Different estimation techniques and data analysis for constant-partially accelerated life tests for power half-logistic distribution.

Partial accelerated life tests (PALTs) are employed when the results of accelerated life testing cannot be extended to usage circumstances. This work discusses the challenge of different estimating strategies in constant PALT with complete data. The lifetime distribution of the test item is assumed to follow the power half-logistic distribution. Several classical and Bayesian estimation techniques are presented to estimate the distribution parameters and the acceleration factor of the power half-logistic distribution. These techniques include Anderson-Darling, maximum likelihood, Cramér von-Mises, ordinary least squares, weighted least squares, maximum product of spacing and Bayesian. Additionally, the Bayesian credible intervals and approximate confidence intervals are constructed. A simulation study is provided to compare the outcomes of various estimation methods that have been provided based on mean squared error, absolute average bias, length of intervals, and coverage probabilities. This study shows that the maximum product of spacing estimation is the most effective strategy among the options in most circumstances when adopting the minimum values for MSE and average bias. In the majority of situations, Bayesian method outperforms other methods when taking into account both MSE and average bias values. When comparing approximation confidence intervals to Bayesian credible intervals, the latter have a higher coverage probability and smaller average length. Two authentic data sets are examined for illustrative purposes. Examining the two real data sets shows that the value methods are workable and applicable to certain engineering-related problems.

The Potential of Phase Constraints for Non-Fourier Radiofrequency-Encoded MRI.

In modern magnetic resonance imaging, it is common to use phase constraints to reduce sampling requirements along Fourier-encoded spatial dimensions. In this work, we investigate whether phase constraints might also be beneficial to reduce sampling requirements along spatial dimensions that are measured using non-Fourier encoding techniques, with direct relevance to approaches that use tailored spatially-selective radiofrequency (RF) pulses to perform spatial encoding along the slice dimension in a 3D imaging experiment. In the first part of the paper, we use the Cramér-Rao lower bound to examine the potential estimation theoretic benefits of using phase constraints. The results suggest that phase constraints can be used to improve experimental efficiency and enable acceleration, but only if the RF encoding matrix is complex-valued and appropriately designed. In the second part of the paper, we use simulations of RF-encoded data to test the benefits of phase constraints combined with optimized RF-encodings, and find that the theoretical benefits are indeed borne out empirically. These results provide new insights into the potential benefits of phase constraints for RF-encoded data, and provide a solid theoretical foundation for future practical explorations.

Improving data interpretability with new differential sample variance gene set tests.

Background: Gene set analysis methods have played a major role in generating biological interpretations from omics data such as gene expression datasets. However, most methods focus on detecting homogenous pattern changes in mean expression and methods detecting pattern changes in variance remain poorly explored. While a few studies attempted to use gene-level variance analysis, such approach remains under-utilized. When comparing two phenotypes, gene sets with distinct changes in subgroups under one phenotype are overlooked by available methods although they reflect meaningful biological differences between two phenotypes. Multivariate sample-level variance analysis methods are needed to detect such pattern changes. Results: We use ranking schemes based on minimum spanning tree to generalize the Cramer-Von Mises and Anderson-Darling univariate statistics into multivariate gene set analysis methods to detect differential sample variance or mean. We characterize these methods in addition to two methods developed earlier using simulation results with different parameters. We apply the developed methods to microarray gene expression dataset of prednisolone-resistant and prednisolone-sensitive children diagnosed with B-lineage acute lymphoblastic leukemia and bulk RNA-sequencing gene expression dataset of benign hyperplastic polyps and potentially malignant sessile serrated adenoma/polyps. One or both of the two compared phenotypes in each of these datasets have distinct molecular subtypes that contribute to heterogeneous differences. Our results show that methods designed to detect differential sample variance are able to detect specific hallmark signaling pathways associated with the two compared phenotypes as documented in available literature. Conclusions: The results in this study demonstrate the usefulness of methods designed to detect differential sample variance in providing biological interpretations when biologically relevant but heterogeneous changes between two phenotypes are prevalent in specific signaling pathways. Software implementation of the developed methods is available with detailed documentation from Bioconductor package GSAR. The available methods are applicable to gene expression datasets in a normalized matrix form and could be used with other omics datasets in a normalized matrix form with available collection of feature sets.

Sine π -power odd-G family of distributions with applications.

This paper investigates a novel category of probability distributions and a specific member within this category. We have formulated a new family of trigonometric distributions by utilizing the odds ratio derived from the distribution function of a base distribution. This newly devised distribution family termed the "Sine pie-power odd-G family" of distributions, is constructed through a transformation involving the sine function. The paper presents an overview of the fundamental characteristics inherent to this proposed distribution family. Using the Weibull distribution as a base reference, we have introduced a member belonging to the proposed distribution family. This member demonstrates various hazard functions such as j, reverse-j, increasing, decreasing, or bathtub shapes. The paper examines essential statistical attributes of this newly introduced distribution. The estimation of the distribution's parameters is carried out via the maximum likelihood estimation method. The accuracy of the parameter estimation procedure is validated through Monte Carlo simulations. The outcomes of these simulations reveal a reduction in biases and mean square errors as sample sizes increase, even for small samples. Two sets of real-engineering data are considered to demonstrate the proposed distribution's applicability. The performance of the suggested distribution is evaluated using some model selection criteria and goodness-of-fit test statistics. Empirical evidence from these evaluations substantiates that the proposed model outperforms six existing models.

UAV-UGV Collaborative Localisation with Minimum Sensing.

This paper presents a novel methodology to localise Unmanned Ground Vehicles (UGVs) using Unmanned Aerial Vehicles (UAVs). The UGVs are assumed to be operating in a Global Navigation Satellite System (GNSS)-denied environment. The localisation of the ground vehicles is achieved using UAVs that have full access to the GNSS. The UAVs use range sensors to localise the UGV. One of the major requirements is to use the minimum number of UAVs, which is two UAVs in this paper. Using only two UAVs leads to a significant complication that results an estimation unobservability under certain circumstances. As a solution to the unobservability problem, the main contribution of this paper is to present a methodology to treat the unobservability problem. A Constrained Extended Kalman Filter (CEKF)-based solution, which uses novel kinematics and heuristics-based constraints, is presented. The proposed methodology has been assessed based on the stochastic observability using the Posterior Cramér-Rao Bound (PCRB), and the results demonstrate the successful operation of the proposed localisation method.

An effective and economic estimation of population mean in stratified random sampling using a linear cost function.

Improvement in the estimation of population mean has been an area of interest in sampling theory. So many estimators have been suggested for elevated estimation of the population mean in stratified random sampling, but there is still a gap for more closely estimating the population mean. In this paper, the authors propose a ratio-product-cum-exponential-cum-logarithmic type estimator for the enhanced estimation of population mean by implying one auxiliary variable in stratified random sampling using conventional ratio, exponential ratio, and logarithmic ratio type estimators. The suggested estimator is a generalization of ratio, exponential ratio, and logarithmic ratio type estimators, and therefore these are special cases of the proposed estimator. The proposed estimator's bias and MSE are determined and compared with those of influential estimators, with the linear cost function being used to investigate and compare alternatives. Use Cramer's rule to determine the optimal value of the proposed estimator. The proposed estimator is more effective than other existing estimators, according to theoretical observations. For various applications, we suggest using a proposed estimator with the minimal MSE, which is verified by a numerical example, to have practical applicability of theoretical conclusions in real life.

Bias-reduced neural networks for parameter estimation in quantitative MRI.

PURPOSE: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. THEORY AND METHODS: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. RESULTS: In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations. CONCLUSION: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Towards non-invasive tissue hydration measurements with optical coherence tomography.

The attenuation coefficient ( µ OCT ) measured by optical coherence tomography (OCT) has been used to determine tissue hydration. Previous dual-wavelength OCT systems could not attain the needed precision, which we attribute to the absence of wavelength-dependent scattering of tissue in the underlying model. Assuming that scattering can be described using two parameters, we propose a triple/quadrupole-OCT system to achieve clinically relevant precision in water volume fraction. In this study, we conduct a quantitative analysis to determine the necessary precision of µ OCT measurements and compare it with numerical simulation. Our findings emphasize that achieving a clinically relevant assessment of a 2% water fraction requires determining the attenuation coefficient with a remarkable precision of 0.01 m m - 1 . This precision threshold is influenced by the chosen wavelength for attenuation measurement and can be enhanced through the inclusion of a fourth wavelength range.

Cramér-Rao Lower Bound for Magnetic Field Localization around Elementary Structures.

The determination of a mobile terminal's position with high accuracy and ubiquitous coverage is still challenging. Global satellite navigation systems (GNSSs) provide sufficient accuracy in areas with a clear view to the sky. For GNSS-denied environments like indoors, complementary positioning technologies are required. A promising approach is to use the Earth's magnetic field for positioning. In open areas, the Earth's magnetic field is almost homogeneous, which makes it possible to determine the orientation of a mobile device using a compass. In more complex environments like indoors, ferromagnetic materials cause distortions of the Earth's magnetic field. A compass usually fails in such areas. However, these magnetic distortions are location dependent and therefore can be used for positioning. In this paper, we investigate the influence of elementary structures, in particular a sphere and a cylinder, on the achievable accuracy of magnetic positioning methods. In a first step, we analytically calculate the magnetic field around a sphere and a cylinder in an outer homogeneous magnetic field. Assuming a noisy magnetic field sensor, we investigate the achievable positioning accuracy when observing these resulting fields. For our analysis, we calculate the Cramér-Rao lower bound, which is a fundamental lower bound on the variance of an unbiased estimator. The results of our investigations show the dependency of the positioning error variance on the magnetic sensor properties, in particular the sensor noise variance and the material properties, i.e., the relative permeability of the sphere with respect to the cylinder and the location of the sensor relative to the sphere with respect to the cylinder. The insights provided in this work make it possible to evaluate experimental results from a theoretical perspective.

Photon Phase Delay Sensing with Sub-Attosecond Uncertainty.

The application of statistical estimation theory to Hong-Ou-Mandel interferometry led to enticing results in terms of the detection limit for photon reciprocal delay and polarisation measurement. In the following paper, a fully fibre-coupled setup operating in the telecom wavelength region proves to achieve, for the first time, in common-path Hong-Ou-Mandel-based interferometry, a detection limit for photon phase delay at the zeptosecond scale. The experimental results are then framed in a theoretical model by calculating the Cramer-Rao bound (CRB) and, after comparison with the obtained experimental results, it is shown that our setup attains the optimal measurement, nearly saturating CRB.

ANOPOW FOR REPLICATED NONSTATIONARY TIME SERIES IN EXPERIMENTS.

We propose a novel analysis of power (ANOPOW) model for analyzing replicated nonstationary time series commonly encountered in experimental studies. Based on a locally stationary ANOPOW Cramér spectral representation, the proposed model can be used to compare the second-order time-varying frequency patterns among different groups of time series and to estimate group effects as functions of both time and frequency. Formulated in a Bayesian framework, independent two-dimensional second-order random walk (RW2D) priors are assumed on each of the time-varying functional effects for flexible and adaptive smoothing. A piecewise stationary approximation of the nonstationary time series is used to obtain localized estimates of time-varying spectra. Posterior distributions of the time-varying functional group effects are then obtained via integrated nested Laplace approximations (INLA) at a low computational cost. The large-sample distribution of local periodograms can be appropriately utilized to improve estimation accuracy since INLA allows modeling of data with various types of distributions. The usefulness of the proposed model is illustrated through two real data applications: analyses of seismic signals and pupil diameter time series in children with attention deficit hyperactivity disorder. Simulation studies, Supplementary Materials (Li, Yue and Bruce, 2023a), and R code (Li, Yue and Bruce, 2023b) for this article are also available.

Bias-Reduced Neural Networks for Parameter Estimation in Quantitative MRI.

Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. Results: In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as non-linear least-squares fitting, while state-of-the-art NNs show larger deviations. Conclusion: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Understanding intentionally and non-intentionally added substances and associated threshold of toxicological concern in post-consumer polyolefin for use as food packaging materials.

The use of post-consumer recycled (PCR) polymers in food contact materials (FCMs) can facilitate achieving a circular economy by reducing environmental waste and landfill accumulation. This study aimed to identify potentially harmful substances, including non-intentionally added substances (NIAS) and unapproved intentionally added substances (IAS), in polyolefin samples from material recovery facilities using gas-chromatography mass-spectrometry. Selected phthalates and bisphenols were quantified by targeted gas-chromatography tandem mass-spectrometry. The analysis detected 9 compounds in virgin polymers and 52 different compounds including alcohols, hydrocarbons, phenols in virgin and hydrocarbons, aromatic, phthalates, organic acids, per- and polyfluoroalkyl substances (PFAS) in PCR polymers. The Cramer classification system was used to assesses the Threshold of Toxicological Concern associated with the detected compounds. The PCR sample showed a slightly higher proportion of Cramer Class III compounds (48.08 %) than the virgin sample (44.44 %), indicating higher toxicity potential. Quantification detected bisphenols only in PCR material including BPA (2.88 ± 0.53 µg/g), BPS (5.12 ± 0.003 µg/g), BPF (3.42 ± 0.01 µg/g), and BADGE (4.638 µg/g). Phthalate concentrations were higher in PCR than virgin samples, with the highest levels detected as DIDP, at 6.18 ± 0.31 µg/g for PCR and 6.04 ± 0.02 for virgin. This study provides critical understanding of the safety and potential risks associated with using PCR polyolefins from different sources in food contact applications.

Empirical optimization of energy bin weights for compressing measurements with realistic photon counting x-ray detectors.

BACKGROUND: Photon counting detectors (PCDs) provide higher spatial resolution, improved contrast-to-noise ratio (CNR), and energy discriminating capabilities. However, the greatly increased amount of projection data in photon counting computed tomography (PCCT) systems becomes challenging to transmit through the slip ring, process, and store. PURPOSE: This study proposes and evaluates an empirical optimization algorithm to obtain optimal energy weights for energy bin data compression. This algorithm is universally applicable to spectral imaging tasks including 2 and 3 material decomposition (MD) tasks and virtual monoenergetic images (VMIs). This method is simple to implement while preserving spectral information for the full range of object thicknesses and is applicable to different PCDs, for example, silicon detectors and CdTe detectors. METHODS: We used realistic detector energy response models to simulate the spectral response of different PCDs and an empirical calibration method to fit a semi-empirical forward model for each PCD. We numerically optimized the optimal energy weights by minimizing the average relative Cramér-Rao lower bound (CRLB) due to the energy-weighted bin compression, for MD and VMI tasks over a range of material area density ρ A , m ${\rho }_{A,m}$ (0-40 g/cm2 water, 0-2.16 g/cm2 calcium). We used Monte Carlo simulation of a step wedge phantom and an anthropomorphic head phantom to evaluate the performance of this energy bin compression method in the projection domain and image domain, respectively. RESULTS: The results show that for 2 MD, the energy bin compression method can reduce PCCT data size by 75% and 60%, with an average variance penalty of less than 17% and 3% for silicon and CdTe detectors, respectively. For 3 MD tasks with a K-edge material (iodine), this method can reduce the data size by 62.5% and 40% with an average variance penalty of less than 12% and 13% for silicon and CdTe detectors, respectively. CONCLUSIONS: We proposed an energy bin compression method that is broadly applicable to different PCCT systems and object sizes, with high data compression ratio and little loss of spectral information.

Uncertainty propagation in absolute metabolite quantification for in vivo MRS of the human brain.

PURPOSE: Absolute spectral quantification is the standard method for deriving estimates of the concentration from metabolite signals measured using in vivo proton MRS (1 H-MRS). This method is often reported with minimum variance estimators, specifically the Cramér-Rao lower bound (CRLB) of the metabolite signal amplitude's scaling factor from linear combination modeling. This value serves as a proxy for SD and is commonly reported in MRS experiments. Characterizing the uncertainty of absolute quantification, however, depends on more than simply the CRLB. The uncertainties of metabolite-specific (T1m , T2m ), reference-specific (T1ref , T2ref ), and sequence-specific (TR , TE ) parameters are generally ignored, potentially leading to an overestimation of precision. In this study, the propagation of uncertainty is used to derive a comprehensive estimate of the overall precision of concentrations from an internal reference. METHODS: The propagated uncertainty is calculated using analytical derivations and Monte Carlo simulations and subsequently analyzed across a set of commonly measured metabolites and macromolecules. The effect of measurement error from experimentally obtained quantification parameters is estimated using published uncertainties and CRLBs from in vivo 1 H-MRS literature. RESULTS: The additive effect of propagated measurement uncertainty from applied quantification correction factors can result in up to a fourfold increase in the concentration estimate's coefficient of variation compared to the CRLB alone. A case study analysis reveals similar multifold increases across both metabolites and macromolecules. CONCLUSION: The precision of absolute metabolite concentrations derived from 1 H-MRS experiments is systematically overestimated if the uncertainties of commonly applied corrections are neglected as sources of error.

Nonlinear event-based state estimation using particle filter under packet loss.

In this research paper, we investigate the problem of remote state estimation for nonlinear discrete systems. Specifically, we focus on scenarios where event-triggered sensor schedules are utilized and where packet drops occur between the sensor and the estimator. In the sensor scheduler, the SOD mechanism is proposed to decrease the amount of data transmitted from the sensor to a remote estimator and the phenomena of packet drops modeled with random variables obeying the Bernoulli distribution. As a consequence of packet drops, the assumption of Gaussianity no longer holds at the estimator side. By fully considering the non-linearity and non-Gaussianity of the dynamic system, this paper develops an event-trigger particle filter algorithm to relieve the communication burden and achieve an appropriate estimation accuracy. First, we derive an explicit expression for the likelihood function when an event trigger occurs and the possible occurrence of packet dropout is taken into consideration. Then, using a special form of sequential Monte-Carlo algorithm, the posterior distribution is approximated and the corresponding minimum mean-squared error is derived. By contrasting the error covariance matrix with the posterior Cramér-Rao lower bound, the estimator's performance is assessed. An illustrative numerical example shows the effectiveness of the proposed design.

Fast and robust quantification of uncertainty in non-linear diffusion MRI models.

Diffusion MRI (dMRI) allows for non-invasive investigation of brain tissue microstructure. By fitting a model to the dMRI signal, various quantitative measures can be derived from the data, such as fractional anisotropy, neurite density and axonal radii maps. We investigate the Fisher Information Matrix (FIM) and uncertainty propagation as a generally applicable method for quantifying the parameter uncertainties in linear and non-linear diffusion MRI models. In direct comparison with Markov Chain Monte Carlo (MCMC) sampling, the FIM produces similar uncertainty estimates at much lower computational cost. Using acquired and simulated data, we then list several characteristics that influence the parameter variances, including data complexity and signal-to-noise ratio. For practical purposes we investigate a possible use of uncertainty estimates in decreasing intra-group variance in group statistics by uncertainty-weighted group estimates. This has potential use cases for detection and suppression of imaging artifacts.

An Improved Orthogonal Matching Pursuit Algorithm for CS-Based Channel Estimation.

Wireless broadband transmission channels usually have time-domain-sparse properties, and the reconstruction of these channels using a greedy search-based orthogonal matching pursuit (OMP) algorithm can effectively improve channel estimation performance while decreasing the length of the reference signal. In this research, the improved OMP and SOMP algorithms for compressed-sensing (CS)-based channel estimation are proposed for single-carrier frequency domain equalization (SC-FDE) systems, which, in comparison with conventional algorithms, calculate the path gain after obtaining the path delay and updating the observation matrices. The reliability of the communication system is further enhanced because the channel path gain is calculated using longer observation vectors, which lowers the Cramér-Rao lower bound (CRLB) and results in better channel estimation performance. The developed method can also be applied to time-domain-synchronous OFDM (TDS-OFDM) systems, and it is applicable to the improvement of other matching pursuit algorithms.

Fisher and Shannon Functionals for Hyperbolic Diffusion.

The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher's information, Shannon's entropy, and the Cramér-Rao inequality, all of which are associated with a positively normalized solution to the telegrapher's equation. In the framework of hyperbolic diffusion, the non-local Fisher's information with the x-parameter is related to the local Fisher's information with the t-parameter. A perturbation theory is presented to calculate Shannon's entropy of the telegrapher's equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times).

Cramér-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI.

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cramér-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. To this end, we introduce an approximate compressed CRB based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of both the CRB and signal losses during compression. Compared to the traditional SVD approach, the proposed method better preserves the CRB across all biophysical parameters with negligible cost to the preserved signal energy, leading to reduced bias and variance of the parameter estimates in simulation. In vivo, improved accuracy and precision are observed in two quantitative neuroimaging applications, permitting the use of smaller basis sizes in subspace reconstruction and offering significant computational savings.