Accuracy Of Point Estimates Research Articles

Application of Residual Structure Time Convolutional Network Based on Attention Mechanism in Remaining Useful Life Interval Prediction of Bearings.

In the context of Industry 4.0, bearings, as critical components of machinery, play a vital role in ensuring operational reliability. The detection of their health status is thus of paramount importance. Existing predictive models often focus on point predictions of bearing lifespan, lacking the ability to quantify uncertainty and having room for improvement in accuracy. To accurately predict the long-term remaining useful life (RUL) of bearings, a novel time convolutional network model with an attention mechanism-based soft thresholding decision residual structure for quantifying the lifespan interval of bearings, namely TCN-AM-GPR, is proposed. Firstly, a spatio-temporal graph is constructed from the bearing sensor signals as the input to the prediction model. Secondly, a residual structure based on a soft threshold decision with a self-attention mechanism is established to further suppress noise in the collected bearing lifespan signals. Thirdly, the extracted features pass through an interval quantization layer to obtain the RUL and its confidence interval of the bearings. The proposed methodology has been verified using the PHM2012 bearing dataset, and the comparison of simulation experiment results shows that TCN-AM-GPR achieved the best point prediction evaluation index, with a 2.17% improvement in R2 compared to the second-best performance from TCN-GPR. At the same time, it also has the best interval prediction comprehensive evaluation index, with a relative decrease of 16.73% in MWP compared to the second-best performance from TCN-GPR. The research results indicate that TCN-AM-GPR can ensure the accuracy of point estimates, while having superior advantages and practical significance in describing prediction uncertainty.

Reliability evaluation in the zero‐failure Weibull case based on double‐modified hierarchical Bayes

AbstractHierarchical Bayes, or E‐Bayes, is frequently used to estimate the failure probability when solving a zero‐failure reliability evaluation model; however, the accuracy of the reliability estimation using these methods is not very good in practice. Due to this, a novel double‐modified hierarchical Bayes (DMH‐Bayes) is proposed for Weibull characteristic data in this study to enhance failure probability estimation and improve reliability point estimation accuracy. Meanwhile, in order to guarantee the preservation of the assessment findings' consistency and confidence level, the parametric Bootstrap method (P‐Bootstrap) and the L‐moment estimation method based on point estimation are introduced to obtain reliability confidence interval estimates. Based on Monte–Carlo simulation testing and analysis of a gyroscope bearing, the new model is confirmed to have better applicability and robustness while improving the accuracy of reliability assessment.

A Variational LSTM Emulator of Sea Level Contribution From the Antarctic Ice Sheet

AbstractThe Antarctic ice sheet (AIS) will be a dominant contributor to global mean sea level rise in the 21st century but remains a major source of uncertainty. The Ice Sheet Model Intercomparison for CMIP6 (ISMIP6) is an ensemble of continental‐scale models for studying the evolution of the AIS and projecting its future contribution to sea level. Due to their complexity and computational cost, ISMIP6 simulations are sparse and generated infrequently. Emulators are smaller‐scale models that approximate ISMs and enable experimentation and exploration into the drivers of sea level change. We introduce a neural network (NN) emulator to approximate the ISMIP6 ensemble, using a variational Long Short‐Term Memory (LSTM) with Monte Carlo dropout to quantify single‐projection uncertainty. The proposed NN emulator is compared to a Gaussian Process (GP) emulator on four criteria: accuracy of point estimates and predictive distributions of individual model projections, approximation of the ensemble projections, and model training time. The NN predicts more accurately on single projections, with a mean absolute error of 0.46 mm Sea Level Equivalent (SLE) versus 0.73 mm SLE for the GP, and has more accurate uncertainty estimates. The NN emulator also better approximates the ensemble distribution of ISMIP6 model projections, with a Kullback‐Leibler divergence of 18.26 versus 199.14 for GP at the projection year 2100. The NN enables more accurate experimentation with a reduced runtime, offering a new tool for understanding the important role of regional precipitation, ice sheet drainage systems, and interannual and longer timescale dynamics.

Efficient seismic fragility analysis method utilizing ground motion clustering and probabilistic machine learning

Machine learning (ML) techniques have been recently adopted in engineering practice to define the relationship between seismic intensity measure (IM) and structural damage measure (DM) based on a limited set of numerical simulations. However, they only offer deterministic prediction, which failing to reflect the aleatoric uncertainty related to input variables (e.g. seismic excitation and structural properties) and the epistemic uncertainty associated with modeling. This paper proposes a probabilistic ML method combined with ground motion clustering for seismic fragility analysis of structures. In the probabilistic ML method, by the natural gradient boosting (NGBoost), the conditional probability distribution can be evaluated for each structural response instead of producing point estimation. In addition, ground motion clustering is based on the time series K-means, which can capture the hidden features and select the representative subset of ground motions. The proposed framework was implemented for seismic fragility analysis of a typical 3-span, 6-storey reinforced concrete (RC) frame system. Analysis results indicated that the point estimation accuracy of the NGBoost was comparable to that based on excellent deterministic ML techniques, e.g. artificial neural network (ANN), random forest (RF), extreme gradient boosting (XGBoost). Moreover, the probabilistic prediction can efficiently provide the conditional probability of exceeding a damaged state in the structure given an IM level, eliminating the need for additional input of uncertainties from structural properties in traditional ML methods. Ultimately, the cluster-based ground motion selection reduced the model uncertainty and improves the prediction accuracy of the probabilistic ML model.

Binomial-Geometric Mixture and Its Applications

A mixture distribution is a combination of two or more probability distributions; it can be obtained from different distribution families or the same distribution families with different parameters. The underlying distributions may be discrete or continuous, so the resulting mixture probability distribution function should be a mass or density function. In the last few years, there has been great interest in the problem of developing a mixture distribution based on the binomial distribution. This paper uses the probability generating function method to develop a new two-parameter discrete distribution called a binomial-geometric (BG) distribution, a mixture of binomial distribution with the number of trials (parameter <img src=image/13428702_01.gif>) taken after a geometric distribution. The quantile function, moments, moment generating function, Shannon entropy, order statistics, stress-strength reliability and simulating the random sample are some of the statistical highlights of the BG distribution that are explored. The model's parameters are estimated using the maximum likelihood method. To examine the performance of the accuracy of point estimates for BG distribution parameters, the Monte Carlo simulation is performed with different scenarios. Finally, the BG distribution is fitted to two real lifetime count data sets from the medical field. As a result, the proposed BG distribution is an overdispersed right-skewed and can accommodate a constant hazard rate function. The proposed BG distribution is appropriate for modelling the overdispersed right-skewed real-life count data sets and it can be an alternative to the negative binomial and geometric distributions.

Distributed Fusion Estimation for the Measurements with Bounded Disturbances

Abstract The information fusion problem is studied for multi-sensor systems in the presence of bounded disturbances. In this paper, a distributed fusion estimation algorithm is proposed based on the set-membership theory, which obtains the overall estimates based on multi-ellipsoids intersection. A parameter adaptive adjustment scheme is derived to guarantee the performance of the algorithm. The feedback mechanism is also introduced to enhance the estimation procedure. Through theoretical analysis and simulation, the performance of the proposed algorithm is analyzed, and some interesting properties of the proposed algorithm are proved. Results show that the proposed algorithm improves the point estimation accuracy. Compared with the algorithm without feedback, the one with feedback has better local estimation. Meanwhile, the effectiveness of the proposed algorithm in improving state estimation accuracy has been proved by the simulation results.

Bayesian neural network priors for edge-preserving inversion

&lt;p style='text-indent:20px;'&gt;We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is introduced, motivated by existing results concerning the infinite-width limit of such networks. We show theoretically that samples from such priors have desirable discontinuous-like properties even when the network width is finite, making them appropriate for edge-preserving inversion. Numerically we consider deconvolution problems defined on one- and two-dimensional spatial domains to illustrate the effectiveness of these priors; MAP estimation, dimension-robust MCMC sampling and ensemble-based approximations are utilized to probe the posterior distribution. The accuracy of point estimates is shown to exceed those obtained from non-heavy tailed priors, and uncertainty estimates are shown to provide more useful qualitative information.&lt;/p&gt;

A Time-Varying Hedonic Approach to quantifying the effects of loss aversion on house prices

Loss aversion is a widely-recognized cognitive bias that can affect house price determination. Existing empirical approaches to quantify its effects require hedonic methods to predict what prices would be in the absence of loss aversion. However, conventional methods for making this counterfactual prediction unrealistically preclude time variation in the hedonic values of housing attributes, thereby exacerbating specification error and reducing the accuracy of point estimates. We show how time-varying hedonic regression (TVHR) can overcome this deficiency by allowing hedonic values to change over time. Applying the method to a dataset of residential transactions from Auckland, New Zealand, that spans 2009 to 2018, we find that loss aversion significantly inflates transaction prices. However, by comparison, existing methods yield imprecise estimates of this premium that are implausibly large and sensitive to the sample period selected. Our findings suggest that THVR is an attractive alternative to conventional approaches to quantifying loss aversion.

Testing Moderation in Business and Psychological Studies with Latent Moderated Structural Equations

Most organizational researchers understand the detrimental effects of measurement errors in testing relationships among latent variables and hence adopt structural equation modeling (SEM) to control for measurement errors. Nonetheless, many of them revert to regression-based approaches, such as moderated multiple regression (MMR), when testing for moderating and other nonlinear effects. The predominance of MMR is likely due to the limited evidence showing the superiority of latent interaction approaches over regression-based approaches combined with the previous complicated procedures for testing latent interactions. In this teaching note, we first briefly explain the latent moderated structural equations (LMS) approach, which estimates latent interaction effects while controlling for measurement errors. Then we explain the reliability-corrected single-indicator LMS (RCSLMS) approach to testing latent interactions with summated scales and correcting for measurement errors, yielding results which approximate those from LMS. Next, we report simulation results illustrating that LMS and RCSLMS outperform MMR in terms of accuracy of point estimates and confidence intervals for interaction effects under various conditions. Then, we show how LMS and RCSLMS can be implemented with Mplus, providing an example-based tutorial to demonstrate a 4-step procedure for testing a range of latent interactions, as well as the decisions at each step. Finally, we conclude with answers to some frequently asked questions when testing latent interactions. As supplementary files to support researchers, we provide a narrated PowerPoint presentation, all Mplus syntax and output files, data sets for numerical examples, and Excel files for conducting the loglikelihood values difference test and plotting the latent interaction effects.

Space–time surveillance of count data subject to linear trends

AbstractThis paper proposes a new space–time cumulative sum (CUSUM) approach for detecting changes in spatially distributed Poisson count data subject to linear drifts. We develop expressions for the likelihood ratio test monitoring statistics and the change point estimators. The effectiveness of the proposed monitoring approach in detecting and identifying trend‐type shifts is studied by simulation under various shift scenarios in regional counts. It is shown that designing the space–time monitoring approach specifically for linear trends can enhance the change point estimation accuracy significantly. A case study for male thyroid cancer outbreak detection is presented to illustrate the application of the proposed methodology in public health surveillance.

Point Estimation with Markers for Effective Mobile Auditory Graphs

While researchers have performed numerous studies to understand the human interpretation of visual graphs in reading, comprehending and interpreting displayed data; visually impaired (VI) students still face many challenges that prevent them from fully benefiting from these graphs in class. In this study, we conducted a test with 20 students to track the work described in studies in an expanded scenario. As we have tried to answer the question as to whether adding multi-reference mapping of sonification to auditory graphs could improve the of point estimation accuracy in non-visual condition. We also emphasize the efficiency of the performance of multi-reference graphs to make them as efficient as mapping using single pitch. Our proposed study improved performance of multi-reference task completion time by having fewer reference note. The results help provide empirical evidence that the multi-reference mode provides more accurate results than the single-pitch mode and confirms that adding contexts to auditory graphs could be used for better comprehension.

Gaussian Processes for improving orbit prediction accuracy

A machine learning (ML) approach has been recently proposed to improve the orbit prediction accuracy of resident space objects (RSOs) through learning from historical data. Previous results have shown that the ML approach can successfully improve the point estimation accuracy. This paper extends the ML approach by introducing Gaussian Processes (GPs) which can generate uncertainty information about its point estimate. Both the simulation environment and the publicly available RSO catalogs are used to test the advanced ML approach. Numerical results demonstrate that the trained GP model can effectively improve the orbit prediction accuracy and generate uncertainty boundaries with high performance. Discussions and insights are also presented during the investigation using real data, including suggestions on designing learning variables and the possible causes for some unsatisfying results.

Gaze point estimation on curved display by using session level calibration for flat screen displays

The advantages of curved screen displays find their place in populations everyday life, therefore it is important to adapt the existing eye tracking systems for estimating the gaze point on a curved screen. In this paper we present a curved screen based gaze point estimation model. This model provides methods for estimating the gaze point position by eye rotation angles, and also transforms flat screen based relative coordinates into curved screen based relative coordinates. The model was validated by using a flat screen based eye tracking system for a gaze point estimation on a curved screen. The eye rotation angle, distance to the screen and gaze point location’s influence were modelled in this paper as well. The results of these experiments prove the up to 4% increase of gaze point estimation accuracy by using the proposed model, by comparing the flat screen mode with the curved screen. However the results found are significant only if the distance to the screen is less than 0.5 of curved screen radius.

Using survival models to estimate bus travel times and associated uncertainties

Transit agencies often provide travelers with point estimates of bus travel times to downstream stops to improve the perceived reliability of bus transit systems. Prediction models that can estimate both point estimates and the level of uncertainty associated with these estimates (e.g., travel time variance) might help to further improve reliability by tempering user expectations. In this paper, accelerated failure time survival models are proposed to provide such simultaneous predictions. Data from a headway-based bus route serving the Pennsylvania State University-University Park campus were used to estimate bus travel times using the proposed survival model and traditional linear regression frameworks for comparison. Overall, the accuracy of point estimates from the two approaches, measured using the root-mean-squared errors (RMSEs) and mean absolute errors (MAEs), was similar. This suggests that both methods predict travel times equally well. However, the survival models were found to more accurately describe the uncertainty associated with the predictions. Furthermore, survival model estimates were found to have smaller uncertainties on average, especially when predicted travel times were small. Tests for transferability over time suggested that the models did not over-fit the dataset and validated the predictive ability of models established with historical data. Overall, the survival model approach appears to be a promising method to predict both expected bus travel times and the uncertainty associated with these travel times.

Ellipsoidal state‐bounding‐based set‐membership estimation for linear system with unknown‐but‐bounded disturbances

This study proposes a fast and stable recursive ellipsoidal state-bounding-based set-membership estimation algorithm for the state estimation of linear system with unknown-but-bounded (UBB) disturbances. The proposed algorithm has a prediction–correction structure in time update and observation update, which is similar to Kalman filter. For both time update and observation update, there is a data-depending weighting factor. The observation weighting factor is acquired by minimising the upper bound on a Lyapunov function of the posteriori estimation error. It has been demonstrated that the estimation error of the proposed algorithm is input-to-state stable when the system is uniformly observable. With the property of selective observation update, the proposed algorithm not only improves the point estimation accuracy but also decreases the computation load of observation weighting factors and the volume of feasible ellipsoid sets. The efficiency of the proposed algorithm has been demonstrated by numerical simulations with different UBB disturbances.

A Method to Calibrate Vehicle-Mounted Cameras Under Urban Traffic Scenes

We address the problem of vehicle-mounted camera calibration under urban traffic scenes regarding the fact that the traditional calibration methods are practically restricted, since the internal parameters should be calibrated in the laboratory and it is impossible for recalibration that resulted from the parameters drifting or re-focusing when driving on roads. In this paper, we propose to utilize the manual lines lying in Manhattan directions in the scenes to compute their corresponding vanishing points for camera calibration, as the urban traffic scenes are usually man-made and the important lines and signs for driving are typically lying in the Manhattan directions. For “Manhattan world” scenes, where there are plenty of lines lying in Manhattan directions, the lines in the scene are detected automatically, and the clusters corresponding to Manhattan directions are obtained using RANSAC-like methods. For the more general “quasi-Manhattan world” scenes, where only the lines in two directions can be found naturally, while the lines in the other direction are usually detected trivially or even can be hardly detected, we propose a method to estimate the lines in the third direction to improve the vanishing point estimation accuracy. The method proposed is tested on both two types of scenes, and the accuracy and practicability of this method are demonstrated. Furthermore, calibration experiments on both one image and multiple images are conducted, which show that the results can be more accurate when more images are used.

Aggregating multiple probability intervals to improve calibration

AbstractWe apply the principles of the “Wisdom of Crowds (WoC)” to improve the calibration of interval estimates. Previous research has documented the significant impact of the WoC on the accuracy of point estimates but only a few studies have examined its effectiveness in aggregating interval estimates. We demonstrate that collective probability intervals obtained by several heuristics can reduce the typical overconfidence of the individual estimates. We re-analyzed data from Glaser, Langer and Weber (2013) and from Soll and Klayman (2004) and applied four heuristics Averaging, Median, Enveloping, Probability averaging-suggested by Gaba, Tsetlin and Winkler (2014) and new heuristics, Averaging with trimming and Quartiles. We used the hit rate and the Mean Squared Error (MSE) to evaluate the quality of the methods. All methods reduced miscalibration to some degree, and Quartiles was the most beneficial securing accuracy and informativeness.

A Kalman-Filter Based Approach to Identification of Time-Varying Gene Regulatory Networks

MotivationConventional identification methods for gene regulatory networks (GRNs) have overwhelmingly adopted static topology models, which remains unchanged over time to represent the underlying molecular interactions of a biological system. However, GRNs are dynamic in response to physiological and environmental changes. Although there is a rich literature in modeling static or temporally invariant networks, how to systematically recover these temporally changing networks remains a major and significant pressing challenge. The purpose of this study is to suggest a two-step strategy that recovers time-varying GRNs.ResultsIt is suggested in this paper to utilize a switching auto-regressive model to describe the dynamics of time-varying GRNs, and a two-step strategy is proposed to recover the structure of time-varying GRNs. In the first step, the change points are detected by a Kalman-filter based method. The observed time series are divided into several segments using these detection results; and each time series segment belonging to two successive demarcating change points is associated with an individual static regulatory network. In the second step, conditional network structure identification methods are used to reconstruct the topology for each time interval. This two-step strategy efficiently decouples the change point detection problem and the topology inference problem. Simulation results show that the proposed strategy can detect the change points precisely and recover each individual topology structure effectively. Moreover, computation results with the developmental data of Drosophila Melanogaster show that the proposed change point detection procedure is also able to work effectively in real world applications and the change point estimation accuracy exceeds other existing approaches, which means the suggested strategy may also be helpful in solving actual GRN reconstruction problem.

Choice of Baseline in Parallel Thorough QT Studies

Although the ICH E14 Guidance [1] was adopted in 2005 there is still much debate on the appropriate baseline needed to adjust for the variable nature of the QT interval and its heart rate corrected value (QTc) in the parallel Thorough QT (TQT) study. Numerous reports have documented the influence of circadian rhythm [2], food ingestion [3], sleep [4], and autonomic tone [5] on the QT/QTc interval. In the absence of baseline measurements, these factors can make it difficult to interpret QT effects of the study drug. In this issue of Drug Safety Dr. Zhang and colleagues [6] advocate the use of a time-matched baseline in parallel TQT studies to maximize the precision and accuracy of point estimates for QTc effects. Their recommendation is based on analyses of commonly used baseline correction methods using a large data set of parallel TQT studies submitted to the FDA for statistical review by sponsors. One assumption in the choice of baseline is that it should have no influence on the magnitude of QT effects (high accuracy) and it should minimize the uncertainty of the effects (high precision). Both accuracy and precision are important for the interpretation of a TQT trial. As a result, there is much focus on the implications of using different baseline adjustments in the parallel TQT study and understanding the role each baseline definition can have in determining the outcome of the trial as either positive or negative. The distinction between a positive or negative TQT study is based on the upper bound of the 95 % one-sided confidence interval (CI) for the largest time-matched mean difference in QTc between drug and placebo (baseline adjusted). If these (double-delta) DDQTc values exclude 10 ms at all study times the result is a negative TQT study [1]. Intensive ECG monitoring is then hardly ever required in subsequent trials (phase II/III). Conversely, drugs for which an effect exceeding 10 ms cannot be excluded almost always require additional QT interval monitoring in target patients including dose-concentration effects, outlier analysis, changes in mean QTc values, analysis of QTc in subgroups of interest, and identification of individuals who develop a markedly prolonged QTc. The need for additional ECG monitoring in late phase trials can add millions to drug development and may ultimately pose financial limitations on the number of medications which can be developed [7]. The importance of correctly adjusting for baseline in the TQT study is therefore evident.

Review of Lecture Notes "Applied Mathematical Statistics. Elements" by Ryszard Zieliński

The lecture notes under review concerns matters which in these kind of books are rarely discussed, such as the central role of alternative hypothesis in the problem of hypothesis testing or the issue of assessing the accuracy of point estimates using confidence interval . While one can argue about whether these issues are not discussed in other books, it certainly must agree with the author in a different matter. What distinguishes the script-reviewed many other books, is a way of presenting the main ideas of mathematical statistics. Not wanting to complicate the lecture by more complex models, author described these ideas as an example a very simple statistical model.