True Parameters Research Articles

The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models

Abstract Because civil engineering structures include stressed structural members and unstressed non-structural members, it isn’t easy to obtain the true parameters of the model when modeling. The article uses a virtual reality fuzzy random modeling to establish a steel bearing force model in civil engineering operations. We determined the relevant bearing capacity parameters based on the corrosion of steel bars in civil engineering. The research found that the numerical simulation method determined in this paper has grasped the essence of stress rate, concrete material properties, and dynamic load effect to a considerable extent.

Assessing small-mammal trapping design using spatially explicit capture recapture (SECR) modeling on long-term monitoring data.

Few studies have evaluated the optimal sampling design for tracking small mammal population trends, especially for rare or difficult to detect species. Spatially explicit capture-recapture (SECR) models present an advancement over non-spatial models by accounting for individual movement when estimating density. The salt marsh harvest mouse (SMHM; Reithrodontomys raviventris) is a federal and California state listed endangered species endemic to the San Francisco Bay-Delta estuary, California, USA; where a population in a subembayment has been continually monitored over an 18-year period using mark-recapture methods. We analyzed capture data within a SECR modeling framework that allowed us to account for differences in detection and movement between sexes. We compared the full dataset to subsampling scenarios to evaluate how the grid size (area) of the trap design, trap density (spacing), and number of consecutive trapping occasions (duration) influenced density estimates. To validate the subsampling methods, we ran Monte Carlo simulations based on the true parameter estimates for each specific year. We found that reducing the area of the trapping design by more than 36% resulted in the inability of the SECR model to replicate density estimates within the SE of the original density estimates. However, when trapping occasions were reduced from 4 to 3-nights the density estimates were indistinguishable from the full dataset. Furthermore, reducing trap density by 50% also resulted in density estimates comparable to the full dataset and was a substantially better model than reducing the trap area by 50%. Overall, our results indicated that moderate reductions in the number of trapping occasions or trap density could yield similar density estimates when using a SECR approach. This approach allows the optimization of field trapping efforts and designs by reducing field efforts while maintaining the same population estimate compared to the full dataset. Using a SECR approach may help other wildlife programs identify sampling efficiencies without sacrificing data integrity for long term monitoring of population densities.

Features of high-density transient electromagnetic sounding data inversion under oil and gas prospecting in the Nepa-Botuoba anteclise area

The data of near-field transient electromagnetic sounding, which are widely used for the purposes of oil and gas exploration within the Nepa-Botuoba anteclise, are typically interpreted in terms of quasi-horizontally-layered models of media. The purpose of this study is to develop an approach to the inversion of transient electromagnetic sounding curves obtained via high-density 3D observation networks. The study was based on mathematical modeling, whose results allowed to estimate the lateral spatial parameters of a non-stationary electromagnetic field as well as to understand the differences between the results of one-dimensional inversion of the transient electromagnetic sounding data and the true parameters of the target horizon. As a result, the characteristic of the electromagnetic field described by an exponential function and used in the lateral-constraint inversion of high-density electromagnetic sounding was obtained. The proposed approach was tested on the practical data within the site under investigation located on the slope of the Nepa-Botuobа anteclise. It is shown that the use of spatial discrepancy under TEM sounding data inversion makes it possible to obtain geoelectric models characterized by lateral consistency of section geoelectric parameters. The application of the spatial stacking-based approach in the inversion process allows to increase the solution stability of the inverse problem of the near-field TEM sounding data.

Parameters estimation approaches of the Moore and Bilikam family with reliability analysis under progressively type-II censoring

The precise investigation of the Moore and Bilikam (MB) family of distributions is essential since they cover several distributions as special cases. We evaluate different estimation procedures for parameters of MB family comprehensively. Moreover, the confidence interval and highest posterior density interval estimators of parameters are provided. The different estimation methods of the parameters of two certain cases of the MB family are compared via the simulation data. Based on the simulation approach, we realized the estimates are convergent to the real values of the parameters and the root mean squared error (RMSE) values derived by the expectation-maximization (EM) algorithm are less than Newton–Raphson (NR), stochastic EM (SEM) and Bayes estimators. Also, the higher values of the sample size lead to better estimates in the sense close to true parameter values and having smaller RMSE values. The reliability analysis of MB family is another topic in this paper, with simulation discussion. The Monte Carlo simulations are provided to assess the performances of estimation methods. We concluded the Bayesian shrinkage estimators are better than other methods of the reliability function, which have the smallest values of the RMSE. The analysis of real dataset has been presented for illustrative purposes, which confirmed simulation results.

Initial excitation based discrete-time multi-model adaptive online identification

This paper proposes a novel multi-model adaptive identification (MMAI) algorithm for discrete-time linear time invariant (LTI) uncertain systems with tunable performance. The uncertain plant parameter vector is assumed to belong to a known convex hull of a finite number of vertices; these vertices are considered as initial choice of vertices of an adaptive model parameter set. The estimated parameter, corresponding to the uncertain plant parameter, is computed at every instant as a convex combination of the model set vertices. To update the vertices of the adaptive model parameter set, a switched adaptive update law is proposed, along with a novel discrete-time initial excitation (IE) condition, which is imposed on the regressor signal. The proposed discrete-time IE condition is online verifiable and is milder than persistence of excitation (PE) condition, required for parameter convergence in classical adaptive estimation routines. The switched adaptive law guarantees exponential convergence of the vertices of the model set as well as the estimated parameter, to the true plant parameter, provided the regressor signal satisfies the IE condition. The properties of the designed MMAI strategy are validated through suitable simulation examples.

Optimizing the Voce–Chaboche Model Parameters for Fatigue Life Estimation of Welded Joints in High-Strength Marine Structures

This work studies the Voce–Chaboche (V–C) material model parameter optimization for high-strength steel welded joints subjected to cyclic loading. The model parameters of each material zone in a S690 steel butt-welded joint were determined using an optimization algorithm based on the Newton trust region (NTR) method and an accumulated true strain parameter. The model parameters were fitted to stress–strain histories from uniaxial strain-controlled cyclic tests. To validate the model, fully-reversed variable amplitude fatigue experiments were performed under load control. The experimental results were then compared to numerical results from a finite element analysis. When the elastic modulus is optimized as a V–C parameter, the results indicate that the V–C model slightly underestimates the strain range, leading to conservative fatigue life estimates. However, the results can be improved by using an elastic modulus obtained experimentally. In this case, the resulting material model slightly overestimates the strain range, leading to a non-conservative, but more accurate, fatigue life estimation. It can be concluded that the NTR-based accumulated true strain approach successfully determined the V–C model parameters for different material zones in the welded joint, and closely estimated the strain range and the fatigue life for a variable amplitude load history.

Estimating Lost Gas Content for Shales Considering Real Boundary Conditions during the Core Recovery Process.

Shale gas has become an important natural gas resource in recent years as the conventional oil and gas resources are depleting. Shale gas content is one of the most important parameters for reserve calculation and sweet-spot prediction. The traditional core recovery method is widely used to determine gas content. However, the estimation of lost gas content is the main factor of error and difficulty. Large errors and uncertainties occur when using the widely used methods, such as the United States Bureau of Mines (USBM) method. Hence, a more accurate method is required. In this work, a full-process model is developed in COMSOL Multiphysics to describe the lost gas with time during the core recovery process as well as the desorption stage after the core is covered. In this method, by setting the initial gas pressure and flow parameters and matching the desorbed gas volume and considering variable diffusivity with respect to temperature, the initial gas content and the gas lost with respect to time are calculated. Overall, 10 field data are tested using this full-process model, and the USBM method is also applied to compare the results. It is found that if the ratio of lost gas volume estimated using the USBM method to the desorbed gas volume of the field data is lower than 2.0, the USBM method underestimates the lost gas compared to the full-process method; if the ratio is about 2.0, the results from the USBM and the full-process methods are comparable; and if the ratio is close to 3.0, the USBM method tends to overestimate the lost gas. The modeling results indicate that this proposed full-process method is more theoretically sound than the USBM method, which has high uncertainties depending on the number of desorbed gas data points used. Nevertheless, this proposed method requires a large number of parameters, leading to the difficulty in finding true parameters. Therefore, an optimization algorithm is required. In summary, this study provides theoretical support and a mathematical model for the inversion calculation of lost gas during shale core recovery. It is helpful to evaluate the resource potential and development economics of shale gas more accurately.

Parameter and Model Recovery of Reinforcement Learning Models for Restless Bandit Problems

Multi-armed restless bandit tasks are regularly applied in psychology and cognitive neuroscience to assess exploration and exploitation behavior in structured environments. These models are also readily applied to examine effects of (virtual) brain lesions on performance, and to infer neurocomputational mechanisms using neuroimaging or pharmacological approaches. However, to infer individual, psychologically meaningful parameters from such data, computational cognitive modeling is typically applied. Recent studies indicate that softmax (SM) decision rule models that include a representation of environmental dynamics (e.g. the Kalman Filter) and additional parameters for modeling exploration and perseveration (Kalman SMEP) fit human bandit task data better than competing models. Parameter and model recovery are two central requirements for computational models: parameter recovery refers to the ability to recover true data-generating parameters; model recovery refers to the ability to correctly identify the true data generating model using model comparison techniques. Here we comprehensively examined parameter and model recovery of the Kalman SMEP model as well as nested model versions, i.e. models without the additional parameters, using simulation and Bayesian inference. Parameter recovery improved with increasing trial numbers, from around .8 for 100 trials to around .93 for 300 trials. Model recovery analyses likewise confirmed acceptable recovery of the Kalman SMEP model. Model recovery was lower for nested Kalman filter models as well as delta rule models with fixed learning rates. Exploratory analyses examined associations of model parameters with model-agnostic performance metrics. Random exploration, captured by the inverse softmax temperature, was associated with lower accuracy and more switches. For the exploration bonus parameter modeling directed exploration, we confirmed an inverse- U-shaped association with accuracy, such that both an excess and a lack of directed exploration reduced accuracy. Taken together, these analyses underline that the Kalman SMEP model fulfills two basic requirements of a cognitive model.

Estimation in tensor Ising models

AbstractThe $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geqslant 2$. This is a natural generalization of the matrix Ising model that provides a convenient mathematical framework for capturing, not just pairwise, but higher-order dependencies in complex relational data. In this paper, we consider the problem of estimating the natural parameter of the $p$-tensor Ising model given a single sample from the distribution on $N$ nodes. Our estimate is based on the maximum pseudolikelihood (MPL) method, which provides a computationally efficient algorithm for estimating the parameter that avoids computing the intractable partition function. We derive general conditions under which the MPL estimate is $\sqrt N$-consistent, that is, it converges to the true parameter at rate $1/\sqrt N$. Our conditions are robust enough to handle a variety of commonly used tensor Ising models, including spin glass models with random interactions and models where the rate of estimation undergoes a phase transition. In particular, this includes results on $\sqrt N$-consistency of the MPL estimate in the well-known $p$-spin Sherrington–Kirkpatrick model, spin systems on general $p$-uniform hypergraphs and Ising models on the hypergraph stochastic block model (HSBM). In fact, for the HSBM we pin down the exact location of the phase transition threshold, which is determined by the positivity of a certain mean-field variational problem, such that above this threshold the MPL estimate is $\sqrt N$-consistent, whereas below the threshold no estimator is consistent. Finally, we derive the precise fluctuations of the MPL estimate in the special case of the $p$-tensor Curie–Weiss model, which is the Ising model on the complete $p$-uniform hypergraph. An interesting consequence of our results is that the MPL estimate in the Curie–Weiss model saturates the Cramer–Rao lower bound at all points above the estimation threshold, that is, the MPL estimate incurs no loss in asymptotic statistical efficiency in the estimability regime, even though it is obtained by minimizing only an approximation of the true likelihood function for computational tractability.

Integrated Calibration of Strap-Down Geomagnetic Vector Measurement System

Strap-down geomagnetic vector measurement system usually consists of three-axis magnetometer and inertial units, which is an effective device for measuring geomagnetic vector. However, its measurement accuracy is limited by disturbance of ferromagnetic material, measurement error of magnetometer and error caused by misalignment. Therefore, an integrated calibration method for strap-down geomagnetic vector measurement system is proposed. Firstly, the integrated error model is established, and a system with linear equations constraint is constructed by the measurements of inertial units, three-axis magnetometer and proton magnetometer; secondly, calibration parameters can be estimated by two-step least squares estimation (LSE); finally, geomagnetic vector measurement can be calibrated with these parameters in real time. Simulation results show that the relative errors between estimation and true parameters are less than 3%. Experimental results demonstrate that the errors of strap-down geomagnetic vector measurement system are suppressed effectively after integrated calibration, where North, Vertical and East component measurement errors are reduced from 809.2 nT, 300.0 nT, 776.8 nT to 14.8 nT (1.83% of uncalibrated value), 11.9 nT (3.97%), 32.5 nT (4.18%) respectively, and measurement accuracy of declination and inclination are achieved to 0.1°. Furthermore, the calibration error and time are least compared with traditional methods.

Confidence regions near singular information and boundary points with applications to mixed models

We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable inference on scale parameters close or equal to zero in mixed models, which is obtained as a special case. The confidence regions are constructed by inverting a continuous extension of the score test statistic standardized by expected information, which we show exists at points of singular information under regularity conditions. Similar results have previously only been obtained for scalar parameters, under conditions stronger than ours, and applications to mixed models have not been considered. In simulations our confidence regions have near-nominal coverage with as few as $n = 20$ independent observations, regardless of how close to the boundary the true parameter is. It is a corollary of our main results that the proposed test statistic has an asymptotic chi-square distribution with degrees of freedom equal to the number of tested parameters, even if they are on the boundary of the parameter set.

Copula miss-specification in REML multivariate genetic animal model estimation

BackgroundIn animal genetics, linear mixed models are used to deal with genetic and environmental effects. The variance and covariance terms of these models are usually estimated by restricted maximum likelihood (REML), which provides unbiased estimators. A strong hypothesis of REML estimation is the multi-normality of the response variables. However, in practice, even if the marginal distributions of each phenotype are normal, the multi-normality assumption may be violated by non-normality of the cross-sectional dependence structure, that is to say when the copula of the multivariate distribution is not Gaussian. This study uses simulations to evaluate the impact of copula miss-specification in a bivariate animal model on REML estimations of variance components.ResultBivariate phenotypes were simulated for populations undergoing selection, considering different copulas for the dependence structure between the error components. Two multi-trait situations were considered: two phenotypes were measured on the selection candidates, or only one phenotype was measured on the selection candidates. Three generations with random selection and five generations with truncation selection based on estimated breeding values were simulated. When selection was performed at random, no significant differences were observed between the REML estimations of variance components and the true parameters even for the non-Gaussian distributions. For the truncation selections, when two phenotypes were measured on candidates, biases were systematically observed in the variance components for high residual dependence in the case of non-Gaussian distributions, especially in the case of a heavy-tailed or asymmetric distribution when the two traits were measured. Conversely, when only one phenotype was measured on candidates, no difference was observed between the Gaussian and non-Gaussian distributions in REML estimations.ConclusionsThis study confirms that REML can be used by geneticists to evaluate breeding values in the multivariate case even if the multivariate phenotypes deviate from normality in the situation of random selection or if one trait is not measured for the candidate under selection. Nevertheless, when the two traits are measured, the violation of the normality assumption may lead to non-negligible biases in the REML estimations of the variance-covariance components.

Clinical and Radiographic Dependences of Functional Status, Indices of the Hip Joint, and Femur Migration in Children with Cerebral Palsy

Relevance: Significant incidence of hip pathology in different groups of children with cerebral palsy and factors that may affect its formation are relevant objects of the study.
 The Goal of the Study: To establish the features of the hip joint’s formation, examining the clinical and radiographic dependences of the functional status and indices of the hip joint in patients with cerebral palsy.
 Materials and Methods: We conducted a clinical and radiographic examination of the hip joints using our own methods and standard anterior-posterior radiography, and statistical analysis of hip parameters and factors that may have influenced their formation. The total number of patients was 47 persons (86 joints).
 Results: Correlation relationships have been established between hip parameters and factors that may affect them: Gross Motor Function Classification System (GMFCS), gait function, level of lesion, developmental dysplasia of the hip, and adductor myotomy in medical history.
 Conclusions: The Reimers’ index showed greater reliability compared to the Wiberg angle. Positioning the patient's body using our own method can be used to screen the hip joints in cerebral palsy based upon the Reimers index while obtaining the true parameters of the femoral neck-shaft angle and torsion of the femur.

Online statistical inference for parameters estimation with linear-equality constraints

Stochastic gradient descent (SGD) and projected stochastic gradient descent (PSGD) are scalable algorithms to compute model parameters in unconstrained and constrained optimization problems. In comparison with SGD, PSGD forces its iterative values into the constrained parameter space via projection. From a statistical point of view, this paper studies the limiting distribution of PSGD-based estimate when the true parameters satisfy some linear-equality constraints. Our theoretical findings reveal the role of projection played in the uncertainty of the PSGD-based estimate. As a byproduct, we propose an online hypothesis testing procedure to test the linear-equality constraints. Simulation studies on synthetic data and an application to a real-world dataset confirm our theory.

Estimation of discontinuous parameters in linear elliptic equations by a regularized inverse problem

To calculate the parameters k in a stationary model Aku=f from measurements yˆ of the solution u, i.e. to solve the inverse problem, usually a regularized minimization problem is solved and its solution kˆ is considered as estimate of the true parameters. We focus on a situation which occurs e.g. for the coefficient functions k of a linear elliptic operator Aku=−divk∇u on a domain Ω⊂Rd and the total variation as regularization term. As functions k∈BV(Ω) of bounded variation can be discontinuous, existence of strong solutions u of Aku=f cannot be guaranteed and existence of minimizers cannot be obtained by standard methods. In this article, we prove solvability and stability for a general regularized minimization problem under weak assumptions, which particularly hold in case of BV(Ω) as parameter space due to a higher integrability result.

The Impact of Sample Size and Various Other Factors on Estimation of Dichotomous Mixture IRT Models.

The purpose of this study was to examine the effects of different data conditions on item parameter recovery and classification accuracy of three dichotomous mixture item response theory (IRT) models: the Mix1PL, Mix2PL, and Mix3PL. Manipulated factors in the simulation included the sample size (11 different sample sizes from 100 to 5000), test length (10, 30, and 50), number of classes (2 and 3), the degree of latent class separation (normal/no separation, small, medium, and large), and class sizes (equal vs. nonequal). Effects were assessed using root mean square error (RMSE) and classification accuracy percentage computed between true parameters and estimated parameters. The results of this simulation study showed that more precise estimates of item parameters were obtained with larger sample sizes and longer test lengths. Recovery of item parameters decreased as the number of classes increased with the decrease in sample size. Recovery of classification accuracy for the conditions with two-class solutions was also better than that of three-class solutions. Results of both item parameter estimates and classification accuracy differed by model type. More complex models and models with larger class separations produced less accurate results. The effect of the mixture proportions also differentially affected RMSE and classification accuracy results. Groups of equal size produced more precise item parameter estimates, but the reverse was the case for classification accuracy results. Results suggested that dichotomous mixture IRT models required more than 2,000 examinees to be able to obtain stable results as even shorter tests required such large sample sizes for more precise estimates. This number increased as the number of latent classes, the degree of separation, and model complexity increased.

A cross-validation statistical framework for asymmetric data integration.

The proliferation of biobanks and large public clinical data sets enables their integration with a smaller amount of locally gathered data for the purposes of parameter estimation and model prediction. However, public data sets may be subject to context-dependent confounders and the protocols behind their generation are often opaque; naively integrating all external data sets equally can bias estimates and lead to spurious conclusions. Weighted data integration is a potential solution, but current methods still require subjective specifications of weights and can become computationally intractable. Under the assumption that local data are generated from the set of unknown true parameters, we propose a novel weighted integration method based upon using the external data to minimize the local data leave-one-out cross validation (LOOCV) error. We demonstrate how the optimization of LOOCV errors for linear and Cox proportional hazards models can be rewritten as functions of external data set integration weights. Significant reductions in estimation error and prediction error are shown using simulation studies mimicking the heterogeneity of clinical data as well as a real-world example using kidney transplant patients from the Scientific Registry of TransplantRecipients.

Estimation Parameters of Dependence Meta-Analytic Model: New Techniques for the Hierarchical Bayesian Model

Dependence in meta-analytic models can happen due to the same collected data or from the same researchers. The hierarchical Bayesian linear model in a meta-analysis that allows dependence in effect sizes is investigated in this paper. The interested parameters on the hierarchical Bayesian linear dependence (HBLD) model which was developed using the Bayesian techniques will then be estimated. The joint posterior distribution of all parameters for the hierarchical Bayesian linear dependence (HBLD) model is obtained by applying the Gibbs sampling algorithm. Furthermore, in order to measure the robustness of the HBLD model, the sensitivity analysis is conducted using a different prior distribution on the model. This is carried out by applying the Metropolis within the Gibbs algorithm. The simulation study is performed for the estimation of all parameters in the model. The results show that the obtained estimated parameters are close to the true parameters, indicating the consistency of the parameters for the model. The model is also not sensitive because of the changing prior distribution which shows the robustness of the model. A case study, to assess the effects of native-language vocabulary aids on second language reading, is conducted successfully in testing the parameters of the models.

Posterior probabilities: Nonmonotonicity, asymptotic rates, log-concavity, and Turán’s inequality

In the standard Bayesian framework data are assumed to be generated by a distribution parametrized by $\theta$ in a parameter space $\Theta$, over which a prior distribution $\pi$ is given. A Bayesian statistician quantifies the belief that the true parameter is $\theta_{0}$ in $\Theta$ by its posterior probability given the observed data. We investigate the behavior of the posterior belief in $\theta_{0}$ when the data are generated under some parameter $\theta_{1},$ which may or may not be the same as $\theta_{0}.$ Starting from stochastic orders, specifically, likelihood ratio dominance, that obtain for resulting distributions of posteriors, we consider monotonicity properties of the posterior probabilities as a function of the sample size when data arrive sequentially. While the $\theta_{0}$-posterior is monotonically increasing (i.e., it is a submartingale) when the data are generated under that same $\theta_{0}$, it need not be monotonically decreasing in general, not even in terms of its overall expectation, when the data are generated under a different $\theta_{1}.$ In fact, it may keep going up and down many times, even in simple cases such as iid coin tosses. We obtain precise asymptotic rates when the data come from the wide class of exponential families of distributions; these rates imply in particular that the expectation of the $\theta_{0}$-posterior under $\theta_{1}\neq\theta_{0}$ is eventually strictly decreasing. Finally, we show that in a number of interesting cases this expectation is a log-concave function of the sample size, and thus unimodal. In the Bernoulli case we obtain this by developing an inequality that is related to Tur\'{a}n's inequality for Legendre polynomials.

Bayesian inference on a microstructural, hyperelastic model of tendon deformation.

Microstructural models of soft-tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they incorporate parameters that are directly linked to the tissue’s microscale structure and constitutive behaviour and can therefore be used to predict the effects of structural changes to the tissue. Although studies have attempted to determine such parameters using diverse, state-of-the-art, experimental techniques, values ranging over several orders of magnitude have been reported, leading to uncertainty in the true parameter values and creating a need for models that can handle such uncertainty. We derive a new microstructural, hyperelastic model for transversely isotropic soft tissues and use it to model the mechanical behaviour of tendons. To account for parameter uncertainty, we employ a Bayesian approach and apply an adaptive Markov chain Monte Carlo algorithm to determine posterior probability distributions for the model parameters. The obtained posterior distributions are consistent with parameter measurements previously reported and enable us to quantify the uncertainty in their values for each tendon sample that was modelled. This approach could serve as a prototype for quantifying parameter uncertainty in other soft tissues.