Statistical Parameter Estimation Research Articles

Quantum Onsager relations

Abstract Using quantum information geometry, I derive quantum generalizations of the Onsager rate equations, which model the dynamics of an open system near a steady state. The generalized equations hold for a flexible definition of the forces as well as a large class of statistical divergence measures and quantum-Fisher-information metrics beyond the conventional definition of entropy production. I also derive quantum Onsager-Casimir relations for the transport tensors by proposing a general concept of time reversal and detailed balance for open quantum systems. The results establish a remarkable connection between statistical mechanics and parameter estimation theory.

Detection of Alcoholic EEG signal using LASSO regression with metaheuristics algorithms based LSTM and enhanced artificial neural network classification algorithms

The world has a higher count of death rates as a result of Alcohol consumption. Identification is possible because Alcoholic EEG waves have a certain behavior that is totally different compared to the non-alcoholic individual. The available approaches take longer to provide the feedback because they analyze the data manually. For this reason, in the present paper we propose a novel approach applied to detect alcoholic EEG signals automatically by using deep learning methods. Our strategy has advantages as far as fast detection is concerned; hence people can help immediately when there is a need. The potential for a significant decrease in deaths from alcohol poisoning and improvement to public health is presented by this advancement. In order to create clusters and classify the alcoholic EEG signals, this research uses a cascaded process. To begin with, an initial clustering and feature extraction is done by LASSO regression. After that, a variety of meta-heuristics algorithms like Particle Swarm Optimization (PSO), Binary Coding Harmony Search (BCHS) as well as Binary Dragonfly Algorithm (BDA) are employed for feature minimization. When this method is used, normal and alcoholic EEG signals may be differentiated using non-linear features. PSO, BCHS, and BDA features allow for estimation of statistical parameters through t-test, Friedman statistic test, Mann-Whitney U test, and Z-Score with corresponding p-values for alcoholic EEG signals. Lastly, classification is done by the use of support vector machines (SVM) (including linear, polynomial, and Gaussian kernels), random forests, artificial neural networks (ANN), enhanced artificial neural networks (EANN), and LSTM models. Results showed that LASSO regression with BDA-based EANN proposed classifier have a classification accuracy of 99.59%, indicating that our method is highly accurate at classifying alcoholic EEG signals.

Physics-Based Continuum Modeling for an Aqueous Rechargeable Zn/MnO2 Battery

While Lithium-ion batteries dominate high-energy-density applications, their reliance on scarce and expensive materials poses a challenge for large-scale renewable energy storage. Aqueous Zinc/Manganese Oxide (Zn/MnO2) batteries, utilizing abundant and cost-effective materials, emerge as a viable alternative. However, the lack of understanding of their fundamental reaction mechanisms hampers their optimization and commercialization. In this study, we present a physics-based model to aid in elucidating the reaction mechanisms governing Zn/MnO2 batteries. When coupled with statistical parameter estimation, the model accurately replicates the discharge behavior across various C-rates and offers predictive insights into the underlying phenomena. Our findings inform the design of future targeted experiments and lay the groundwork for in-depth mechanistic studies. Moreover, the model serves as a tool for in-silico optimization, accelerating the path to commercial viability.

Estimation methods based on ranked set sampling for the power logarithmic distribution

The sample strategy employed in statistical parameter estimation issues has a major impact on the accuracy of the parameter estimates. Ranked set sampling (RSS) is a highly helpful technique for gathering data when it is difficult or impossible to quantify the units in a population. A bounded power logarithmic distribution (PLD) has been proposed recently, and it may be used to describe many real-world bounded data sets. In the current work, the three parameters of the PLD are estimated using the RSS technique. A number of conventional estimators using maximum likelihood, minimum spacing absolute log-distance, minimum spacing square distance, Anderson-Darling, minimum spacing absolute distance, maximum product of spacings, least squares, Cramer-von-Mises, minimum spacing square log distance, and minimum spacing Linex distance are investigated. The different estimates via RSS are compared with their simple random sampling (SRS) counterparts. We found that the maximum product spacing estimate appears to be the best option based on our simulation results for the SRS and RSS data sets. Estimates generated from SRS data sets are less efficient than those derived from RSS data sets. The usefulness of the RSS estimators is also investigated by means of a real data example.

Fisher information contained in incomplete observations

The accuracy of statistical estimates of unknown distribution parameters depends not only on the bulk of sampling data but also on the method of data acquisition. The information content of experimental data is one of the basic requirements. Problems of mathematical statistics, in particular parametric estimation based on censored observations, have specific features. Typical representatives of models of incomplete observations on a straight line are models of random censoring, competing risks of (single, multiple) random censoring. The purpose of this study is to show that censoring does not always lead to loss of (Fisher) information. It is shown that if censoring is informative, i.e., the distribution of censoring random variables depends on the same parameter, it is possible to specify a model where information can be preserved due to censoring. On the contrary, if the censoring is not informative, then the loss of information is inevitable. The Cramer – Rao efficiency was taken as a criterion for the quality of the assessment, whereas the Fisher information was taken as the criterion for information about the unknown parameter.

SSN2: The next generation of spatial stream network modeling in R.

The SSN2 R package provides tools for spatial statistical modeling, parameter estimation, and prediction on stream (river) networks. SSN2 is the successor to the SSN R package (Ver Hoef, Peterson, Clifford, & Shah, 2014), which was archived alongside broader changes in the R-spatial ecosystem (Nowosad, 2023) that included 1) the retirement of rgdal (Bivand, Keitt, & Rowlingson, 2021), rgeos (Bivand & Rundel, 2020), and maptools (Bivand & Lewin-Koh, 2021) and 2) the lack of active development of sp (Bivand, Pebesma, & Gómez-Rubio, 2013). SSN2 maintains compatibility with the input data file structures used by the SSN R package but leverages modern R-spatial tools like sf (Pebesma, 2018). SSN2 also provides many useful features that were not available in the SSN R package, including new modeling and helper functions, enhanced fitting algorithms, and simplified syntax consistent with other R generic functions.

Dynamic off-resonance correction improves functional image analysis in fMRI of awake behaving non-human primates.

Use of functional MRI in awake non-human primate (NHPs) has recently increased. Scanning animals while awake makes data collection possible in the absence of anesthetic modulation and with an extended range of possible experimental designs. Robust awake NHP imaging however is challenging due to the strong artifacts caused by time-varying off-resonance changes introduced by the animal's body motion. In this study, we sought to thoroughly investigate the effect of a newly proposed dynamic off-resonance correction method on brain activation estimates using extended awake NHP data. We correct for dynamic B0 changes in reconstruction of highly accelerated simultaneous multi-slice EPI acquisitions by estimating and correcting for dynamic field perturbations. Functional MRI data were collected in four male rhesus monkeys performing a decision-making task in the scanner, and analyses of improvements in sensitivity and reliability were performed compared to conventional image reconstruction. Applying the correction resulted in reduced bias and improved temporal stability in the reconstructed time-series data. We found increased sensitivity to functional activation at the individual and group levels, as well as improved reliability of statistical parameter estimates. Our results show significant improvements in image fidelity using our proposed correction strategy, as well as greatly enhanced and more reliable activation estimates in GLM analyses.

On the impact of spatial covariance matrix ordering on tile low‐rank estimation of Matérn parameters

AbstractSpatial statistical modeling involves processing an symmetric positive definite covariance matrix, where denotes the number of locations. However, when is large, processing this covariance matrix using traditional methods becomes prohibitive. Thus, coupling parallel processing with approximation can be an elegant solution by relying on parallel solvers that deal with the matrix as a set of small tiles instead of the full structure. The approximation can also be performed at the tile level for better compression and faster execution. The tile low‐rank (TLR) approximation has recently been used to compress the covariance matrix, which mainly relies on ordering the matrix elements, which can impact the compression quality and the efficiency of the underlying solvers. This work investigates the accuracy and performance of location‐based ordering algorithms. We highlight the pros and cons of each ordering algorithm and give practitioners hints on carefully choosing the ordering algorithm for TLR approximation. We assess the quality of the compression and the accuracy of the statistical parameter estimates of the Matérn covariance function using TLR approximation under various ordering algorithms and settings of correlations through simulations on irregular grids. Our conclusions are supported by an application to daily soil moisture data in the Mississippi Basin area.

Sobolev Calibration of Imperfect Computer Models

Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer models, Sobolev calibration, which can rule out calibration parameters that generate overfitting calibrated functions. We prove that the Sobolev calibration enjoys desired theoretical properties including fast convergence rate, asymptotic normality and semiparametric efficiency. We also demonstrate an interesting property that the Sobolev calibration can bridge the gap between two influential methods: L 2 calibration and Kennedy and O’Hagan’s calibration. In addition to exploring the deterministic physical experiments, we theoretically justify that our method can transfer to the case when the physical process is indeed a Gaussian process, which follows the original idea of Kennedy and O’Hagan’s. Numerical simulations as well as a real-world example illustrate the competitive performance of the proposed method.

Multiple Imputation When Variables Exceed Observations: An Overview of Challenges and Solutions

Missing data are a prevalent problem in psychological research that can reduce statistical power and bias parameter estimates. These problems can be mostly resolved with multiple imputation, a modern missing data treatment that is increasingly used. Imputation, however, requires the number of variables to be smaller than the number of observations (i.e., non-missing values), and this number is often exceeded due to, e.g., large assessments, high missing data rates, the inclusion of variables predictive of missing values, and the inclusion of non-linear transformations. Even when the ratio of variables to observations meets the minimum requirement, convergence failure can occur in large, complex models. Specialized techniques have been developed to overcome the challenges related to having too many variables in an imputation model, but they are still relatively unknown by researchers in psychology. Accordingly, this paper presents an overview of four imputation techniques that can be used to reduce the number of predictors in an imputation model: item aggregation with scales and parcels, passive imputation, principal component analysis (PcAux) and two-fold fully conditional specification. The purpose, advantages, limitations, and applications of each method are discussed, along with recommendations and illustrative examples, with the aims of (1) understanding different imputation methods and (2) identifying methods that could be useful for one’s imputation problem.

Genetic and phenotypic analysis of reproductive traits in the Murciano-Granadina does: Predictive ability of the statistical models and estimation of genetic parameters

In the present study, data collected between 2016 and 2022 from a private dairy farm of the Murciano-Granadina goat breed, in Ghale-Ganj city, located in the southern area of Kerman province, Iran was used for model comparison and estimation of genetic parameters for reproductive performance. Studied reproductive traits included litter size at birth per doe kidding (LSB), litter size at weaning per doe kidding (LSW), total litter weight at birth per doe kidding (TLWB), and total litter weight at weaning per doe kidding (TLWW). Four univariate animal models comprising various combinations of direct additive genetic, animal permanent environmental, and service sires effects were fitted for each trait. The predictive ability of models was evaluated by applying the predictive ability measure including the mean square of error (MSE) and the Pearson's correlation coefficient between observed and predicted values (r(y,y ̂)) through a two-fold cross-validation study. For LSW, TLWB, and TLWW, the model with direct additive genetic, animal permanent environmental, and service sires effects had the lowest MSE and the highest values for r(y,y ̂) than other models. For LSB, the model included direct additive genetic and animal permanent environmental was identified as the best model among the tested models. The posterior means for heritability estimates of the studied traits were low values of 0.02 ± 0.01, 0.07 ± 0.01, 0.02 ± 0.01, and 0.03 ± 0.01 for LSB, LSW, TLWB, and TLWW, respectively. The posterior means for repeatability estimates were 0.04 ± 0.01, 0.08 ± 0.02, 0.03 ± 0.01, and 0.04 ± 0.01 for LSB, LSW, TLWB, and TLWW, respectively. The posterior means for the ratio of service sires variance to phenotypic variance (S2) for LSW, TLWB, and TLWW were 0.09 ± 0.02, 0.02 ± 0.01, and 0.02 ± 0.01, respectively. Genetic correlation estimates were high in magnitude and ranged from 0.69 ± 0.09 (LSB-TLWW) to 0.97 ± 0.02 (LSB-LSW). Phenotypic correlations were low to medium estimates and ranged from 0.17 ± 0.01 (TLWB-TLWW) to 0.55 ± 0.02 (LSB-LSW). Because of low heritability estimates for the studied reproductive traits in the Murciano-Granadina goat breed genetic progress resulting from direct genetic selection for these traits is likely to be slow and improvement in environmental conditions is of great importance for improving the reproductive performance. No genetic and phenotypic antagonism were found among the studied traits. Therefore, it should be possible to simultaneously improve these traits.

Coupled hydrogeophysical inversion of an artificial infiltration experiment monitored with ground-penetrating radar: synthetic demonstration

Abstract. In this study, we investigate the use of ground-penetrating radar (GPR) time-lapse monitoring of artificial soil infiltration experiments. The aim is to evaluate this protocol in the context of estimating the hydrodynamic unsaturated soil parameter values and their associated uncertainties. The originality of this work is to suggest a statistical parameter estimation approach using Markov chain Monte Carlo (MCMC) methods to have direct estimates of the parameter uncertainties. Using the GPR time data from the moving wetting front only does not provide reliable results. Thus, we propose to use additional information from other types of reflectors to optimize the quality of the parameter estimation. Water movement and electromagnetic wave propagation in the unsaturated zone are modeled using a one-dimensional hydrogeophysical model. The GPR travel time data are analyzed for different reflectors: a moving reflector (the infiltration wetting front) and three fixed reflectors located at different depths in the soil. Global sensitivity analysis (GSA) is employed to assess the influence of the saturated hydraulic conductivity Ks, the saturated and residual water contents θs and θr, and the Mualem–van Genuchten shape parameters α and n of the soil on the GPR travel time data of the reflectors. Statistical calibration of the soil parameters is then performed using the MCMC method. The impact of the type of reflector (moving or fixed) is then evaluated by analyzing the calibrated model parameters and their confidence intervals for different scenarios. GSA results show that the sensitivities of the GPR data to the hydrodynamic soil parameters are different between moving and fixed reflectors, whereas fixed reflectors at various depths have similar sensitivities. Ks has a similar and strong influence on the data of both types of reflectors. Concerning the other parameters, for the wetting front, only θs and α have an influence, and only at long time steps since the total variance is zero at the very beginning of the experiment. On the other hand, for the fixed reflectors, the total variance is not zero at the very start and the parameters θs, θr, α and n can have an influence from the very beginning of the infiltration. Results of parameter estimation show that the use of calibration data from the moving or fixed reflectors alone does not enable a good identification of all soil parameters. With the moving reflector, the error between the estimated mean value and the exact target value for θr and α is 9 % and 45 %, respectively, and less than 3 % for the other parameters. The best reduction of the size of the parameter distribution is obtained for n, with a posterior distribution 9 times smaller than the prior one. For the others, this reduction ratio varies between 1 and 5. For the fixed reflectors, the estimated mean values are far from the target values for α, θr and n, representing for a reflector located at 120 cm 15 %, 27 %, and 121 %, respectively. On the other hand, when both data are combined, all soil parameters can be well estimated with narrow confidence intervals. For instance, when using both data from the moving wetting front and a fixed reflector located at 120 cm for calibration, the estimated mean values of the errors of all parameters are less than 5 %. Moreover, all parameter distributions are well reduced, with a maximum reduction for Ks, leading to a posterior distribution being 46 times smaller than the prior one, and the worst but still satisfactory being for θr for which the posterior distribution is 8 times smaller than the prior one. The methodology was applied to fine, medium, and coarse sands with very good results, particularly for the finest soil. The thickness of the unsaturated zone was also tested (0.5, 1, and 2 m) and a better estimation of the hydrodynamic parameters is obtained when the water table is deeper. In addition, the height of water applied in the infiltrometry test influences the speed of the test without affecting the performance of the proposed method.

New Generalized Nadarajah Haghighi Distribution: Characterization and Applications

A new Generalized Nadarajah Haghighi (NGNH) distribution following the Exponential T-X (ETX) family was studied. Structural statistical properties and parameter estimation discussed. Simulation study was executed with impressive results. The applicability and usefulness of NGNH was demonstrated using lifetime data sets. The NGNH distribution was compared with other competing distributions.

Classical Fisher information for differentiable dynamical systems.

Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a form of uncertainty. Infinitesimal perturbations to the initial conditions can grow exponentially in time, a signature of deterministic chaos. As a measure of this uncertainty, we introduce another classical information, specifically for the deterministic dynamics of isolated, closed, or open classical systems not subject to noise. This classical measure of information is defined with Lyapunov vectors in tangent space, making it less akin to the classical Fisher information and more akin to the quantum Fisher information defined with wavevectors in Hilbert space. Our analysis of the local state space structure and linear stability leads to upper and lower bounds on this information, giving it an interpretation as the net stretching action of the flow. Numerical calculations of this information for illustrative mechanical examples show that it depends directly on the phase space curvature and speed of the flow.

Effect of Product Pricing on Equity Return of Manufacturing Firms Listed at Nairobi Securities Exchange in Kenya

Purpose of Study: The study aimed to assess how product pricing affects the equity return of manufacturing firms listed at the Nairobi Securities Exchange in Kenya.
 Research Design: The study employed both longitudinal and cross-sectional research designs.
 Place and Study Duration: the study covered manufacturing firms listed at Nairobi Securities Exchange in Kenya. Data was collected from the year 2008 to the year 2021.
 Research Methodology: The study's target population included 7 listed manufacturing companies in the Nairobi securities exchange. The current study relied on secondary data sources for the period between the year 2008 and year 2021 that was gathered from the Nairobi Securities Exchange, the capital market authority library and the annual reports of individual companies that were obtained from their websites. Descriptive and inferential measurements were used to evaluate the secondary data. Descriptive statistics comprised the mean and the standard deviation. Inferential statistics on the other hand comprised panel regression and Pearson's product-moment correlation analysis. Analysis was conducted using Stata 14 software to produce tables, graphs, charts, diagrams and statistical parameter estimates.
 Results: The findings showed that product pricing has a positive influence on the equity returns of listed manufacturing firms in the Nairobi Securities Exchange. Also, the influence was found to be significant. This meant that product pricing had a positive significant influence on the equity returns of listed manufacturing firms in the Nairobi Securities Exchange. The study, therefore, rejected the null hypothesis and concluded that product pricing has a positive significant influence on equity returns of listed manufacturing firms in the Nairobi Securities Exchange.
 Conclusions: According to the study's findings, product price has a favourable impact on the equity returns of manufacturing companies listed on the Nairobi Securities Exchange. The impact was also shown to be substantial. This indicated that product pricing had an important beneficial impact on the equity returns of manufacturing companies listed on the Nairobi Securities Exchange.

Impact of parameters the design of diesel engines on technical indicators work of their operation

The article analyzes the impact of the design execution of engines on their technical and economic performance work. The information characteristic of 15 tractor diesels of all power levels is considered. Statistical estimates of parameters are obtained and correlation relationship between them is established. Patterns of changes in the studied factors were revealed, which make it possible to determine the main directions of engines improvement. Keywords diesel engines, parameters of construct, technical indicators, range of change, correlation, regularities

Influence of microphone tilt angle on instability identification in micromilling of thin-walled Ti6Al4V

High speed micromilling is the most preferred manufacturing process to fabricate complex 3D featured thin-walled structures like stents, turbine blades, micro-fins, cabin parts etc., that are extensively used in bio-medical, energy, automobile and aerospace sectors. Fabricating thin-walled structures with high dimensional and geometrical accuracy requires chatter free machining parameters. Different sensors like accelerometer, current sensors, laser based sensors, vibration pick-ups etc. are available for capturing the vibration while machining thin-walled structures. Each sensor has its own advantages and disadvantages, like laser based sensors adds noise to response as chips fly past in the laser path and accelerometer captures deflection of both micro-cutting tool and thin-walled workpiece. Hence, In-process chatter identification is a challenging task in thin-wall micromilling. Also, the Filtering of signals to remove the noise from signals captured via contact type and laser based sensors results in loss of low-amplitude chatter data in high-speed micromilling. Consequently, there is a need of sensor, which functions similar to contact type with less or no loss in low-amplitude chatter data. The proposed work compares vibration signal captured using accelerometer and microphone at different tilt angles for radial milling of thin-walled Ti6Al4V at different radial immersion to analyse the effect of tilt-angle on chatter identification. The recorded signals from both accelerometer and microphone are analysed in time domain by estimation and comparison of statistical parameters, in frequency domain by analysing the distributed frequency and in time–frequency domain by analysing the energy of the signals. Complete characterization of the signals in time, frequency and time–frequency domain/methods indicated that microphone at 60° tilt angle can be used as an alternative sensor for chatter onset identification without loss in chatter data irrespective of cutting condition. Machined surface analysis of thin-walled structures complements the microphone as an effective chatter identification sensor.

Relationship between residential house damage and flood characteristics: A case study in the Teesta River Basin, Bangladesh

The flood damage function model is indispensable for flood damage assessment as it can provide useful information for establishing flood protection strategies. For the assessment of residential house damage in different areas, flood damage function models have been traditionally proposed considering only the depth–damage curve. However, flood duration and flood may also have an influence on flood damage. Conventionally, the damage rate was estimated based on information about monetary losses collected from local people or insurance payout databases. This research proposes a new methodology to establish a flood damage function model that considers flood depth, flood duration, and flood velocity. Field surveys were conducted in the Teesta River Basin of rural Bangladesh. For each house, a questionnaire survey was conducted to identify the flood information (flood depth, flood duration, and the qualitative representation of flood velocity), household structure information (area, plinth height, and ceiling height), structural damage mechanism, and the required amount of material and labor to repair the damage after each flood event. Finally, a flood damage function model including the impacts of house types and different flood parameters was established through multiple regression analysis. The consistency of the model was verified through the estimation of different statistical parameters. It can serve as a flood loss estimation model as it correlates flooding with various parameters, such as building materials and their damage mechanism.

Hubble constant by natural selection: Evolution chips in the Hubble tension

The Approximate Bayesian Computation (ABC) algorithm considers natural selection in biology as a guiding principle for statistical model selection and parameter estimation. We take this ABC approach to cosmology and use it to infer which ΛCDM model anchored on a choice of a Hubble constant prior would be preferred by the data. We find in all of our runs that the Planck Hubble constant (H0=67.4±0.5 km s−1Mpc−1) always emerges naturally selected by the ABC over the SH0ES estimate (H0=73.30±1.04 km s−1Mpc−1). The result holds regardless of how we mix our data sets, including supernovae, cosmic chronometers, baryon acoustic oscillations, and growth data. Compared with the traditional MCMC, we find that the ABC always results with narrower cosmological constraints, but remain consistent inside the corresponding MCMC posteriors.

Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems.

We investigate various estimators based on extreme value theory (EVT) for determining the local fractal dimension of chaotic dynamical systems. In the limit of an infinitely long time series of an ergodic system, the average of the local fractal dimension is the system's global attractor dimension. The latter is an important quantity that relates to the number of effective degrees of freedom of the underlying dynamical system, and its estimation has been a central topic in the dynamical systems literature since the 1980s. In this work, we propose a framework that combines phase space recurrence analysis with EVT to estimate the local fractal dimension around a particular state of interest. While the EVT framework allows for the analysis of high-dimensional complex systems, such as the Earth's climate, its effectiveness depends on robust statistical parameter estimation for the assumed extreme value distribution. In this study, we conduct a critical review of several EVT-based local fractal dimension estimators, analyzing and comparing their performance across a range of systems. Our results offer valuable insights for researchers employing the EVT-based estimates of the local fractal dimension, aiding in the selection of an appropriate estimator for their specific applications.