importance of accounting for imperfect detection of plants in the estimation of population growth rates

Detection of plant individuals is imperfect. Not accounting for this issue can result in biased estimates of demographic parameters as important as population growth rates. In mobile organisms, a common practice is to explicitly account for detection probability during the estimation of most demographic parameters, but no study in plant populations has examined the consequences of ignoring imperfect detectability on the estimation of population growth rates. The lack of accounting for detection probability occurs because plant demographers have frequently assumed that detection is perfect, and because there is a scarcity of studies that formally compare the performance of estimation methods that incorporate detection probabilities with respect to methods that ignore detectabilities. Based on field data of five plant species and data simulations, we compared the performance of three methods that estimate population growth rates, two that do not estimate detection probabilities (direct counts of individuals and the minimum‐number‐alive method) and the other that explicitly accounts for detection probabilities (temporal symmetry models). Our aims were 1) to estimate detection probabilities, and 2) to evaluate the performance of these three methods by calculating bias, accuracy, and precision in their estimates of population growth rates. Our five plant species had imperfect detection. Estimates of population growth rates that explicitly incorporate detectabilities had better performance (less biased estimates, with higher accuracy and precision) than those obtained with the two methods that do not calculate detection probabilities. In these latter methods, bias increases as detection probability decreases. Our findings highlight the importance of using robust analytical methods that account for detection probability of plants during the estimation of critical demographic parameters such as population growth rates. In this way, estimates of plant population parameters will reliably indicate their actual status and quantitative trends.

Periodicity search in the timing of the 25 millisecond pulsars from the second data release of the European pulsar timing array

Abstract In this work, we investigated the presence of strictly periodic, as well as quasi-periodic signals, in the timing of the 25 millisecond pulsars from the EPTA DR2 dataset. This is especially interesting in the context of the recent hints of a gravitational wave background in these data, and the necessary further study of red-noise timing processes, which are known to behave quasi-periodically in some normal pulsars. We used Bayesian timing models developed through the run_enterprise pipeline: a strict periodicity was modelled as the influence of a planetary companion on the pulsar, while a quasi-periodicity was represented as a Fourier-domain Gaussian process. We found that neither model would clearly improve the timing models of the 25 millisecond pulsars in this dataset. This implies that noise and parameter estimates are unlikely to be biased by the presence of a (quasi-)periodicity in the timing data. Nevertheless, the results for PSRs J1744−1134 and J1012+5307 suggest that the standard noise models for these pulsars may not be sufficient. We also measure upper limits for the projected masses of planetary companions around each of the 25 pulsars. The data of PSR J1909−3744 yielded the best mass limits, such that we constrained the 95-percentile to ∼2 × 10−4 M⊕ (roughly the mass of the dwarf planet Ceres) for orbital periods between 5 d–17 yr. These are the best pulsar planet mass limits to date.

Removal of acidic dyes; acid yellow 25 and acid red 4 from wastewater by degassed activated carbon

Abstract Activated carbon was prepared at 300 °C and 600 °C, characterized by SEM, EDX and XRD, and was then used as an adsorbent for the removal of acidic dyes; acid yellow 25 and acid red 4. The activated carbon prepared at high temperature (600 °C) due to its high carbon contents and surface area was subsequently used as adsorbent for the selected dyes adsorption using batch adsorption approaches to estimate different adsorption parameters. For the estimation of kinetics and equilibrium parameters a number of kinetics and isotherm models were employed. Dyes were adsorbed on activated carbon surface at a high rate for the first 15 min, after which it began to diffuse into the micro pores and thus the process became steady. The rate constant was estimated for first and second order kinetics models. The maximum adsorption capacities recorded were 526.32 mg g−1 for acid red 4 and 555.55 mg g−1 for acid yellow 25. The enthalpy change values recorded were; 19.44 kJ mol−1 for acid yellow 25 adsorption and 16 kJ mol−1 for acid red 4 adsorption, meant that the process is endothermic. The negative values of Gibbs free energy change (−393.28, −1,515.48, −2,634.68 J mol−1) of acid red 4 and acid yellow 25 (−251.72, −1,058.06, −2,367.84 J mol−1) at tested temperatures, confirmed the feasibility and spontaneity of the adsorption processes. The adsorption of dyes on the carbon surface was diffusion-controlled process, as demonstrated by the linear graph of intraparticle diffusion model.

A novel statistical approach to COVID-19 variability using the Weibull-Inverse Nadarajah Haghighi distribution

Researchers have devoted decades to striving to create a plethora of distinctive distributions in order to meet specific objectives. The argument is that traditional distributions have typically been found to lack fit in real-world situations, which include pharmaceutical studies, the field of engineering, hydrology, environmental science, and a number of others. The Weibull-inverse Nadarajah Haghighi (WINH) distribution is developed by combining the Weibull and inverse Nadarajah Haghighi distributions. The proposed distribution's fundamental characteristics have been established and analyzed. Several plots of the distributional properties, notably probability density function (PDF) with corresponding cumulative distribution function (CDF) are displayed. The estimation of model parameter is performed via the MLE procedure. Simulation-based research is conducted to demonstrate the performance of proposed estimator’s using some measure, like the average bias, variance, and associated mean square error (MSE). Two real datasets represent the morality due to COVID 19 in France and Canada are illustrated to see the practicality of the recommended model.

Landslide Analysis with Incomplete Data: A Framework for Critical Parameter Estimation

Landslides are one of the most common geohazards, posing significant risks to infrastructure, recreation, and human life. Slope stability analyses rely on detailed data, accurate materials testing, and careful model parameter selection. These factors are not always readily available, and estimations must be made, introducing uncertainty and error to the final slope stability analysis results. The most critical slope stability parameters that are often missing or incompletely constrained include slope topography, depth to water table, depth to failure plane, and material property parameters. Though estimation of these values is common practice, there is limited guidance or best practice instruction for this important step in the analysis. Guidance is provided for the estimation of: original and/or post-failure slope topography via traditional methods as well as the use of open-source digital elevation models, water table depth across variable hydrologic settings, and the iterative estimation of depth to failure plane and slope material properties. Workflows are proposed for the systematic estimation of critical parameters based primarily on slide type and scale. The efficacy of the proposed estimation techniques, uncertainty quantification, and final parameter estimation protocol for data-sparse landslide analysis is demonstrated via application at a landslide in Colorado, USA.

Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theory

This work introduces a novel and efficient Bayesian federated learning algorithm, namely, the Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC), for parameter estimation and uncertainty quantification. We establish rigorous convergence guarantees of FA-HMC on non-iid distributed datasets, under the strong convexity and Hessian smoothness assumptions. Our analysis investigates the effects of parameter space dimension, noise on gradients and momentum, and the frequency of communication (between the central node and local nodes) on the convergence and communication costs of FA-HMC. Beyond that, we establish the tightness of our analysis by showing that the convergence rate cannot be improved even for continuous FA-HMC process. Moreover, extensive empirical studies demonstrate that FA-HMC outperforms the existing Federated Averaging-Langevin Monte Carlo (FA-LD) algorithm. Supplementary materials for this article are available online.

Extension of the characterization of non-Gaussianity in gravitational wave detectors with a statistical hypothesis test

Abstract In gravitational wave (GW) astronomy, non-Gaussian noise, such as scattered light noise disturbs stable interferometer operation, limiting the interferometer’s sensitivity, and reducing the reliability of the analyses. In scattered light noise, the non-Gaussian noise dominates the sensitivity in a low frequency range of less than a few hundred Hz, which is sensitive to GWs from compact binary coalescence. This non-Gaussian noise prevents reliable parameter estimation, since several analysis methods are optimized only for Gaussian noise. Therefore, identifying data contaminated by non-Gaussian noise is important. In this work, we extended the conventional method to evaluate non-Gaussian noise, the Rayleigh statistic, by using a statistical hypothesis test to determine a threshold for non-Gaussian noise. First, we estimated the distribution of the Rayleigh statistic against Gaussian noise, called the background distribution, and validated that our extension serves as the hypothetical test. The threshold on the Rayleigh statistic is estimated at 0.73 and 1.28 when the significance level is 0.05, and the sample size is 39. Moreover, we investigated the detection efficiency by assuming two non-Gaussian noise models. For example, for the model with strong scattered light noise, the true positive rate (TPR) was always above 0.7 when the significance level was 0.05. For the demonstration, we applied our extension with the estimated thresholds to the real data. We confirmed our extension provides the binarized outputs of the statistical tests and contributes to finding the non-Gaussian noise in the real data. The results showed that our extension can contribute to an initial detection of non-Gaussian noise and lead to further investigation of the origin of the non-Gaussian noise.

Comparison of estimation limits for quantum two-parameter estimation

Measurement estimation bounds for local quantum multiparameter estimation, which provide lower bounds on possible measurement uncertainties, have so far been formulated in two ways: by extending the classical Cramér-Rao bound (e.g., the quantum Cramér-Rao bound and the Nagaoka Cramér-Rao bound) and by incorporating the parameter estimation framework with the uncertainty principle, as in the Lu-Wang uncertainty relation. In this work, we present a general framework that allows a direct comparison between these different types of estimation limits. Specifically, we compare the attainability of the Nagaoka Cramér-Rao bound and the Lu-Wang uncertainty relation, using analytical and numerical techniques. We show that these two limits can provide different information about the physically attainable precision. We present an example where both limits provide the same attainable precision and an example where the Lu-Wang uncertainty relation is not attainable even for pure states. We further demonstrate that the unattainability in the latter case arises because the figure of merit underpinning the Lu-Wang uncertainty relation (the difference between the quantum and classical Fisher information matrices) does not necessarily agree with the conventionally used figure of merit (mean-squared error). The results offer insights into the general attainability and applicability of the Lu-Wang uncertainty relation. Furthermore, our proposed framework for comparing bounds of different types may prove useful in other settings. Published by the American Physical Society 2024