Uncertainty In Parameter Estimates Research Articles

Indian Buffet process factor model for counterfactual analysis

This article proposes a factor model-based counterfactual analysis. We explicitly estimate the underlying factor structure of the outcome variables and estimate the counterfactual values of the unit subject to an intervention. With the help of the non-parametric Bayesian Indian Buffet Process prior, our approach is capable of exploring heterogeneous factor exposures, and the number of latent factors is endogenously determined in the estimation process. The flexible Markov Chain Monte Carlo algorithm utilizes the maximal intervention-free information provided by the data, whereas the original synthetic control only uses pre-intervention data. The counterfactual values are estimated by simulating from the posterior predictive distribution so that we can integrate out any parameter estimation uncertainty. We also calculate the posterior predictive upper- and lower-quantile bounds for inference. The two applications, namely California’s Tobacco Control Program and the West German Reunification, demonstrate the usefulness of our approach compared to the synthetic control method and the elastic net model. The Monte Carlo simulation study also shows the robustness of our approach with respect to nonlinear dynamics in the underlying factor process.

Robust Nonlinear Control with Estimation of Disturbances and Parameter Uncertainties for UAVs and Integrated Brushless DC Motors

Robust Nonlinear Control with Estimation of Disturbances and Parameter Uncertainties for UAVs and Integrated Brushless DC Motors

Reducing thermal noise in high-resolution quantitative magnetic resonance imaging rotating frame relaxation mapping of the human brain at 3 T.

Quantitative maps of rotating frame relaxation (RFR) time constants are sensitive and useful magnetic resonance imaging tools with which to evaluate tissue integrity in vivo. However, to date, only moderate image resolutions of 1.6 x 1.6 x 3.6 mm3 have been used for whole-brain coverage RFR mapping in humans at 3 T. For more precise morphometrical examinations, higher spatial resolutions are desirable. Towards achieving the long-term goal of increasing the spatial resolution of RFR mapping without increasing scan times, we explore the use of the recently introduced Transform domain NOise Reduction with DIstribution Corrected principal component analysis (T-NORDIC) algorithm for thermal noise reduction. RFR acquisitions at 3 T were obtained from eight healthy participants (seven males and one female) aged 52 ± 20 years, including adiabatic T1ρ, T2ρ, and nonadiabatic Relaxation Along a Fictitious Field (RAFF) in the rotating frame of rank n = 4 (RAFF4) with both 1.6 x 1.6 x 3.6 mm3 and 1.25 x 1.25 x 2 mm3 image resolutions. We compared RFR values and their confidence intervals (CIs) obtained from fitting the denoised versus nondenoised images, at both voxel and regional levels separately for each resolution and RFR metric. The comparison of metrics obtained from denoised versus nondenoised images was performed with a two-sample paired t-test and statistical significance was set at pless than 0.05 after Bonferroni correction for multiple comparisons. The use of T-NORDIC on the RFR images prior to the fitting procedure decreases the uncertainty of parameter estimation (lower CIs) at both spatial resolutions. The effect was particularly prominent at high-spatial resolution for RAFF4. Moreover, T-NORDIC did not degrade map quality, and it had minimal impact on the RFR values. Denoising RFR images with T-NORDIC improves parameter estimation while preserving the image quality and accuracy of all RFR maps, ultimately enabling high-resolution RFR mapping in scan times that are suitable for clinical settings.

Treating gaps and biases in biodiversity data as a missing data problem.

Big biodiversity data sets have great potential for monitoring and research because of their large taxonomic, geographic and temporal scope. Such data sets have become especially important for assessing temporal changes in species' populations and distributions. Gaps in the available data, especially spatial and temporal gaps, often mean that the data are not representative of the target population. This hinders drawing large-scale inferences, such as about species' trends, and may lead to misplaced conservation action. Here, we conceptualise gaps in biodiversity monitoring data as a missing data problem, which provides a unifying framework for the challenges and potential solutions across different types of biodiversity data sets. We characterise the typical types of data gaps as different classes of missing data and then use missing data theory to explore the implications for questions about species' trends and factors affecting occurrences/abundances. By using this framework, we show that bias due to data gaps can arise when the factors affecting sampling and/or data availability overlap with those affecting species. But a data set per se is not biased. The outcome depends on the ecological question and statistical approach, which determine choices around which sources of variation are taken into account. We argue that typical approaches to long-term species trend modelling using monitoring data are especially susceptible to data gaps since such models do not tend to account for the factors driving missingness. To identify general solutions to this problem, we review empirical studies and use simulation studies to compare some of the most frequently employed approaches to deal with data gaps, including subsampling, weighting and imputation. All these methods have the potential to reduce bias but may come at the cost of increased uncertainty of parameter estimates. Weighting techniques are arguably the least used so far in ecology and have the potential to reduce both the bias and variance of parameter estimates. Regardless of the method, the ability to reduce bias critically depends on knowledge of, and the availability of data on, the factors creating data gaps. We use this review to outline the necessary considerations when dealing with data gaps at different stages of the data collection and analysis workflow.

Evaluating the robustness of parameter estimates in cognitive models: A meta-analytic review of multinomial processing tree models across the multiverse of estimation methods.

Researchers have become increasingly aware that data-analysis decisions affect results. Here, we examine this issue systematically for multinomial processing tree (MPT) models, a popular class of cognitive models for categorical data. Specifically, we examine the robustness of MPT model parameter estimates that arise from two important decisions: the level of data aggregation (complete-pooling, no-pooling, or partial-pooling) and the statistical framework (frequentist or Bayesian). These decisions span a multiverse of estimation methods. We synthesized the data from 13,956 participants (164 published data sets) with a meta-analytic strategy and analyzed the magnitude of divergence between estimation methods for the parameters of nine popular MPT models in psychology (e.g., process-dissociation, source monitoring). We further examined moderators as potential sources of divergence. We found that the absolute divergence between estimation methods was small on average (<.04; with MPT parameters ranging between 0 and 1); in some cases, however, divergence amounted to nearly the maximum possible range (.97). Divergence was partly explained by few moderators (e.g., the specific MPT model parameter, uncertainty in parameter estimation), but not by other plausible candidate moderators (e.g., parameter trade-offs, parameter correlations) or their interactions. Partial-pooling methods showed the smallest divergence within and across levels of pooling and thus seem to be an appropriate default method. Using MPT models as an example, we show how transparency and robustness can be increased in the field of cognitive modeling. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Effects of probability model misspecification on the number of ground motions required for seismic performance assessment

The number of ground motions used in nonlinear response history analysis (NRHA) determines the precision of the parameter estimates obtained in seismic performance assessments. While this issue has been extensively studied in the earthquake engineering literature, the relationship of probability model misspecification to parameter estimation uncertainty, and the implication to the required number of ground motions needed for NRHA, has not been examined. Probability model misspecification has the potential to increase estimation uncertainty and hence requires a greater number of ground motions to achieve the same precision compared to when misspecification is disregarded. This study develops a procedure to determine the required number of ground motions in seismic code-prescriptive and risk-based assessments with possible probability model misspecification. Specifically, we employ the quasi-maximum likelihood estimation (QMLE), which is robust to probability model misspecification, to evaluate estimation uncertainty. The QMLE approach is applied to an archetype California bridge under the two seismic assessment scenarios. In the code-prescriptive assessment, misspecification errors are identified for dispersion estimates of the bridge column ductility demand. In the most extreme case of the risk-based evaluation, misspecification increases the estimation uncertainty of the mean annual frequency of exceeding a limit state by as much as three times, which substantially increases the required number of ground motions. Based on the findings from this study, we advocate for the use of QMLE to detect and rectify the implications of model misspecification to estimation uncertainty and the number of ground motions used in probabilistic seismic performance assessments.

A comprehensive framework for stochastic calibration and sensitivity analysis of large-scale groundwater models

Abstract. We introduce a comprehensive and robust theoretical framework and operational workflow that can be employed to enhance our understanding, modeling and management capability of complex heterogeneous large-scale groundwater systems. Our framework encapsulates key components such as the three-dimensional nature of groundwater flows, river–aquifer interactions, probabilistic reconstruction of three-dimensional spatial distributions of geomaterials and associated properties across the subsurface, multi-objective optimization for model parameter estimation through stochastic calibration, and informed global sensitivity analysis (GSA). By integrating these components, we effectively consider the inherent uncertainty associated with subsurface system characterizations as well as their interactions with surface waterbodies. The approach enables us to identify parameters impacting diverse system responses. By employing a coevolutionary optimization algorithm, we ensure efficient model parameterization, facilitating simultaneous and informed optimization of the defined objective functions. Additionally, estimation of parameter uncertainty naturally leads to quantification of uncertainty in system responses. The methodology is designed to increase our knowledge of the dynamics of large-scale groundwater systems. It also has the potential to guide future data acquisition campaigns through an informed global sensitivity analysis. We demonstrate the effectiveness of our proposed methodology by applying it to the largest groundwater system in Italy. We address the challenges posed by the characterization of the heterogeneous spatial distribution of subsurface attributes across large-scale three-dimensional domains upon incorporating a recent probabilistic hydrogeological reconstruction specific to the study case. The system considered faces multiple challenges, including groundwater contamination, seawater intrusion, and water scarcity. Our study offers a promising modeling strategy applicable to large-scale subsurface systems and valuable insights into groundwater flow patterns that can then inform effective system management.

Evaluating the utility of multi-gene, multi-disease population-based panel testing accounting for uncertainty in penetrance estimates.

Panel germline testing allows for the efficient detection of deleterious variants for multiple conditions, but the benefits and harms of identifying these variants are not always well understood. We present a multi-gene, multi-disease aggregate utility formula that allows the user to consider adding or removing each gene in a panel based on variant frequency, estimated penetrances, and subjective disutilities for testing positive but not developing the disease and testing negative but developing the disease. We provide credible intervals for utility that reflect uncertainty in penetrance estimates. Rare, highly penetrant deleterious variants tend to contribute positive net utilities for a wide variety of user-specified disutilities, even when accounting for parameter estimation uncertainty. However, the clinical utility of deleterious variants with moderate, uncertain penetrance depends more on assumed disutilities. The decision to include a gene on a panel depends on variant frequency, penetrance, and subjective utilities and should account for uncertainties around these factors.

Identifiability investigation of within-host models of acute virus infection.

Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we use four mathematical models of influenza A infection with increased degrees of biological realism. We test the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refine the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we present insight into the sources of uncertainty in parameter estimation and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.

Levelized cost of electricity in renewable energy communities: Uncertainty propagation analysis

Renewable Energy Communities (RECs) are being deployed all around the World as a technically feasible solution to decreasing users' dependence on fossil fuels. Several demonstration facilities have shown their potential to provide final consumers with clean energy and all associated environmental benefits. However, the economic evaluation of these systems as a whole set is more complex than evaluating generation technologies individually, which can be considered a barrier, and it may be more complicated to calculate its uncertainty with precision. This paper deals with this challenge and adapts a model for the evaluation of the global Levelized Cost of Electricity (LCOE) of a polygeneration microgrid to the characteristics of a typical REC, allowing the assessment of the distribution of the LCOE depending on the uncertainty of the input parameters. Thanks to its simple analytical formulation, the proposed model, that can be used for any combination of technologies (both renewable and conventional), provides relevant information on uncertainty propagation in a symbolic way that avoids the need to run numerical simulations or make assumptions on the distribution of the random input parameters. A case study has been presented, considering a typical small electrical REC with photovoltaic plants and micro wind turbines. Although the model can be defined to any market, as a representative example, it has been evaluated according to the current Spanish and Italian regulations, which are analyzed in depth with reference to the scientific literature. Results show that uncertainties in parameter estimates give rise to a very large scatter in the LCOE, pointing out a set of quantities whose role is crucial for a reliable estimate, among which electricity purchase and selling prices, yearly power load, and self-consumption / virtually-shared energy rates stand out.

Nonstandard Errors

ABSTRACTIn statistics, samples are drawn from a population in a data‐generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence‐generating process (EGP). We claim that EGP variation across researchers adds uncertainty—nonstandard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for more reproducible or higher rated research. Adding peer‐review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants.

CovXtreme : MATLAB software for non-stationary penalised piecewise constant marginal and conditional extreme value models

The covXtreme software provides functionality for estimation of marginal and conditional extreme value models, non-stationary with respect to covariates, and environmental design contours. Generalised Pareto (GP) marginal models of peaks over threshold are estimated, using a piecewise-constant representation for the variation of GP threshold and scale parameters on the (potentially multidimensional) covariate domain of interest. The conditional variation of one or more associated variates, given a large value of a single conditioning variate, is described using the conditional extremes model of Heffernan and Tawn (2004), the slope term of which is also assumed to vary in a piecewise constant manner with covariates. Optimal smoothness of marginal and conditional extreme value model parameters with respect to covariates is estimated using cross-validated roughness-penalised maximum likelihood estimation. Uncertainties in model parameter estimates due to marginal and conditional extreme value threshold choice, and sample size, are quantified using a bootstrap resampling scheme. Estimates of environmental contours using various schemes, including the direct sampling approach of Huseby et al. 2013, are calculated by simulation or numerical integration under fitted models. The software was developed in MATLAB for metocean applications, but is applicable generally to multivariate samples of peaks over threshold data. The software and case study data can be downloaded from GitHub, with an accompanying user guide.

Bayesian Mechanistic Inference, Statistical Mechanics, and a New Era for Monte Carlo.

On the one hand, much of computational chemistry is concerned with "bottom-up" calculations which elucidate observable behavior starting from exact or approximated physical laws, a paradigm exemplified by typical quantum mechanical calculations and molecular dynamics simulations. On the other hand, "top down" computations aiming to formulate mathematical models consistent with observed data, e.g., parametrizing force fields, binding or kinetic models, have been of interest for decades but recently have grown in sophistication with the use of Bayesian inference (BI). Standard BI provides an estimation of parameter values, uncertainties, and correlations among parameters. Used for "model selection," BI can also distinguish between model structures such as the presence or absence of individual states and transitions. Fortunately for physical scientists, BI can be formulated within a statistical mechanics framework, and indeed, BI has led to a resurgence of interest in Monte Carlo (MC) algorithms, many of which have been directly adapted from or inspired by physical strategies. Certain MC algorithms─notably procedures using an "infinite temperature" reference state─can be successful in a 5-20 parameter BI context which would be unworkable in molecular spaces of 103 coordinates and more. This Review provides a pedagogical introduction to BI and reviews key aspects of BI through a physical lens, setting the computations in terms of energy landscapes and free energy calculations and describing promising sampling algorithms. Statistical mechanics and basic probability theory also provide a reference for understanding intrinsic limitations of Bayesian inference with regard to model selection and the choice of priors.

Addressing age measurement errors in fish growth estimation from length-stratified samples.

Fish growth models are crucial for fisheries stock assessments and are commonly estimated using fish length-at-age data. This data is widely collected using length-stratified age sampling (LSAS), a cost-effective two-phase response-selective sampling method. The data may contain age measurement errors (MEs). We propose a methodology that accounts for both LSAS and age MEs to accurately estimate fish growth. The proposed methods use empirical proportion likelihood methodology for LSAS and the structural errors in variables methodology for age MEs. We provide a measure of uncertainty for parameter estimates and standardized residuals for model validation. To model the age distribution, we employ a continuation ratio-logit model that is consistent with the random nature of the true age distribution. We also apply a discretization approach for age and length distributions, which significantly improves computational efficiency and is consistent with the discrete age and length data typically encountered in practice. Our simulation study shows that neglecting age MEs can lead to significant bias in growth estimation, even with small but non-negligible age MEs. However, our new approach performs well regardless of the magnitude of age MEs and accurately estimates SEs of parameter estimators. Real data analysis demonstrates the effectiveness of the proposed model validation device. Computer codes to implement the methodology are provided.

Bayesian calibration of ball grid array lifetime models for solder fatigue

One of the primary failure modes for solder joints is caused by temperature cycling of the component. The induced stress causes creeping which leads to crack initiation and propagation until failure. Finite element analysis can be used to simulate occurring creep-strain for different temperatures and geometries. Subsequently, creep-strain is used as damage parameter together with a lifetime model to estimate the reliability of the component. Economic factors constrain data available for calibration of the lifetime model, leading to uncertainties in parameter estimates and reliability. Therefore, we propose a model calibration method for solder fatigue with the Coffin–Manson lifetime model based on Bayesian inference. The approach is able to incorporate respective uncertainties from data variability and sparsity, and takes prior knowledge into account. We show how to obtain reliability estimates from the calibrated model considering uncertainties from parameter estimation. Furthermore, we apply the Bayesian calibration method to experimental data obtained from ball-grid arrays with lead-free SAC305 solder joints. In our ablation study we show that our approach is more robust and accurate upon the prevalent calibration method used, especially if only limited data is available.

Effect of mountainous rainfall on uncertainty in flood model parameter estimation

Abstract Explaining the significant variability of rainfall in orographically complex mountainous regions remains a challenging task even for modern raingauge networks. To address this issue, a real-time spatial rainfall field estimation model, called WREPN (WRF Rainfall-Elevation Parameterized Nowcasting), has been developed, incorporating the influence of mountain effect based on ground raingauge networks. In this study, we examined the effect of mountainous rainfall estimates on the uncertainty of flood model parameter estimation. As a comparison, an inverse distance weighting technique was applied to ground raingauge data to estimate the spatial rainfall field. To convert the spatial rainfall fields into flood volumes, we employed the ModClark model, a conceptual rainfall–runoff model with distributed rainfall input. Bayesian theory was applied for parameter estimation to incorporate uncertainty analysis. The ModClark model demonstrated good flood reproducibility regardless of the estimation method for spatial rainfall fields. Parameter estimation results indicated that the WREPN spatial rainfall field, which accounted for the influence of the mountain effect, led to lower curve numbers due to higher estimated rainfall compared to the IDW spatial rainfall field, while the concentration time and storage coefficient showed minimal differences.

Land Subsidence Model Inversion with the Estimation of Both Model Parameter Uncertainty and Predictive Uncertainty Using an Evolutionary-Based Data Assimilation (EDA) and Ensemble Model Output Statistics (EMOS)

The nonlinearity nature of land subsidence and limited observations cause premature convergence in typical data assimilation methods, leading to both underestimation and miscalculation of uncertainty in model parameters and prediction. This study focuses on a promising approach, the combination of evolutionary-based data assimilation (EDA) and ensemble model output statistics (EMOS), to investigate its performance in land subsidence modeling using EDA with a smoothing approach for parameter uncertainty quantification and EMOS for predictive uncertainty quantification. The methodology was tested on a one-dimensional subsidence model in Kawajima (Japan). The results confirmed the EDA’s robust capability: Model diversity was maintained even after 1000 assimilation cycles on the same dataset, and the obtained parameter distributions were consistent with the soil types. The ensemble predictions were converted to Gaussian predictions with EMOS using past observations statistically. The Gaussian predictions outperformed the ensemble predictions in predictive performance because EMOS compensated for the over/under-dispersive prediction spread and the short-term bias, a potential weakness for the smoothing approach. This case study demonstrates that combining EDA and EMOS contributes to groundwater management for land subsidence control, considering both the model parameter uncertainty and the predictive uncertainty.

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

Tridiagonal interval matrices are relevant in diverse applications, especially in dealing with parameter estimation, optimization and circuit analysis uncertainties. This research paper aims to improve the computational efficiency of obtaining the inverse of a general tridiagonal interval matrix. This matrix is pivotal in electric circuit analysis. We achieve this by employing interval arithmetic operations in the LU decomposition process, enabling effective handling of circuit parameter uncertainties. This approach generates an inverse interval matrix that addresses uncertainties in circuit analyses.

Multistatic radar distribution geometry effects on parameter estimation accuracy

AbstractAn analysis of the parameter estimation uncertainty for the target location and velocity achievable using a single‐transmitter‐multiple‐receiver multistatic radar system is presented. A framework for establishing measures of multistatic radar parameter uncertainties by expansion of the bistatic radar parameter uncertainty measures is presented for systems containing omnidirectionally radiating nodes. The methodology uses analytical methods based on the Cramér–Rao Lower Bounds applied to scenarios in a two‐dimensional physical space with a single target exhibiting Doppler characteristics and a bistatic angle dependent radar cross‐section. A set of geometric descriptors is proposed to characterise the system, and parameter uncertainty results are reported as a function of these descriptors. The results indicate that angular separation between the transmitter and the centre of the receiver distribution is of greater importance than the quantity of receivers within the system when low uncertainty estimation capabilities are desired, though a minimum of two receivers must be available. The proportion of receivers within the system which contributed information crucial to obtaining the minimum estimation uncertainty is reported for systems containing different quantities of receivers. It was observed that, as the total number of receivers available increased, the proportion of receivers required to achieve the minimal uncertainty level reduces significantly.

Modelling the population-level benefits and cost-effectiveness of cell-based quadrivalent influenza vaccine for children and adolescents aged 6 months to 17 years in the US

ABSTRACT Background Cell-based quadrivalent influenza vaccines (QIVc) can increase effectiveness against seasonal influenza by avoiding mismatch from egg adaption of vaccine viruses. This study evaluates the population-level cost-effectiveness and impacts on health outcomes of QIVc versus an egg-based vaccine (QIVe) in children aged 6 months to 17 years in the US. Research Design and Methods A dynamic age-structured susceptible-exposed-infected-recovered model was used to simulate influenza transmission in low and high incidence seasons for two scenarios: 1. QIVe for 6 months–17 year-olds, QIVc for 18–64 year-olds, and adjuvanted QIV (aQIV) for ≥ 65 year-olds, and 2. QIVc for 6 months–64 year-olds, and aQIV for ≥ 65 year-olds. Probabilistic sensitivity analysis was performed to account for uncertainty in parameter estimates. Cost-effectiveness was evaluated as incremental cost-effectiveness ratios (ICERs). Results Extension of QIVc to children resulted in 3–4% reductions in cases (1,656,271), hospitalizations (16,688), and deaths (2,126) at a population level in a high incidence season, and 65% reductions (cases: 2,856,384; hospitalizations: 31667; deaths: 4,163) in a low incidence season. Use of QIVc would be cost-saving, with ICERs of -$16,427/QALY and -$8,100/QALY from a payer perspective and -$22,669/QALY and -$15,015/QALY from a societal perspective, for low and high incidence seasons respectively. Cost savings were estimated at approximately $468 million and $1.366 billion for high and low incidence seasons, respectively. Conclusion Use of QIVc instead of QIVe in children > 6 months of age in the US would reduce the disease burden and be cost-saving from both a payer and societal perspective.