Single-value Estimates Research Articles

Safe learning-based model predictive control using the compatible models approach

In this paper, we introduce a novel approach to safe learning-based Model Predictive Control (MPC) for nonlinear systems. This approach, which we call the “compatible model approach”, relies on computing two models of the given unknown system using data generated from the system. The first model is a set-valued over-approximation guaranteed to contain the system’s dynamics. This model is used to find a set of provably safe controller actions at every state. The second model is a single-valued estimation of the system’s dynamics used to find a controller that minimises a cost function. If the two models are compatible, in the sense that the estimation is included in the over-approximation, we show that we can use the set of safe controller actions to constrain the minimisation problem and guarantee the feasibility and safety of the learning-based MPC controller at all times. We present a method to build an over-approximation for nonlinear systems with bounded derivatives on a partition of the states and inputs spaces. Then, we use piecewise multi-affine functions (defined on the same partition) to calculate a system’s dynamics estimation that is compatible with the previous over-approximation. Finally, we show the effectiveness of the approach by considering a path-planning problem with obstacle avoidance.

Efficient Sensor Calibration Via Machine Learning-Based Resampling Methods

It remains a challenge to accurately and precisely calibrate a sensor in an experimentally-efficient manner. The calibration task at hand is to quantify the functional relationship between the sensor’s response (denoted as y) and the target analyte concentration (denoted as x) based on laboratory experiments. In practical use, the sensor’s mathematical calibration model needs to be coupled with the device to make inference regarding the concentration of the analyte in an environment based on the observed sensor response. It is critical to provide a single-value estimate for the analyte concentration, as well as to quantify the uncertainty of the target estimate (i.e., to provide the possible range of the underlying concentration level).However, classic statistical methods are not able to provide valid inference on the target quantity of interest due to the following difficulties in sensor calibration. First, not only the typical forward modeling but also the inverse estimation is involved. The former refers to the generation of a calibration model functionally relating the analyte concentration to the sensor response (x→y) based on experimental data; The latter concerns the use of the calibration model in practical setting to obtain from the observed response the estimation of the unknown concentration (y→x). Second, the variability of the sensor responses tends to be heterogeneous as opposed to homogeneous, which is an assumption that classic statistical methods rely on.In light of the above, a computational resampling method was adapted in this work to address the machine learning (ML)-based inference issues (i.e., the uncertainty quantification of the estimated analyte concentrations). Built on the inference capability, a two-stage experimental design procedure was developed to guide the efficient sampling of calibration data via laboratory experiments.The ML-based inference and experimental design methods are integrated in the chemometric calibration procedure, which was applied on a simulated biosensor to demonstrate its efficiency over traditional methods. The sensor simulator is developed from the real experimental data for a paper-based lateral flow strip (PLFS) designed to measure in blood the diagnosis biomarkers for traumatic brain injury. PLFS is finding increasing applications in detection of various diseases in point-of-care testing settings. Figure 1

Efficient Sensor Calibration Via Machine Learning-Based Resampling Methods

A sensor’s performance relies on the calibration model functionally relating the sensor’s response (denoted as y) to the target analyte concentration (denoted as x). However, classic statistical methods are not able to adequately quantify the uncertainty of the x concentration estimates. In this work, a machine learning (ML)-based computational resampling method was adapted to address the uncertainty quantification issues, based on which a two-stage procedure was developed for efficient sampling and modeling of the calibration data obtained via laboratory experiments. The outputs of the procedure allow for not only a single-value estimate, but also a high-likelihood range for the underlying analyte concentration in an unknown sample being tested. The calibration procedure was applied on a simulated biosensor, and evaluated through large amount of validation data. The sensor simulator was developed from a paper-based lateral flow strip (PLFS) designed for traumatic brain injury (TBI) diagnosis.

Ecophysiological modeling of yield and yield components in winter wheat using hierarchical Bayesian analysis

AbstractYield components are widely recognized as drivers of wheat (Triticum aestivum L.) yield across environments and genotypes. In this study, we used a hierarchical Bayesian approach to model wheat grain yield in Oklahoma on an eco‐physiological basis using yield component traits thousand kernel weight (TKW) and nonyield biomass (NYB). The Bayesian approach allowed us to quantify uncertainties around the parameter values rather than obtaining a single value estimate for a parameter. The main objectives of this study were to (a) explain wheat yield as a function of component traits TKW and NYB, and thereby examine the implications for source‐sink balance; and (b) assess their association with weather conditions during key stages of wheat development. A secondary objective was to introduce Bayesian estimation for eco‐physiological modeling. Fifteen wheat genotypes planted in three locations in Oklahoma (Altus, Chickasha, and Lahoma) were evaluated across three harvest years (2017 to 2019), whereby the combination of location and year defined an environment. Results indicate that the environment explained a greater proportion of the variability in yield than genotypes or than genotype × environment (G × E) interaction; however, evidence for G × E was substantial. Yield was expected to increase with increasing TKW and NYB, which would suggest a source limitation to achieve potential yield. Yet, the contribution of early reproductive stage weather variables to the relationship between yield and NYB pointed in the direction of sink strength being compromised. In summary, our approach provides evidence for source‐sink co‐limitation in grain yield of this sample of hard red winter wheat genotypes.

A spectral approach to estimating the timescale-dependent uncertainty of paleoclimate records – Part 2: Application and interpretation

Abstract. Proxy climate records are an invaluable source of information about the earth's climate prior to the instrumental record. The temporal and spatial coverage of records continues to increase; however, these records of past climate are associated with significant uncertainties due to non-climate processes that influence the recorded and measured proxy values. Generally, these uncertainties are timescale dependent and correlated in time. Accounting for structure in the errors is essential for providing realistic error estimates for smoothed or stacked records, detecting anomalies, and identifying trends, but this structure is seldom accounted for. In the first of these companion articles, we outlined a theoretical framework for handling proxy uncertainties by deriving the power spectrum of proxy error components from which it is possible to obtain timescale-dependent error estimates. Here in Part 2, we demonstrate the practical application of this theoretical framework using the example of marine sediment cores. We consider how to obtain estimates for the required parameters and give examples of the application of this approach for typical marine sediment proxy records. Our new approach of estimating and providing timescale-dependent proxy errors overcomes the limitations of simplistic single-value error estimates. We aim to provide the conceptual basis for a more quantitative use of paleo-records for applications such as model–data comparison, regional and global synthesis of past climate states, and data assimilation.

Geosynthetic reinforcement stiffness for analytical and numerical modelling of reinforced soil structures

Many analytical and numerical analysis and design methods for geosynthetic-reinforced soil structures require a single-value (constant) estimate of reinforcement stiffness. However, geosynthetic reinforcement products are rate-dependent polymeric materials meaning that they exhibit time and strain-dependent behaviour under load. Hence, the appropriate selection of a constant (elastic) stiffness value requires careful consideration. A simple hyperbolic stiffness model is shown to be a useful approximation to the constant-load isochronous creep-strain behaviour of these materials at low load levels applicable to operational (serviceability) conditions of geosynthetic-reinforced soil structures. A large database of 606 creep tests on 89 different geosynthetic reinforcement products falling within seven different product categories was collected. From these data, isochronous stiffness values were determined for different combinations of duration of loading and strain level. Data from products falling within the same category were collected together to provide approximations linking the isochronous load-strain (creep) stiffness to the ultimate tensile strength of the material. These approximations are useful for analytical and numerical modelling particularly when parametric studies are undertaken to identify the sensitivity of model outcomes to reinforcement stiffness. Finally, three different geosynthetic-reinforced soil application examples are provided to demonstrate the important role of tensile stiffness on analysis and design outcomes.

Euclidpreparation

Forthcoming large photometric surveys for cosmology require precise and accurate photometric redshift (photo-z) measurements for the success of their main science objectives. However, to date, no method has been able to produce photo-zs at the required accuracy using only the broad-band photometry that those surveys will provide. An assessment of the strengths and weaknesses of current methods is a crucial step in the eventual development of an approach to meet this challenge. We report on the performance of 13 photometric redshift code single value redshift estimates and redshift probability distributions (PDZs) on a common set of data, focusing particularly on the 0.2 − 2.6 redshift range that theEuclidmission will probe. We designed a challenge using emulatedEucliddata drawn from three photometric surveys of the COSMOS field. The data was divided into two samples: one calibration sample for which photometry and redshifts were provided to the participants; and the validation sample, containing only the photometry to ensure a blinded test of the methods. Participants were invited to provide a redshift single value estimate and a PDZ for each source in the validation sample, along with a rejection flag that indicates the sources they consider unfit for use in cosmological analyses. The performance of each method was assessed through a set of informative metrics, using cross-matched spectroscopic and highly-accurate photometric redshifts as the ground truth. We show that the rejection criteria set by participants are efficient in removing strong outliers, that is to say sources for which the photo-zdeviates by more than 0.15(1 + z) from the spectroscopic-redshift (spec-z). We also show that, while all methods are able to provide reliable single value estimates, several machine-learning methods do not manage to produce useful PDZs. We find that no machine-learning method provides good results in the regions of galaxy color-space that are sparsely populated by spectroscopic-redshifts, for examplez > 1. However they generally perform better than template-fitting methods at low redshift (z < 0.7), indicating that template-fitting methods do not use all of the information contained in the photometry. We introduce metrics that quantify both photo-zprecision and completeness of the samples (post-rejection), since both contribute to the final figure of merit of the science goals of the survey (e.g., cosmic shear fromEuclid). Template-fitting methods provide the best results in these metrics, but we show that a combination of template-fitting results and machine-learning results with rejection criteria can outperform any individual method. On this basis, we argue that further work in identifying how to best select between machine-learning and template-fitting approaches for each individual galaxy should be pursued as a priority.

Strategic information sharing in online retailing under a consignment contract with revenue sharing

This work develops a general model of a two-echelon supply chain in which a dominant retailer interacts with a manufacturer via a consignment contract with revenue sharing. The manufacturer’s cost function is known only to him, whereas the retailer has only an estimation of this function, which is based on common knowledge. We formulate the interaction between the parties as a Stackelberg game in which the less informed party (the retailer) moves first. We investigate a strategic information-sharing policy of the manufacturer under general formulations of (i) the supply chain’s revenue and cost functions, and (ii) the manufacturer’s decision functions. Two models are considered: (i) a point-estimation model—the retailer relies on a single-valued estimation of the manufacturer’s cost function, based on her “best belief”; and (ii) an interval-estimation model—the retailer faces uncertainty with regard to the cost function and thus estimates its parameter values within intervals. We find a condition that distinguishes between a case in which it is optimal for both parties for the manufacturer to share his exact cost function and a case in which such information-sharing is not optimal for the manufacturer but is optimal for the retailer. In the interval-estimation model, equilibrium is obtained using a normative (probabilistic) approach as well as behavioral-decision criteria (max–max, max–min and regret minimization). Under a normative approach both hidden and known superiority of the manufacturer are considered. Finally, we use our model to analyze a supply chain of a mobile application.

3D Anatomy and Muscle Architecture of the Human Hand: new approaches for imaging and education

New three‐dimensional digital imaging technologies permit much richer reconstructions of soft‐tissue anatomy. We used algorithmic fiber‐tracking software, or 3D muscle tractography to model the muscle architecture of distal forearm and hand muscles via diffusible iodine contrast‐enhanced computed tomography (DiceCT) of a deidentified donor. Excellent soft‐tissue staining and high CT resolution (<50 μm) allowed for the visualization of many tissues difficult to simultaneously resolve using other imaging modalities, including muscle fascicles, integumentary collagen fibers, as well as bony trabeculae. Muscle fascicles were tracked and modeled as curved cylinders from which fascicle‐specific information, such as length and orientation, was gathered. By modeling numerous fascicles within a whole muscle, we collected muscle‐wide distributions, rather than single‐value estimates, of quantitative muscle architecture variables. These comprehensive data afforded by DiceCT and algorithmic fascicle modeling promise to aid in biomechanical modeling. Further, the volume and fascicle models produced by these methods are an excellent teaching resource in medical education.Support or Funding InformationNSF IOS 1457319, NSF EAR 1631684, Missouri Research Council, Life Sciences Research Fellowship, University of Missouri Department of Pathology and Anatomical SciencesThis abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

RADIO SOURCE DIRECTION FINDING IN WIDE FREQUENCY BAND USING CIRCULAR ANTENNA ARRAY

For the VHF broadband direction finder, coherent and incoherent direction finding algorithms for switched and non-switched connection of the antenna array (AR) to receiving device in single-signal and multi-signal direction finding modes are developed and investigated.Their synthesis is based on the methods of space-time theory of radio systems. Numerical calculation of the direction finding characteristics of the algorithms for different number of antenna array elements determines the operating range upper limiting frequency, in which this configuration provides single-value estimates of the azimuth and elevation angle. Statistical simulation modeling shows that for an odd number of antennas, the antenna array amplitudephase response is unique in a wider frequency band than for an even number of antennas. Due to this MUSIC based property applied in the space of antenna array elements, direction finding algorithm is developed for wide frequency band with several signals overlapping in frequency, with switched and non-switched AR connection to a radio receiver. It is shown that the use of ESPRIT and MUSIC methods in free-space diagram does not allow for direction finding in a wide frequency band with the antenna array fixed configuration. The results of the field studies of the developed algorithms are presented for the single-signal and multi-signal modes of operation, software and hardware implemented in the VHF radio direction finder. A comparative analysis of the developed algorithms with the known APs with fixed configuration is performed. It is shown that with the same AR configuration, it is the direction finding algorithm that determines the frequency range in which the direction finding is unique.

Short-Term Forecasting in the Trading Markets: Suggested Capture Intervals for Bloomberg™ FA-Downloads

General Context: Forecasting in the market trading world has been recognized as the core decision-making imperative. Archimedes remarked: Give Me a Fulcrum, and I Shall Move the World; the simile in the market trading world is; Give Me an Effective Forecasting Model and I can make Bill Gates and Sam Walton look like Paupers. An essential aspect of creating forecasts that can inform decision-makers are confidence intervals on forecasting projections.Research Focus: The Bloomberg™ terminals [BBT] provide a treasure-trove of historical data and also, on a selected basis, single-valued forecasting projections. However, these forecasts are single-value estimates, usually one or two periods-ahead only for the Income Statement variables. The focus of this research report is to produce an interval that can be: (1) simply oriented from reported BBT-information, and (2) used to better develop a decision-context for the information accessible through the FA-link of the BBT.Results: Using forecasting models in the OLS regression-class for: Time-Series, Y = f(X) versions, and a Moving Average Model, seven forecasting capture intervals were developed from randomly selected firms offered by the BBT. These capture intervals were used to produce standardized-capture-scalar-coefficients that were applied to the reported values offered by the BBT to create one-period-ahead capture intervals. This modeling protocol is referred to as the Empirical Interval Capture Model [EICM]. The EICM produces a capture interval with precision of about 30% where the capture rate was on the order of 90%.

Determination of confocal profile and curved focal plane for OCT mapping of the attenuation coefficient.

The attenuation coefficient has proven to be a useful tool in numerous biological applications, but accurate calculation is dependent on the characterization of the confocal effect. This study presents a method to precisely determine the confocal effect and its focal plane within a sample by examining the ratio of two optical coherence tomography (OCT) images. The method can be employed to produce a single-value estimate, or a 2D map of the focal plane accounting for the curvature or tilt within the sample. Furthermore, this method is applicable to data obtained with both high numerical aperture (NA) and low-NA lenses, thereby furthering the applicability of the attenuation coefficient to high-NA OCT data. We test and validate this method using standard samples of Intralipid 20% and 5%, improving the accuracy to 99% from 65% compared to the traditional method and preliminarily show applicability to real biological data of glioblastoma acquired in vivo in a murine model.

Interval Estimation for Conditional Failure Rates of Transmission Lines With Limited Samples

The estimation of the conditional failure rate (CFR) of an overhead transmission line (OTL) is essential for power system operational reliability assessment. It is hard to predict the CFR precisely, although great efforts have been made to improve the estimation accuracy. One significant difficulty is the lack of available outage samples, due to which the law of large numbers is no longer applicable and no convincing statistical result can be obtained. To address this problem, in this paper a novel imprecise probabilistic approach is proposed to estimate the CFR of an OTL. The imprecise Dirichlet model (IDM) is applied to establish the imprecise probabilistic relation between a single conditional variable and the failure rate of an OTL. Then a credal network is constructed to integrate the IDM estimation results corresponding to different conditional variables and infer the CFR. Instead of providing a single-valued estimation result, the proposed approach predicts the possible interval of the CFR in order to explicitly indicate the uncertainty of the estimation and more objectively represent the available knowledge. The proposed approach is illustrated by estimating the CFRs of two LGJ-300 transmission lines located in the same region; the test results validate its effectiveness.

Variability of HOMA and QUICKI insulin sensitivity indices

Assessment of insulin sensitivity based on a single measurement of insulin and glucose, is both easy to understand and simple to perform. The tests most often used are HOMA and QUICKI. The aim of this study was to assess the biological variability of estimates of insulin sensitivity using HOMA and QUICKI indices. After a 12-h fast, blood was sampled for insulin and glucose determination. Sampling lasted for 90 min with an intersample interval of 2 min. A total of 56 subjects were included in the study, and in nine subjects sampling was done before and after weight reduction, so total number of analyzed series was 65. To compute the reference value of the insulin sensitivity index, averages of all 46 insulin and glucose samples were used. We also computed point estimates (single value estimates) of the insulin sensitivity index based on the different number of insulin/glucose samples (1–45 consecutive samples). To compute the variability of point estimates a bootstrapping procedure was used using 1000 resamples for each series and for each number of samples used to average insulin and glucose. Using a single insulin/glucose sample HOMA variability was 26.18 ± 4.31%, and QUICKI variability was 3.30 ± 0.54%. For 10 samples variability was 11.99 ± 2.22% and 1.62 ± 0.31% respectively. Biological variability of insulin sensitivity indices is significant, and it can be reduced by increasing the number of samples. Oscillations of insulin concentration in plasma are the major cause of variability of insulin sensitivity indices.

One-Sample based Single-Valued Estimation of the Interface Profile from Intersubband Integrated Absorption Intensity Data

We prove the integrated absorption intensity due to intersubband optical transition in a quantum well (QW) to be a function of the correlation length of the interface roughness profile and independent of the roughness amplitude. We then develop a novel way to perform single-valued estimation of the interface roughness profile of QW from experiments conducted merely on one sample. The new method that we propose in this paper would be replicable and more economical than the traditional counterparts, which usually require at least two samples.

Correction of biased climate simulated by biased physics through parameter estimation in an intermediate coupled model

Imperfect physical parameterization schemes are an important source of model bias in a coupled model and adversely impact the performance of model simulation. With a coupled ocean-atmosphere-land model of intermediate complexity, the impact of imperfect parameter estimation on model simulation with biased physics has been studied. Here, the biased physics is induced by using different outgoing longwave radiation schemes in the assimilation and “truth” models. To mitigate model bias, the parameters employed in the biased longwave radiation scheme are optimized using three different methods: least-squares parameter fitting (LSPF), single-valued parameter estimation and geography-dependent parameter optimization (GPO), the last two of which belong to the coupled model parameter estimation (CMPE) method. While the traditional LSPF method is able to improve the performance of coupled model simulations, the optimized parameter values from the CMPE, which uses the coupled model dynamics to project observational information onto the parameters, further reduce the bias of the simulated climate arising from biased physics. Further, parameters estimated by the GPO method can properly capture the climate-scale signal to improve the simulation of climate variability. These results suggest that the physical parameter estimation via the CMPE scheme is an effective approach to restrain the model climate drift during decadal climate predictions using coupled general circulation models.

Frequency-change in DPOAE evoked by 1 s/octave sweeping primaries in newborns and adults

Distortion product otoacoustic emissions (DPOAE) in newborns and adults were evoked by sweeping primaries up and down in frequency at 1 s/octave. Sweeping up and down in frequency resulted in changes in the amplitude vs. frequency functions of the composite DPOAE and its two major components. In addition, DPOAE component phases differed slightly between the up- and down-swept conditions. The changes in amplitude vs. frequency functions were quantified using a covariate correlation technique, yielding single-valued estimates of the magnitude of the frequency changes. Separate analyses were performed for the entire DPOAE frequency range and split into low and high frequency ranges. There were consistent changes in newborn and adult composite DPOAEs and reflection components, but not generator components. Adults had significant frequency changes in the composite DPOAE for all frequency ranges and in the reflection component for the entire frequency range. Newborns had significant frequency change in the reflection component for all frequency ranges. Differences in frequency change between adults and newborns may stem from developmental changes in cochlear processing. Alignment of the component phase differences between the up- and down-swept conditions resulted in elimination of frequency-change in reconstructed composite DPOAEs.

Exploring the uncertainties in cancer risk assessment using the integrated probabilistic risk assessment (IPRA) approach.

Current methods for cancer risk assessment result in single values, without any quantitative information on the uncertainties in these values. Therefore, single risk values could easily be overinterpreted. In this study, we discuss a full probabilistic cancer risk assessment approach in which all the generally recognized uncertainties in both exposure and hazard assessment are quantitatively characterized and probabilistically evaluated, resulting in a confidence interval for the final risk estimate. The methodology is applied to three example chemicals (aflatoxin, N-nitrosodimethylamine, and methyleugenol). These examples illustrate that the uncertainty in a cancer risk estimate may be huge, making single value estimates of cancer risk meaningless. Further, a risk based on linear extrapolation tends to be lower than the upper 95% confidence limit of a probabilistic risk estimate, and in that sense it is not conservative. Our conceptual analysis showed that there are two possible basic approaches for cancer risk assessment, depending on the interpretation of the dose-incidence data measured in animals. However, it remains unclear which of the two interpretations is the more adequate one, adding an additional uncertainty to the already huge confidence intervals for cancer risk estimates.

Confidence interval for statistical power using a sample variance estimate

To improve estimation of statistical power by constructing its confidence interval. Statistical power is often computed using a sample variance estimated from previous studies. The sample variance deviates from the population variance and its use makes the estimated statistical power less accurate. The estimated power thus computed may be higher than the actual statistical power in the planned study. The standard deviation for body mass index is estimated by using the standard literature on weight-loss research. This is a methodology paper. Researchers avoid estimating the population variance in statistical power analysis by using the standardised effect size. The rule-of-thumb numbers for 'small', 'medium' and 'large' standardised effect sizes are .2,.5, and .8, but these numbers may not fit all the studies in different contexts. It is recommended that researchers start with a simple effect size that has some clinical importance and then estimate the population variance in running statistical power analysis. The use of an estimated variance in power analysis introduces uncertainty to the computed statistical power. To account for the uncertainty in estimating the variance, researchers can use the confidence interval to accurately assess the actual statistical power in planned hypothesis testing. The confidence interval provides a more realistic view of power than a single-value estimate of the nominal power does, which tends to be higher than the actual power in a clinical study. The authors have introduced a useful technique to construct a confidence interval on statistical power using a sample variance from a previous study. The method can be easily implemented to plan statistical power and sample size in a clinical study.

Single-valued estimation of the interface profile from intersubband absorption linewidth data

We study the ratio between different linewidths of the intersubband absorption in a quantum well. For roughness-related absorption, this ratio turns out to be independent of the roughness amplitude, so being a function of the correlation length only. Therefore, in contrast to the earlier belief, we may propose an efficient method for individual single-valued estimation of the two sizes of an interface profile from optical data. Instead of the simultaneous fitting of both sizes to the functional dependence of the linewidth at many experimental points, we perform a two-step fitting of (i) correlation length to the linewidth ratio at one point and then (ii) roughness amplitude to a linewidth at one point. This method is useful for experimental study of the interface morphology.