True Parameter Values Research Articles

The Correlation between Rotational Gravity and Magnetic Field of Celestial Body

The magnetic field of the earth plays an important role in the ecosystem, and the magnetic field of celestial bodies is also important in the formation of cosmic large-scale structures, but the origin and evolution of the celestial magnetic field is still an unresolved mystery. Many hypotheses to explain the origin have been proposed, but there are some insurmountable difficulties for each one. At present, the theory widely accepted in scientific society is the dynamo model, it says that, the movement of magnetofluid inside celestial bodies, which can overcome the Ohmic dissipative effect and generate persistent weak electric current and macroscopic magnetic field. However, this model needs an initial seed magnetic field, and the true values of many physical parameters inside the celestial body are difficult to obtain, and there is no stable solution to the large range of fluid motion. These are all difficulties for the dynamo model. Furthermore, it is difficult for the dynamo to explain the correlation between the dipole magnetic field and angular momentum of a celestial body. In this paper, by calculating the interaction between spin of particles and gravity of celestial body according to Clifford algebra, we find that a rotational celestial body provides a field Ωα for spins, which is similar to the magnetic field of a dipole, and the spins of charged particles within the celestial body are arranged along the flux line of Ωα, then a macroscopic magnetic field is induced. The calculation shows that the strength of Ωα is proportional to the angular momentum of the celestial body, which explains the correlation between the magnetic intensity and angular momentum. The results of this paper suggest that further study of the effects of internal variables such as density, velocity, pressure and temperature of a celestial body on Ωα may provide some new insights into the origin and evolution of celestial magnetic field.

Uncertainty Quantification of Regional Cardiac Tissue Properties in Arrhythmogenic Cardiomyopathy Using Adaptive Multiple Importance Sampling.

Introduction: Computational models of the cardiovascular system are widely used to simulate cardiac (dys)function. Personalization of such models for patient-specific simulation of cardiac function remains challenging. Measurement uncertainty affects accuracy of parameter estimations. In this study, we present a methodology for patient-specific estimation and uncertainty quantification of parameters in the closed-loop CircAdapt model of the human heart and circulation using echocardiographic deformation imaging. Based on patient-specific estimated parameters we aim to reveal the mechanical substrate underlying deformation abnormalities in patients with arrhythmogenic cardiomyopathy (AC).Methods: We used adaptive multiple importance sampling to estimate the posterior distribution of regional myocardial tissue properties. This methodology is implemented in the CircAdapt cardiovascular modeling platform and applied to estimate active and passive tissue properties underlying regional deformation patterns, left ventricular volumes, and right ventricular diameter. First, we tested the accuracy of this method and its inter- and intraobserver variability using nine datasets obtained in AC patients. Second, we tested the trueness of the estimation using nine in silico generated virtual patient datasets representative for various stages of AC. Finally, we applied this method to two longitudinal series of echocardiograms of two pathogenic mutation carriers without established myocardial disease at baseline.Results: Tissue characteristics of virtual patients were accurately estimated with a highest density interval containing the true parameter value of 9% (95% CI [0–79]). Variances of estimated posterior distributions in patient data and virtual data were comparable, supporting the reliability of the patient estimations. Estimations were highly reproducible with an overlap in posterior distributions of 89.9% (95% CI [60.1–95.9]). Clinically measured deformation, ejection fraction, and end-diastolic volume were accurately simulated. In presence of worsening of deformation over time, estimated tissue properties also revealed functional deterioration.Conclusion: This method facilitates patient-specific simulation-based estimation of regional ventricular tissue properties from non-invasive imaging data, taking into account both measurement and model uncertainties. Two proof-of-principle case studies suggested that this cardiac digital twin technology enables quantitative monitoring of AC disease progression in early stages of disease.

Joint analysis of preferences and drop out data in discrete choice experiments

Choice data appear together with drop out data indicating if respondents completed the exercise. In case of non-completion, the choice sequences end at the tasks where the respondents exited the study. In the analysis of choice data, the focus is always on choices made while the drop out behavior is completely ignored. However, the choice making and the drop out process could be latently related. For instance, respondents who are more likely to drop out of the exercise could give less consistent choices throughout or just before they exit. In such cases, ignoring the drop out dimension could lead to biased or inefficient results. In this paper, we use shared random effects and covariate effects to model the association between a scaled multinomial logit model for the choices and two different models for the drop out component. Through simulations, we show that a joint model provides less biased and more precise estimates and its 95% credible intervals have better coverage for true parameter values.

Hydraulic Model Calibration Using CryoSat‐2 Observations in the Zambezi Catchment

AbstractGeodetic altimeters provide unique observations of the river surface longitudinal profile due to their long repeat periods and densely spaced ground tracks. This information is valuable for calibrating hydraulic model parameters, and thus, for producing reliable simulations of water level for flood forecasting and river management, particularly in poorly instrumented catchments. In this study, we present an efficient calibration approach for hydraulic models based on a steady‐state hydraulic solver and CryoSat‐2 observations. In order to ensure that only coherent forcing/observation pairs are considered in the calibration, we first propose an outlier filtering approach for CryoSat‐2 observations in data‐scarce regions using a simulated runoff produced by a hydrologic model. In the hydraulic calibration, a steady‐state solver computes the water surface elevation (WSE) profile along the river for selected discharges corresponding to the days of CryoSat‐2 overpass. In synthetic calibration experiments, the global search algorithm generally recovers the true parameter values in portions of the river where observations are available, illustrating the benefit of dense spatial sampling from geodetic altimetry. The most sensitive parameters are the bed elevations. In calibration experiments with real CryoSat‐2 data, validation performance against both Sentinel‐3 WSE and in situ records is similar to previous studies, with Root Mean Square Deviation ranging from 0.43 to 1.14 m against Sentinel‐3 and from 0.60 to 0.73 against in situ WSE observations. Performance remains similar when transferring parameters to a one‐dimensional hydrodynamic model. Because the approach is computationally efficient, model parameters can be inverted at high spatial resolution to fully exploit the information contained in geodetic CryoSat‐2 altimetry.

Bayesian inference of root architectural model parameters from synthetic field data

Background and aimsCharacterizing root system architectures of field-grown crops is challenging as root systems are hidden in the soil. We investigate the possibility of estimating root architecture model parameters from soil core data in a Bayesian framework.MethodsIn a synthetic experiment, we simulated wheat root systems in a virtual field plot with the stochastic CRootBox model. We virtually sampled soil cores from this plot to create synthetic measurement data. We used the Markov chain Monte Carlo (MCMC) DREAM(ZS) sampler to estimate the most sensitive root system architecture parameters. To deal with the CRootBox model stochasticity and limited computational resources, we essentially added a stochastic component to the likelihood function, thereby turning the MCMC sampling into a form of approximate Bayesian computation (ABC).ResultsA few zero-order root parameters: maximum length, elongation rate, insertion angles, and numbers of zero-order roots, with narrow posterior distributions centered around true parameter values were identifiable from soil core data. Yet other zero-order and higher-order root parameters were not identifiable showing a sizeable posterior uncertainty.ConclusionsBayesian inference of root architecture parameters from root density profiles is an effective method to extract information about sensitive parameters hidden in these profiles. Equally important, this method also identifies which information about root architecture is lost when root architecture is aggregated in root density profiles.

Bias and consistency in three-way gravity models

We study the incidental parameter problem for the “three-way” Poisson Pseudo-Maximum Likelihood (“PPML”) estimator recently recommended for identifying the effects of trade policies and in other panel data gravity settings. Despite the number and variety of fixed effects involved, we confirm PPML is consistent for fixed T and we show it is in fact the only estimator among a wide range of PML gravity estimators that is generally consistent in this context when T is fixed. At the same time, asymptotic confidence intervals in fixed-T panels are not correctly centered at the true parameter values, and cluster-robust variance estimates used to construct standard errors are generally biased as well. We characterize each of these biases analytically and show both numerically and empirically that they are salient even for real-data settings with a large number of countries. We also offer practical remedies that can be used to obtain more reliable inferences of the effects of trade policies and other time-varying gravity variables, which we make available via an accompanying Stata package called ppml_fe_bias.

Solution of SIR Infection Equation Using Data Assimilation

The new coronavirus infection (COVID-19) is rampant. The most troublesome part of this infection is the time between infection and onset and the infectiveness for several days even in the not-onset state. Therefore, a considerable number of infected persons with infectivity are left unchecked. Therefore, even if the infection status is simulated by the SIR equation or the like, the true values of the infection parameters and the true number of infected persons cannot be grasped. However, it is possible to observe the infection status, and the daily number of infected people and the cumulative number of infected people are announced. These numbers are not true values, but they reflect true values. It is impossible to grasp the true value only by the SIR equation, but it will be possible to estimate the true value by combining it with the observation equation. In short, the data assimilation framework is considered to be effective. We report this effectiveness because we were able to confirm this effectiveness from the numerical results.

Potential for New Constraints on Tropical Cyclone Surface-Exchange Coefficients through Simultaneous Ensemble-Based State and Parameter Estimation

AbstractThe tropical cyclone (TC) surface-exchange coefficients of enthalpy (Ck) and momentum (Cd) at high wind speeds have been notoriously challenging to estimate. This difficulty arises from many factors, including the difficulties in collecting observations within the turbulent TC boundary layer, and the complex coupled physical interactions between the TC boundary layer and ocean surface, which are challenging to accurately model. Motivated by recent studies highlighting the limited practical predictability of TC intensity as a result of uncertainty in the physical representation of the air–sea fluxes of momentum and enthalpy at high wind speeds, we investigate the potential to estimate the surface enthalpy and momentum exchange coefficients through ensemble data assimilation. Significant ensemble correlations between tangential wind, radial wind, and simulated infrared brightness temperatures with parameters controlling the enthalpy and momentum exchange coefficients suggest potential to use all-sky satellite and/or airborne radial velocity observations to estimate these unknown parameters. Using a series of observing system simulation experiments (OSSEs), simulated infrared brightness temperature observations, and a known truth, we demonstrate some potential for simultaneous state and parameter estimation with an ensemble-based data assimilation system to converge toward the correct known parameter values. In all OSSEs with either one or multiple unknown parameters, the initial parameter errors are reduced through simultaneous model state and parameter estimation. However, challenges still exist in converging to the precise true parameter values, as state errors during rapid intensification can project onto the parameter estimates.

Bayesian Inference on Regression Model with an Unknown Change Point

In this work, we describe a Bayesian procedure for detection of change-point when we have an unknown change point in regression model. Bayesian approach with posterior inference for change points was provided to know the particular change point that is optimal while Gibbs sampler was used to estimate the parameters of the change point model. The simulation experiments show that all the posterior means are quite close to their true parameter values. The performance of this method is recommended for multiple change points.

Effects of Outliers on the Maximum Correntropy Estimation: A Robustness Analysis

Recently, maximum correntropy criterion (MCC) has been widely and successfully used in robust signal processing and machine learning, in which the correntropy is maximized instead of minimizing the popular mean square error (MSE) to improve the robustness with respect to outliers or impulsive noises. A lot of efforts have been devoted to derive different adaptive algorithms under MCC, but to date, little insight has been gained as to how the MCC solution will be influenced by outliers. In this paper, we investigate this problem and our focus is mainly on the parameter estimation of a simple linear errors-in-variables (EIVs) model with scalar variables. Under some conditions, we derive an upper bound on the absolute value of the estimation error and show that the MCC solution can get very close to the true value of the unknown parameter even with arbitrarily large outliers in both the input and output variables. Illustrative examples are provided to verify and clarify the theory.

Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution

Fusion learning refers to synthesizing inferences from multiple sources or studies to make a more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on parametric model assumptions, such as normality, which often do not hold in practice. We propose a general nonparametric fusion learning framework for synthesizing inferences for multiparameters from different studies. The main tool underlying the proposed framework is the new notion of depth confidence distribution (depth-CD), which is developed by combining data depth and confidence distribution. Broadly speaking, a depth-CD is a data-driven nonparametric summary distribution of the available inferential information for a target parameter. We show that a depth-CD is a powerful inferential tool and, moreover, is an omnibus form of confidence regions, whose contours of level sets shrink toward the true parameter value. The proposed fusion learning approach combines depth-CDs from the individual studies, with each depth-CD constructed by nonparametric bootstrap and data depth. The approach is shown to be efficient, general and robust. Specifically, it achieves high-order accuracy and Bahadur efficiency under suitably chosen combining elements. It allows the model or inference structure to be different among individual studies. And, it readily adapts to heterogeneous studies with a broad range of complex and irregular settings. This last property enables the approach to use indirect evidence from incomplete studies to gain efficiency for the overall inference. We develop the theoretical support for the proposed approach, and we also illustrate the approach in making combined inference for the common mean vector and correlation coefficient from several studies. The numerical results from simulated studies show the approach to be less biased and more efficient than the traditional approaches in nonnormal settings. The advantages of the approach are also demonstrated in a Federal Aviation Administration study of aircraft landing performance. Supplementary materials for this article are available online.

Biases in Orbital Fitting of Directly Imaged Exoplanets with Small Orbital Coverage

Abstract The eccentricity of a planet’s orbit and the inclination of its orbital plane encode important information about its formation and history. However, exoplanets detected via direct imaging are often only observed over a very small fraction of their period, making it challenging to perform reliable physical inferences given wide, unconstrained posteriors. The aim of this project is to investigate biases (deviation of the median and mode of the posterior from the true values of orbital parameters, and the width and coverage of their credible intervals) in the estimation of orbital parameters of directly imaged exoplanets, particularly their eccentricities, and to define general guidelines to perform better estimations of uncertainty. For this, we constructed various orbits and generated mock data for each spanning ∼0.5% of the orbital period. We used the Orbits For The Impatient algorithm to compute orbit posteriors and compared those to the true values of the orbital parameters. We found that the inclination of the orbital plane is the parameter that most affects our estimations of eccentricity, with orbits that appear near edge on producing eccentricity distributions skewed away from the true values and often bimodal. We also identified a degeneracy between eccentricity and inclination that makes it difficult to distinguish posteriors of face-on, eccentric orbits and edge-on, circular orbits. For the exoplanet-imaging community, we propose practical recommendations, guidelines, and warnings relevant to orbit fitting.

Bayes Estimators of Exponentiated Inverse Rayleigh Distribution using Lindleys Approximation

In this paper, Bayes estimators of the unknown shape and scale parameters of the Exponentiated Inverse Rayleigh Distribution (EIRD) have been derived using both the frequentist and bayesian methods. The Bayes theorem was adopted to obtain the posterior distribution of the shape and scale parameters of an Exponentiated Inverse Rayleigh Distribution (EIRD) using both conjugate and non-conjugate prior distribution under different loss functions (such as Entropy Loss Function, Linex Loss Function and Scale Invariant Squared Error Loss Function). The posterior distribution derived for both shape and scale parameters are intractable and a Lindley approximation was adopted to obtain the parameters of interest. The loss function were employed to obtain the estimates for both scale and shape parameters with an assumption that the both scale and shape parameters are unknown and independent. Also the Bayes estimate for the simulated datasets and real life datasets were obtained. The Bayes estimates obtained under dierent loss functions are close to the true parameter value of the shape and scale parameters. The estimators are then compared in terms of their Mean Square Error (MSE) using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

Method for estimating time length using simultaneous phase measurements in the system of simultaneously and independently operating generators

Introduction. This paper is devoted to the development of a method for estimating the current time-frequency parameters of each of a set of simultaneously and independently operating generators in the radio electronic system. A general case is considered, in which the deviation of true values of the nominal generator parameters from the assumed values of these parameters is determined not only by random, but also by long-term frequency deviation. The work objective is to generalize the method for estimating the time-frequency parameters of signals (long-term nominal frequency and current frequency deviation from the nominal value) based on the simultaneous measurement of the phases of signals generated in the system of independently functioning generators. The research task is to consider a system of simultaneously and independently operating generators. Each of them generates harmonic signals, whose time-frequency parameters, such as the average frequency, are constant during a certain interval of observation. But herewith, these time-frequency parameters are known with insufficient accuracy due to the influence of external factors (changes in temperature, pressure, supply voltage, etc.). It is required to obtain estimates of the time-frequency parameters of signals (the duration of the measuring interval, values of the long-term frequency and the standard deviation) from the results of measurements of the phases of signals formed by the generators at measuring intervals belonging to the observation interval, within which the average frequency remains constant. Materials and Methods. A system of simultaneously and independently functioning generators is considered. The long- term value of signal frequency for each of the generators over the observation interval remains constant, but it is known with some margin of error. During the observation interval, several measurements of the signal phase of each of the generators are performed. At the same time, the current values of the signal frequency and the duration of the measuring interval have random deviations from the long-term values, and follow the normal distribution law with zero mathematical expectation and a known variance. The estimation of time-frequency parameters based on the results of measuring the signal phases is carried out using a multidimensional likelihood function. The maximum is found on the base of solving the redefined system of linear algebraic equations. Results. A new mathematical model and a numerical-analytical method for determining the time-frequency parameters of signals are developed. They take into account both the long-term constant frequency deviation and short-term random deviations. Discussion and Conclusions. The results obtained can be used under the development and creation of data-measuring and information-telecommunication systems, including geographically distributed systems. The resulting estimates of the time-frequency parameters enable to increase the signal frequency stability and, accordingly, to improve the accuracy of measurements and the quality of information transfer.

Diagnostic utility of alarm features in predicting malignancy in patients with dyspeptic symptoms

BackgroundClinical features are of modest benefit in determining the etiology of dyspepsia. Dyspeptic patients with alarm features are suspected to have malignancy; but the proportions of patients and true cutoff values of various quantitative parameters in predicting malignancy are explored to a lesser extent.MethodsThis is a prospective observational study of consecutive patients undergoing esophagogastroduodenoscopy (EGD) for dyspeptic symptoms. Patients’ alarm features and clinical details were recorded in a predesigned questionnaire. The diagnostic accuracy of alarm features in predicting malignancy was studied.ResultsNine hundred patients, 678 (75.3%) males, with a mean (standard deviation [SD]) age of 44.6 (13.54) years were enrolled. Commonest indication for EGD was epigastric pain in 614 (68.2%) patients. Dyspepsia was functional in 311 (34.6%) patients. EGD revealed benign lesions in 340 (37.8%) and malignancy in 50 (5.5%) patients. Among the malignant lesions, gastric malignancy was present in 28 (56%) and esophageal malignancy in 20 (40%) patients. Alarm features were present in 206 (22.9%), out of which malignant lesions were seen in 46 (22.3%) patients. Altogether, the alarm features had a sensitivity of 92% and specificity of 81.2% for predicting malignancy. The sensitivity and specificity for weight loss were 76% and 90.8%, while that of abdominal mass were 10% and 99.9% respectively. Based on receiver operating characteristic curve, the optimal age for screening of malignancy was 46.5 years in this population.ConclusionsPatients of age group 40 to 49 years with dyspeptic alarm symptoms (predominant weight loss) need prompt endoscopy to screen for malignancy. The alarm features are inexpensive screening tools, found to be useful in India, and should be utilized in countries with similar healthcare conditions and disease epidemiology.

Bayesian Estimation in Shared Positive Stable Frailty Models

The concept of frailty provides a suitable way to introduce random effects in the model to account for association and unobserved heterogeneity. In its simplest form, a frailty is an unobserved random factor that modifies multiplicatively the hazard function of an individual or a group or cluster of individuals. In this paper, we study positive stable distribution as frailty distribution and two different baseline distributions namely Pareto and linear failure rate distribution. We estimate parameters of proposed models by introducing Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique. In the present study a simulation is done to compare the true values of parameters with the estimated value. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991) related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better model.

A New Version of the Exponentiated Burr X distribution

A new version of the Exponentiated Burr X (EBX) distribution was introduced and studied in this paper. The method of Nadarajah and Kotz (2006) that was based on Gupta et al., (1998) proposition was used. Mathematical and statistical properties of the EBX distribution such as the limit behaviour, quantile function, moments, moment generating function, entropy and order statistics were explicitly derived. Further, the maximum likelihood estimators of the model parameters were obtained. These estimators were employed in a simulation study using varying sample sizes and true parameter values to assess the performance of this distribution. Application to real data set shows that the EBX distribution has a good model fitting capacity using several selection statistical criteria

Asymptotic behaviour of the posterior distribution in approximate Bayesian computation

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. In the context of Hidden Markov Models (HMMs), we analyze the asymptotic behavior of the posterior distribution in ABC based Bayesian parameter estimation. In particular we show that Bernstein-von Mises type results still hold but that the resulting posterior is biased in the sense that it concentrates around a point in parameter space that differs from the true parameter value. Furthermore we obtain precise rates for the size of this bias with respect to a natural accuracy parameter of the ABC method. Finally we discuss, via a numerical example, the implications of our results for the practical implementation of ABC.

Two-stage surrogate model-assisted Bayesian framework for groundwater contaminant source identification

Groundwater contaminant source identification is normally a prerequisite for contaminant remediation. This study proposes a new two-stage surrogate-assisted Markov chain Monte Carlo (MCMC)-based Bayesian framework to identify contaminant source parameters for groundwater polluted by dense nonaqueous phase liquid. In the framework, an adaptive update feedback process is proposed to construct a locally accurate surrogate model over posterior distributions to replace the time-consuming multiphase flow model. To increase the efficiency of the MCMC simulation, a multiobjective feasibility-enhanced particle swarm optimization algorithm (MOFEPSO) is adopted to generate the initial guess of the contamination source parameters. The accuracy and efficiency of the proposed framework are confirmed via a synthetic study. The contaminant source parameters generated by the proposed approach are compared with those computed by the one-stage surrogate-assisted MCMC-based Bayesian approach. The results demonstrate that the root mean squared error (RMSE) between true value of parameters and maximum a-posteriori density values (MAP) obtained by the proposed method decreased by 71.3% compared with those obtained by one-stage surrogate-based framework. To further assess the efficiency of MOFEPSO, the same inversion problem is solved with random values as the initial guesses of the unknown parameters during MCMC simulation; the other conditions are the same as the proposed framework. The results indicate that adopting MOFEPSO improves the efficiency of MCMC simulation. Therefore, the proposed approach can accurately and effectively identify the contaminant source parameters with achieving about 148 times of speed-up compared to the simulation-based MCMC simulation.

The convexity of optimal transport-based waveform inversion for certain structured velocity models

Full--waveform inversion (FWI) is a method used to determine properties of the Earth from information on the surface. We use the squared Wasserstein distance (squared $W_2$ distance) as an objective function to invert for the velocity of seismic waves as a function of position in the Earth, and we discuss its convexity with respect to the velocity parameter. In one dimension, we consider constant, piecewise increasing, and linearly increasing velocity models as a function of position, and we show the convexity of the squared $W_2$ distance with respect to the velocity parameter on the interval from zero to the true value of the velocity parameter when the source function is a probability measure. Furthermore, we consider a two--dimensional model where velocity is linearly increasing as a function of depth and prove the convexity of the squared $W_2$ distance in the velocity parameter on large regions containing the true value. We discuss the convexity of the squared $W_2$ distance compared with the convexity of the squared $L^2$ norm, and we discuss the relationship between frequency and convexity of these respective distances. We also discuss multiple approaches to optimal transport for non--probability measures by first converting the wave data into probability measures.