Uncertainty In Parameter Estimates Research Articles

Three-dimensional field of view and impact angle constrained guidance with terminal speed maximization

A three-dimensional strap-down seeker based multi-constrained guidance law for an interceptor is proposed in this paper to achieve near zero miss distance with minimal control effort (lateral acceleration) and interception time. When the interceptor is guided based on strap-down seeker measurements, the field of view limit throughout the flight trajectory is one of the major concerns to guarantee tracking of the target. To enhance the capability of warhead while approaching a target, the interceptor needs to ensure the desired impact angles and maximum speed at terminal time as well as various path inequality constraints throughout the trajectory, such as lateral acceleration limit and field of view limit. To meet these requirements, the proposed guidance is designed using a new extended version of the computationally efficient, suboptimal generalized model predictive static programming (GMPSP) technique in an unspecified final time framework. In addition, to make all the states available, to estimate parameter uncertainties and to filter out the sensor measurement noises, an extended Kalman filter based state and parameter estimation is incorporated with this proposed guidance law. Using simulation studies, the efficacy of the proposed GMPSP based suboptimal guidance method is shown and compared with that of the Chebyshev pseudo-spectral method as well. The extensive simulation results also demonstrate that the proposed robust suboptimal guidance design can perform well, in the presence of aerodynamic parameter uncertainties and sensor noises.

Accelerating Jackknife Resampling for the Canonical Polyadic Decomposition

The Canonical Polyadic (CP) tensor decomposition is frequently used as a model in applications in a variety of different fields. Using jackknife resampling to estimate parameter uncertainties is often desirable but results in an increase of the already high computational cost. Upon observation that the resampled tensors, though different, are nearly identical, we show that it is possible to extend the recently proposed Concurrent ALS (CALS) technique to a jackknife resampling scenario. This extension gives access to the computational efficiency advantage of CALS for the price of a modest increase (typically a few percent) in the number of floating point operations. Numerical experiments on both synthetic and real-world datasets demonstrate that the new workflow based on a CALS extension can be several times faster than a straightforward workflow where the jackknife submodels are processed individually.

GLUEOS: A high performance computing system based on the orchestration of containers for the GLUE parameter calibration of a crop growth model

The cultivar parameters of crop growth models are typically estimated through calibration procedures based on a global optimization method such as Generalized Likelihood Uncertainty Estimation (GLUE). A system that supports parallel processing would accelerate the calibration of cultivar parameters using GLUE, which requires a large amount of computation. In the present study, a framework for a distributed computing system was proposed to aid calibration of model parameters, which was referred to as Generalized Likelihood Uncertainty Estimation Orchestration System (GLUEOS). GLUEOS was designed to manage multiple containers in a distributed computing system and to provide a simple web-based interface. In a case study, the cultivar parameters of the CERES-Rice model were calibrated for a rice cultivar Shindongjin using GLUEOS. The calibration procedures were repeated 100 times to take into account the uncertainties of parameter estimates. The elapsed wall time for the parameter calibration process was compared between two computing systems including low end single board (LESB) and high end desktop (HEDT) computers. It was found that GLUEOS completed with less wall time for HEDT than LESB. However, the absolute time difference between these systems was considerably small on average, e.g., 22 s, when 32 containers were used for a single round of calibration procedure. The computing efficiency of GLUEOS was affected by the configurations for the containers, e.g., the number of containers per node. The mean value of calibrated parameter sets resulted in reliable estimate of heading dates for both calibration and validation datasets. These results suggested that GLUEOS would allow for calibration of cultivar parameters with less wall time for computation and minimum expertise required for distributed computing. Utilizing GLUEOS with other crop models would facilitate a wider range of studies for any research that requires parameter calibration.

Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics

Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

Bayesian Nonlinear Models for Repeated Measurement Data: An Overview, Implementation, and Applications

Nonlinear mixed effects models have become a standard platform for analysis when data is in the form of continuous and repeated measurements of subjects from a population of interest, while temporal profiles of subjects commonly follow a nonlinear tendency. While frequentist analysis of nonlinear mixed effects models has a long history, Bayesian analysis of the models has received comparatively little attention until the late 1980s, primarily due to the time-consuming nature of Bayesian computation. Since the early 1990s, Bayesian approaches for the models began to emerge to leverage rapid developments in computing power, and have recently received significant attention due to (1) superiority to quantify the uncertainty of parameter estimation; (2) utility to incorporate prior knowledge into the models; and (3) flexibility to match exactly the increasing complexity of scientific research arising from diverse industrial and academic fields. This review article presents an overview of modeling strategies to implement Bayesian approaches for the nonlinear mixed effects models, ranging from designing a scientific question out of real-life problems to practical computations.

Simultaneously estimating food web connectance and structure with uncertainty.

Food web models explain and predict the trophic interactions in a food web, and they can infer missing interactions among the organisms. The allometric diet breadth model (ADBM) is a food web model based on the foraging theory. In the ADBM, the foraging parameters are allometrically scaled to body sizes of predators and prey. In Petchey et al. (Proceedings of the National Academy of Sciences, 2008; 105: 4191), the parameterization of the ADBM had two limitations: (a) the model parameters were point estimates and (b) food web connectance was not estimated.The novelty of our current approach is: (a) We consider multiple predictions from the ADBM by parameterizing it with approximate Bayesian computation, to estimate parameter distributions and not point estimates. (b) Connectance emerges from the parameterization, by measuring model fit using the true skill statistic, which takes into account prediction of both the presences and absences of links.We fit the ADBM using approximate Bayesian computation to 12 observed food webs from a wide variety of ecosystems. Estimated connectance was consistently greater than previously found. In some of the food webs, considerable variation in estimated parameter distributions occurred and resulted in considerable variation (i.e., uncertainty) in predicted food web structure.These results lend weight to the possibility that the observed food web data is missing some trophic links that do actually occur. It also seems likely that the ADBM likely predicts some links that do not exist. The latter could be addressed by accounting in the ADBM for additional traits other than body size. Further work could also address the significance of uncertainty in parameter estimates for predicted food web responses to environmental change.

Parameter sensitivity analysis of a physico-chemical lithium-ion battery model with combined discharge voltage and electrochemical impedance data

Physico-chemical battery models are capable of better simulation of lithium-ion cell behaviour due to their more physically descriptive modelling approach using many physical parameters. Accuracy of simulations highly depend on the correct identification of parameters. However, large parameter estimation uncertainties and model complexities increase the model parameterization difficulties. Therefore, pre-analysis of parameter sensitivities to model outputs can greatly help determining the best conditions and techniques for identifying many parameters with better accuracy. This work demonstrates a next step in improving the parameter identification accuracy by combined parameter sensitivity analysis of both discharge voltage and EIS data. A commercially available NMC-graphite based lithium-ion cell is modelled and 26 physical parameters are analysed for their sensitivity. For discharge voltage, capacity-related and non-capacity-related parameters clearly show different sensitivity patterns at different C-rates and depth of discharge regions. Moreover, non-dimensional EIS spectra states are introduced for correct identification of impedance-based parameter sensitivities and accurate parameter sensitivities are observed matching the frequency bands truly affected by the parameter kinetics. The ranked analysis of the parameter sensitivities clearly demonstrate the ability to identify many discharge voltage insensitive parameters using impedance measurements, which would greatly increase the number of identifiable parameters of a physico-chemical battery model.

An adaptive remaining useful life prediction approach for single battery with unlabeled small sample data and parameter uncertainty

Accurate prediction of the remaining useful life (RUL) of lithium-ion battery is of great significance for the reliability of electronic equipment. In the conventional approaches, there are notable challenges in the RUL prediction for a single battery lacking historical data. To predict the battery’s RUL under the condition of unlabeled small sample data and to describe the uncertainty of the parameter estimation in the degradation model, a novel adaptive approach based on Kalman filter and expectation maximum with Rauch–Tung–Striebel (KF-EM-RTS) is proposed to predict the battery’s RUL. Specifically, without RUL labels and offline training, an online KF adaptive-update model based on the Wiener process is proposed for a single battery, in which the uncertainty of parameter estimation is described. Furthermore, the unknown model parameters can be adaptively estimated using EM-RTS to overcome the constraints of strong Markov characteristics, the convergence of which is proved. The real-world battery dataset provided by NASA Ames research center is applied to verify the proposed RUL prediction approach. Experimental results show that the proposed approach outperforms the existing conventional data-driven approaches for predicting the battery’s RUL.

EVALUATING THE POTENTIAL OF DESIS TO INFER PLANT TAXONOMICAL AND FUNCTIONAL DIVERSITIES IN EUROPEAN FORESTS

Abstract. Tackling the accelerated human-induced biodiversity loss requires tools able to map biodiversity and its changes globally. Remote sensing (RS) offers unique capabilities of characterizing Earth surfaces; therefore, it could map plant biodiversity continuously and globally. This approach is supported by the Spectral Variation Hypothesis (SVH), which states that spectra and species (taxonomic and trait) diversities are linked through environmental heterogeneity. In this work, we evaluate the capability of the DESIS hyperspectral imager to capture plant diversity patterns as measured in dedicated plots of the network FunDivEUROPE. We computed functional and taxonomical diversity metrics from field taxonomic, structural, and foliar measurements in vegetation plots sampled in Spain and Romania. In addition, we also computed functional diversity metrics both from the DESIS reflectance factors and from vegetation parameters estimated via inversion of a radiative transfer model. Results showed that only metrics computed from spectral reflectance were able to capture taxonomic variability in the area. However, the lack of sensitivity was related to the insufficient plot size and the lack of spatial match between remote sensing and field data, but also the differences between the information contained in the field traits and remote sensing data, and the potential uncertainties in the remote estimates of vegetation parameters. Thus, while DESIS showed some sensitivity to plant diversity, further efforts are needed to deploy suitable biodiversity evaluation and validation plots and networks that support the development of biodiversity remote sensing products.

ESCROpath, a Bayesian mixing model to quantify diets and trophic flows in aquatic food webs

Abstract Food‐web modelling is a key tool to provide a global and comprehensive knowledge on community structure, biodiversity and ecosystem processes and functioning. In particular, it allows computing integrative and holistic indices describing food web characteristics, topology and functioning. However, one of the main sources of uncertainty in most food‐web models is the estimation of diet matrices. In the present work, we propose an innovative approach that combines (a) a Bayesian mixing model using both isotopes and contaminants as chemical tracers with (b) classical mass‐balance equations. This dual approach allows the simultaneous estimation of diet composition, isotopic enrichment, contaminant biomagnification, and contaminants and biomass flows in the whole food web. This original model named ESCROpath also provides food‐web indices derived from ecological network analysis (ENA). As a case study, the approach was implemented in the Gironde estuarine food web (SW France) for which isotopes, contaminants and trophic data exist. Two sets of priors were constructed accounting for more or less uncertainty in trophic parameter estimates. Outputs were compared with previous published Ecopath results. A constrained calibration led to very similar outputs as Ecopath (which shows that the method is able to find the initial set of parameters if it is forced to do so), whereas a free calibration led to slight differences in trophic parameters and ENA indice estimations (which shows that the Ecopath solution was not fully optimal). Quite different diet matrices and estimations of flows distribution within the food web can thus be obtained. ESCROpath is an original flexible food‐web modelling tool that, for the first time, makes it possible to go from a model mainly built on an ‘estimate’ of the parameters based on expert knowledge (which constitutes the main criticism formulated against Ecopath) to a statistical Bayesian framework for the estimation of the trophic parameters. It thus provides a very integrated framework for food‐web modelling by estimating simultaneously trophic parameters, diet compositions and trophic enrichment/magnification factors. By doing this, it notably provides reliable and robust uncertainty estimations for output parameters.

Strong-lensing source reconstruction with variationally optimized Gaussian processes

ABSTRACT Strong-lensing images provide a wealth of information both about the magnified source and about the dark matter distribution in the lens. Precision analyses of these images can be used to constrain the nature of dark matter. However, this requires high-fidelity image reconstructions and careful treatment of the uncertainties of both lens mass distribution and source light, which are typically difficult to quantify. In anticipation of future high-resolution data sets, in this work we leverage a range of recent developments in machine learning to develop a new Bayesian strong-lensing image analysis pipeline. Its highlights are (a) a fast, GPU-enabled, end-to-end differentiable strong-lensing image simulator; (b) a new, statistically principled source model based on a computationally highly efficient approximation to Gaussian processes that also takes into account pixellation; and (c) a scalable variational inference framework that enables simultaneously deriving posteriors for tens of thousands of lens and source parameters and optimizing hyperparameters via stochastic gradient descent. Besides efficient and accurate parameter estimation and lens model uncertainty quantification, the main aim of the pipeline is the generation of training data for targeted simulation-based inference of dark matter substructure, which we will exploit in a companion paper.

State estimation-based robust optimal control of influenza epidemics in an interactive human society

This paper presents a state estimation-based robust optimal control strategy for influenza epidemics in an interactive human society in the presence of modeling uncertainties. Interactive society is influenced by random entrance of individuals from other human societies whose effects can be modeled as a non-Gaussian noise. Since only the number of exposed and infected humans can be measured, the states of the influenza epidemics are first estimated by an extended maximum correntropy Kalman filter (EMCKF) to provide a robust state estimation in the presence of the non-Gaussian noise. An online quadratic program (QP) optimization is then synthesized subject to a robust control Lyapunov function (RCLF) to minimize susceptible and infected humans, while minimizing and bounding the rates of vaccination and antiviral treatment. The main contribution of this work is twofold. First, the joint QP-RCLF-EMCKF strategy meets multiple design specifications such as state estimation, tracking, pointwise control optimality, and robustness to parameter uncertainty and state estimation errors that have not been achieved simultaneously in previous studies. Second, the uniform ultimate boundedness (UUB)/convergence of all error trajectories is guaranteed by using a Lyapunov stability argument. Simulation results show that the proposed approach achieves appropriate tracking and state estimation performance with good robustness.

Hierarchical Bayesian modeling framework for model updating and robust predictions in structural dynamics using modal features

The hierarchical Bayesian modeling (HBM) framework has recently been developed to tackle the uncertainty quantification and propagation in structural dynamics inverse problems. This new framework characterizes the ensemble variability of structural parameters observed over multiple datasets together with the estimation uncertainty obtained based on the discrepancy between the measured and model outputs. The present paper expands on this framework, developing it further for model inference based on modal features. It generalizes the HBM framework by considering an additional hyper distribution to characterize the uncertainty of prediction error variances across different datasets. Moreover, asymptotic approximations are integrated into the HBM framework to simplify the computation of the posterior distribution of hyper-parameters, providing insights on different sources of uncertainties and the relation of the estimates of the hyper-parameters with the parameter variability and estimation uncertainties. Conditions are presented under which the approximations are expected to be accurate. Introducing the HBM formulation is beneficial, particularly for the propagation of uncertainty based on both structural and prediction error parameters providing reasonable uncertainty bounds. The posterior uncertainty of the structural and prediction error parameters is propagated to estimate data-informed output quantities of interests, including failure probabilities, which offers robustness to the variability over datasets. The proposed approximations are tested and verified using simulated and experimental examples. The effects of the uncertainty due to dataset variability and the prediction error uncertainty are illustrated in these examples.

Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods.

Identifying the reactions that govern a dynamical biological system is a crucial but challenging task in systems biology. In this work, we present a data-driven method to infer the underlying biochemical reaction system governing a set of observed species concentrations over time. We formulate the problem as a regression over a large, but limited, mass-action constrained reaction space and utilize sparse Bayesian inference via the regularized horseshoe prior to produce robust, interpretable biochemical reaction networks, along with uncertainty estimates of parameters. The resulting systems of chemical reactions and posteriors inform the biologist of potentially several reaction systems that can be further investigated. We demonstrate the method on two examples of recovering the dynamics of an unknown reaction system, to illustrate the benefits of improved accuracy and information obtained.

Hadronization model tuning in genie v3

The GENIE neutrino Monte Carlo describes neutrino-induced hadronization with an effective model, known as AGKY, which is interfaced with PYTHIA at high invariant mass. Only the low-mass AGKY model parameters were extracted from hadronic shower data from the FNAL 15 ft and BEBC experiments. In this paper, the first hadronization tune on averaged charged multiplicity data from deuterium and hydrogen bubble chamber experiments is presented, with a complete estimation of parameter uncertainties. A partial tune on deuterium data only highlights the tensions between hydrogen and deuterium datasets.

Quantifying the effect of probability model misspecification in seismic collapse risk assessment

One of the main steps in probabilistic seismic collapse risk assessment is estimating the fragility function parameters. The maximum likelihood estimation (MLE) approach, which is widely used for this purpose, contains the underlying assumption that the likelihood function is known to follow a specified parametric probability distribution. However, this assumed distribution may not always be consistent with the “true” probability distribution of the collapse data. This paper implements the Information matrix equivalence theorem to identify the presence of model misspecification i.e., if the assumed collapse probability distribution is, in fact, the “true” one. In the presence of model misspecification, the fragility parameter estimates continue to be asymptotically normally distributed but the variance–covariance matrix is no longer equal to the inverse of the Fisher’s Information matrix. To increase the robustness of the variance–covariance matrix, the Huber–White sandwich estimator is implemented. Using collapse data from eight woodframe buildings, the effect of model misspecification on fragility parameter estimates and collapse rate is quantified. For the considered building cases, the parameter estimation uncertainty in the collapse risk did not increase when the “sandwich” estimator was used compared to when probability model misspecification was not considered (i.e., using MLE). The proposed framework should be used to further investigate the issue of probability model misspecification as it relates to fragility parameter estimation since only a single construction type (woodframe buildings) and limit state (collapse) was considered in the current study.

Computer Model Calibration with Time Series Data Using Deep Learning and Quantile Regression

Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data such as large time series due to the difficulty in building an emulator and the non-identifiability between effects from input parameters and data-model discrepancy. To overcome these challenges we propose a new calibration framework based on a deep neural network (DNN) with long-short term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the 'learning with noise' idea we train our DNN model to filter out the effects from data model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with WRF-hydro model we show that our approach can yield accurate point estimates and well calibrated interval estimates for input parameters.

Information Based Diagnostic for Genetic Variance Parameter Estimation in Multi-Environment Trials.

Plant breeding programs evaluate varieties in series of field trials across years and locations, referred to as multi-environment trials (METs). These are an essential part of variety evaluation with the key aim of the statistical analysis of these datasets to accurately estimate the variety by environment (VE) effects. It has previously been thought that the number of varieties in common between environments, referred to as “variety connectivity,” was a key driver of the reliability of genetic variance parameter estimation and that this in turn affected the reliability of predictions of VE effects. In this paper we have provided the link between the objectives of this work and those in model-based experimental design. We propose the use of the -optimality criterion as a diagnostic to capture the information available for the residual maximum likelihood (REML) estimation of the genetic variance parameters. We demonstrate the methods for a dataset with pedigree information as well as evaluating the performance of the diagnostic using two simulation studies. This measure is shown to provide a superior diagnostic to the traditional connectivity type measure in the sense of better forecasting the uncertainty of genetic variance parameter estimates.

Systematically Measuring Ultra-diffuse Galaxies (SMUDGes). II. Expanded Survey Description and the Stripe 82 Catalog

Abstract We present 226 large ultra-diffuse galaxy (UDG) candidates (r e > 5.″3, μ 0,g > 24 mag arcsec−2) in the SDSS Stripe 82 region recovered using our improved procedure developed in anticipation of processing the entire Legacy Surveys footprint. The advancements include less constrained structural parameter fitting, expanded wavelet filtering criteria, consideration of Galactic dust, estimates of parameter uncertainties and completeness based on simulated sources, and refinements of our automated candidate classification. We have a sensitivity ∼1 mag fainter in μ 0,g than the largest published catalog of this region. Using our completeness-corrected sample, we find that (1) there is no significant decline in the number of UDG candidates as a function of μ 0,g to the limit of our survey (∼26.5 mag arcsec−2); (2) bluer candidates have smaller Sérsic n; (3) most blue (g–r < 0.45 mag) candidates have μ 0,g ≲ 25 mag arcsec−2 and will fade to populate the UDG red sequence we observe to ∼26.5 mag arcsec−2; (4) any red UDGs that exist significantly below our μ 0,g sensitivity limit are not descendent from blue UDGs in our sample; and (5) candidates with lower μ 0,g tend to smaller n. We anticipate that the final SMUDGes sample will contain ∼30 × as many candidates.

Understanding the Effects of Systematics in Exoplanetary Atmospheric Retrievals

Abstract Retrieval of exoplanetary atmospheric properties from their transmission spectra commonly assumes that the errors in the data are Gaussian and independent. However, non-Gaussian noise can occur due to instrumental or stellar systematics and the merging of discrete data sets. We investigate the effect of correlated noise and constrain the potential biases incurred in the retrieved posteriors. We simulate multiple noise instances of synthetic data and perform retrievals to obtain statistics of the goodness of retrieval for varying noise models. We find that correlated noise allows for overfitting the spectrum, thereby yielding a better goodness of fit on average but degrading the overall accuracy of retrievals. In particular, correlated noise can manifest as an apparent non-Rayleigh slope in the optical range, leading to an incorrect estimate of cloud/haze parameters. We also find that higher precision causes correlated results to be further off from the input values in terms of estimated errors. Finally, we show that while correlated noise cannot be reliably distinguished with Hubble Space Telescope observations, inferring its presence and strength may be possible with James Webb Space Telescope observations. As such, we emphasize that caution must be taken in analyzing retrieved posteriors and that estimated parameter uncertainties are best understood as lower limits.