Simultaneous Parameter Estimation Research Articles

Noninvasive Input Function Acquisition and Simultaneous Estimations With Physiological Parameters for PET Quantification: A Brief Review

The recent introduction of high-resolution and high-speed PET/CT is making noninvasive absolute quantification of physiological function more convenient and feasible. A key issue for absolute quantification is the accurate estimation of the time-activity curve (TAC) in plasma (PTAC). We provide a brief survey of the population-based and the image-derived PTAC approaches together with their performance characterizations. We then give a summary of the recent report on the image-derived PTAC from the first total-body PET/CT device, uEXPLORER. We finally summarize the kinetic model-based simultaneous estimation of input functions and physiological parameters (SIME) method. SIME has several advantages, including the more adequately estimated local input function for adjacent tissue TACs; simultaneous correction of spillover and partial-volume effect; smoothing the measurement noise and alleviating the need for the measurement of the PTAC peak; and simultaneous estimation of multiple input functions for organs such as the liver where blood is supplied from the hepatic artery and the portal vein. As the SIME approach is intended to improve the quality of quantification, it is expected that the image-derived PTAC from the total-body PET scanner together with the SIME approach will advance future PET absolute quantitative studies.

Variable selection in multivariate multiple regression.

IntroductionIn many practical situations, we are interested in the effect of covariates on correlated multiple responses. In this paper, we focus on estimation and variable selection in multi-response multiple regression models. Correlation among the response variables must be modeled for valid inference.MethodWe used an extension of the generalized estimating equation (GEE) methodology to simultaneously analyze binary, count, and continuous outcomes with nonlinear functions. Variable selection plays an important role in modeling correlated responses because of the large number of model parameters that must be estimated. We propose a penalized-likelihood approach based on the extended GEEs for simultaneous parameter estimation and variable selection.Results and conclusionsWe conducted a series of Monte Carlo simulations to investigate the performance of our method, considering different sample sizes and numbers of response variables. The results showed that our method works well compared to treating the responses as uncorrelated. We recommend using an unstructured correlation model with the Bayesian information criterion (BIC) to select the tuning parameters. We demonstrated our method using data from a concrete slump test.

Joint Structural Break Detection and Parameter Estimation in High-Dimensional Nonstationary VAR Models

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to assume piecewise stationarity, where the model can change at potentially many change points. We propose a three-stage procedure for simultaneous estimation of change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and solve it using a penalized least square estimator with a total variation penalty. We show that the penalized estimation method over-estimates the number of change points, and propose a selection criterion to identify the change points. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We prove that the proposed procedure consistently detects the number and location of change points, and provides consistent estimates of VAR parameters. The performance of the method is illustrated through several simulated and real data examples. Supplementary materials for this article are available online.

UD-Based Pairwise and MIMO Kalman-Like Filtering for Estimation of Econometric Model Structures

One of the modern research lines in econometrics studies focuses on translating a wide variety of structural econometric models into their state-space form, which allows for efficient unknown dynamic system state and parameter estimations by the Kalman filtering scheme. The mentioned trend yields advanced state-space model structures, which demand innovative estimation techniques driven by application requirements to be devised. This article explores both the linear time-invariant multiple-input- multiple-output system (LTI MIMO) and the pairwise Markov model (PMM) with the related pairwise Kalman filter (PKF). In particular, we design robust gradient-based adaptive Kalman-like filtering methods for the simultaneous state and parameter estimation in the outlined model structures. Our methods are fast and accurate because their analytically computed gradient is utilized in the calculation instead of its numerical approximation. Also, these employ the numerically robust UDUT-factorization-based Kalman filter implementation, which is reliable in practice. Our novel techniques are examined on numerical examples and used for treating one stochastic model in econometrics.

Thermophysical modelling and parameter estimation of small Solar system bodies via data assimilation

ABSTRACT Deriving thermophysical properties such as thermal inertia from thermal infrared observations provides useful insights into the structure of the surface material on planetary bodies. The estimation of these properties is usually done by fitting temperature variations calculated by thermophysical models to infrared observations. For multiple free model parameters, traditional methods such as least-squares fitting or Markov chain Monte Carlo methods become computationally too expensive. Consequently, the simultaneous estimation of several thermophysical parameters, together with their corresponding uncertainties and correlations, is often not computationally feasible and the analysis is usually reduced to fitting one or two parameters. Data assimilation (DA) methods have been shown to be robust while sufficiently accurate and computationally affordable even for a large number of parameters. This paper will introduce a standard sequential DA method, the ensemble square root filter, for thermophysical modelling of asteroid surfaces. This method is used to re-analyse infrared observations of the MARA instrument, which measured the diurnal temperature variation of a single boulder on the surface of near-Earth asteroid (162173) Ryugu. The thermal inertia is estimated to be 295 ± 18 $\mathrm{J\, m^{-2}\, K^{-1}\, s^{-1/2}}$, while all five free parameters of the initial analysis are varied and estimated simultaneously. Based on this thermal inertia estimate the thermal conductivity of the boulder is estimated to be between 0.07 and 0.12,$\mathrm{W\, m^{-1}\, K^{-1}}$ and the porosity to be between 0.30 and 0.52. For the first time in thermophysical parameter derivation, correlations and uncertainties of all free model parameters are incorporated in the estimation procedure that is more than 5000 times more efficient than a comparable parameter sweep.

Usage of the GO estimator in high dimensional linear models

This paper discusses simultaneous parameter estimation and variable selection and presents a new penalized regression method. The method is based on the idea that the coefficient estimates are shrunken towards a predetermined coefficient vector which represents the prior information. This method can result in smaller length estimates of the coefficients depending on the prior information compared to elastic net. In addition to the establishment of the grouping property, we also show that the new method has the grouping effect when the predictors are highly correlated. Simulation studies and real data example show that the prediction performance of the new method is improved over the well-known ridge, lasso and elastic net regression methods yielding a lower mean squared error and competes about the variable selection under sparse and non-sparse situations.

A probabilistic approach to phase calibration – I. Effects of source structure on fringe-fitting

ABSTRACT We propose a probabilistic framework for performing simultaneous estimation of source structure and fringe-fitting parameters in very long baseline interferometry (VLBI) observations. As a first step, we demonstrate this technique through the analysis of synthetic short-duration Event Horizon Telescope observations of various geometric source models at 230 GHz, in the presence of baseline-dependent thermal noise. We perform Bayesian parameter estimation and model selection between the different source models to obtain reliable uncertainty estimates and correlations between various source and fringe-fitting related model parameters. We also compare the Bayesian posteriors with those obtained using widely used VLBI data reduction packages such as casa and aips, by fringe-fitting 200 Monte Carlo simulations of each source model with different noise realizations, to obtain distributions of the maximum a posteriori estimates. We find that, in the presence of resolved asymmetric source structure and a given array geometry, the traditional practice of fringe-fitting with a point source model yields appreciable offsets in the estimated phase residuals, potentially biasing or limiting the dynamic range of the starting model used for self-calibration. Simultaneously estimating the source structure earlier in the calibration process with formal uncertainties improves the precision and accuracy of fringe-fitting and establishes the potential of the available data, especially when there is little prior information. We also note the potential applications of this method to astrometry and geodesy for specific science cases and the planned improvements to the computational performance and analyses of more complex source distributions.

Simultaneous Hierarchical Bayesian Parameter Estimation for Reinforcement Learning and Drift Diffusion Models: a Tutorial and Links to Neural Data

Cognitive models have been instrumental for generating insights into the brain processes underlying learning and decision making. In reinforcement learning it has recently been shown that not only choice proportions but also their latency distributions can be well captured when the choice function is replaced with a sequential sampling model such as the drift diffusion model. Hierarchical Bayesian parameter estimation further enhances the identifiability of distinct learning and choice parameters. One caveat is that these models can be time-consuming to build, sample from, and validate, especially when models include links between neural activations and model parameters. Here we describe a novel extension to the widely used hierarchical drift diffusion model (HDDM) toolbox, which facilitates flexible construction, estimation, and evaluation of the reinforcement learning drift diffusion model (RLDDM) using hierarchical Bayesian methods. We describe the types of experiments most applicable to the model and provide a tutorial to illustrate how to perform quantitative data analysis and model evaluation. Parameter recovery confirmed that the method can reliably estimate parameters with varying numbers of synthetic subjects and trials. We also show that the simultaneous estimation of learning and choice parameters can improve the sensitivity to detect brain–behavioral relationships, including the impact of learned values and fronto-basal ganglia activity patterns on dynamic decision parameters.

Joint analysis of semicontinuous data with latent variables

A two-part latent variable model is proposed to analyze semicontinuous data in the presence of latent variables. The proposed model comprises two major components. The first component is a structural equation model (SEM), which characterizes latent variables using corresponding multiple attributes and examines the interrelationships among them. The second component is a two-part model to assess a semicontinuous response of interest. The semicontinuous variable is characterized by a mixture of zero values and continuously distributed positive values. The two-part model manages this semicontinuous variable by splitting it into two random variables; one is a binary indicator to determine whether the response is zero, another is a continuous variable to determine the actual level of the positive response. A full Bayesian approach coupled with spike-and-slab lasso prior is developed for simultaneous variable selection and parameter estimation. The proposed methodology is demonstrated by a simulation study and applied to the analysis of the Chinese General Social Survey dataset. New insights into the interrelationships among non-cognitive ability, education level, and annual income are obtained.

Efficient empirical Bayes estimates for risk parameters of Pareto distributions

Pareto distributions are useful for modeling the loss data in many fields such as actuarial science, economics, insurance, hydrology and reliability theory. In this paper, we consider the simultaneous estimation of the risk parameters of Pareto distributions from the perspective of empirical Bayes, novel SURE-type shrinkage estimators are developed by employing the Stein’s unbiased estimate of risk (SURE). Specifically, due to the lacking of the analytic form for the risk function, we propose to estimate the hyperparameters by minimizing an unbiased estimate of an approximation of the risk function. Under mild conditions, we prove the optimality of the new shrinkage estimators. The performance of our estimators is illustrated with simulation studies and an analysis of a real auto insurance claim dataset.

The use of augmented loss functions for estimating dynamic energy budget parameters

We propose an extension of a parameter-free loss function for the estimation of Dynamic Energy Budget parameters for a set of related species that is symmetric in the role of data and predictions. The extension allows that particular parameters might vary, but not by much, among species, while the degree of variation is controlled by weight coefficients. We discuss the choice of these coefficients and illustrate the application with an example of two species of catfish, with their mutual hybrids. In our simultaneous parameter estimation for this example, we could reduce the variation in a parameter, here the energy conductance, substantially with a minor effect on the goodness of fit. We selected this parameter among the ones that varied, because its value was poorly determined by the data. We discuss this example in some detail. The software for implementing this augmented loss function has been implemented in the available software DEBtool_M on Github (www.github.com/add-my-pet/DEBtool_M).

Joint Estimation of Battery Parameters and State of Charge Using an Extended Kalman Filter: A Single-Parameter Tuning Approach

The joint estimation of the state of charge (SoC) and the parameters of a battery model is typically done using nonlinear extensions of the Kalman filter (KF), such as the well-known and widely used extended KF (EKF), in combination with a simple but relatively accurate equivalent-circuit model. The main limitation of the joint EKF is that extensive tuning of the covariance matrices is required when implementing the observer in an application. This tuning is a tedious task with no clear guidelines for the tuning procedure. Furthermore, the joint EKF and its extensions do not explicitly address model uncertainty and sensor noise, which may be the cause for the problematic tuning. In this article, we combine a nonlinear observer with the structured representation of model uncertainty and disturbances as typically used in a robust-observer design approach. Therefore, the joint EKF for simultaneous estimation of SoC and model parameters will be presented for the case that includes cross-correlated noises. Moreover, inspired by the conditions for enforcing convergence of the SoC estimation error, a so-called forgetting factor will be introduced to the joint EKF. These adaptations lead to an observer with a single tuning parameter. The experimental results show that tuning of the proposed observer is straightforward and the performance is similar to a regular joint EKF with a root-mean-square SoC error of 0.5%.

Online jointly estimation of hysteretic structures using the combination of central difference Kalman filter and Robbins–Monro technique

Rapid assessment of structural safety and performance right after the occurrence of significant earthquake shaking is crucial for building owners and decision-makers to make informed risk management decisions. Hence, it is vital to develop online and pseudo-online health monitoring methods to quantify the health of the building right after significant earthquake shaking. Many Bayesian inference–based methods have been developed in the past which allow the users to estimate the unknown states and parameters. However, one of the most challenging part of the Bayesian inference–based methods is the determination of the parameter noise covariance matrix. It is especially difficult when the number of unknown states and parameters is large. In this study, an effective online joint estimation method for nonlinear hysteretic structures, with consideration of degradation and pinching phenomena, is proposed. Simultaneous estimation of states and parameters is conducted using the combination of a central difference Kalman filter as an effective estimator and the Robbins–Monro stochastic approximation technique as the parameters noise covariance matrix regulator. The proposed algorithm is implemented on three shear buildings with 36, 54, and 90 unknown states and parameters. To verify the performance of the system identification method, robust simulations with synthetic measurement noises and modeling errors were generated using the Monte Carlo random simulation method. The result shows the proposed method can be used to estimate the unknown parameters and states of highly nonlinear systems efficiently and effectively.

A Decentralized Framework for Parameter and State Estimation of Infiltration Processes

The Richards’ equation is widely used in the modeling soil water dynamics driven by the capillary and gravitational forces in the vadose zone. Its state and parameter estimation based on field soil moisture measurements is important and challenging for field applications of the Richards’ equation. In this work, we consider simultaneous state and parameter estimation of systems described by the three dimensional Richards’ equation with multiple types of soil. Based on a study on the interaction between subsystems, we propose to use decentralized estimation schemes to reduce the complexity of the estimation problem. Guidelines for subsystem decomposition are discussed and a decentralized estimation scheme developed in the framework of moving horizon state estimation is proposed. Extensive simulation results are presented to show the performance of the proposed decentralized approach.

A robust adaptive Lasso estimator for the independent contamination model

The Lasso has become a benchmark method for simultaneous parameter estimation and variable selection in regression analysis. It is based on the least-squares estimator and, therefore, suffers from the presence of outliers. Robust Lasso methods combine the objective function of a robust estimator with ℓ1-penalization. We address robustness for cases in which the number of observations is smaller (or not much larger) than the number of predictors. Further, we assume that the regression matrix may contain cellwise outliers. In such settings, even a few highly contaminated predictors can cause existing robust methods that are based on the commonly used rowwise contamination model to break down. Therefore, we propose a new adaptive Lasso type regularization. It takes into account cellwise outlyingness in the regression matrix and uses this information for robust variable selection. The proposed regularization term is integrated into the objective function of the MM-estimator, which yields the proposed MM-Robust Weighted Adaptive Lasso (MM-RWAL). A performance comparison to existing robust Lasso estimators is provided using Monte Carlo experiments. Further, the MM-RWAL is applied to determine the temporal releases of the European Tracer Experiment (ETEX) at the source location. This sparse and ill-conditioned linear inverse problem contains cellwise and rowwise outliers.

Actuator fault tolerant control for steer-by-wire systems

Automotive steer-by-wire (SbW) system is a safety-critical system where the safety and reliability issues must be addressed during the operation. This paper proposes a fault detection and isolation-based actuator fault tolerant control for SbW system based on model predictive control. The fault detection and isolation module uses a two-stage Kalman filtering algorithm to provide simultaneous control parameter and state estimation to detect the occurrence of actuator failure. Additionally, a model predictive controller is designed to maintain the original functionality of the SbW systems using the output of fault detection and isolation to update the fault information. We evaluate the performance of the proposed approach by numerical simulations and experiments on our SbW platform. The simulation and experimental results illustrate that our approach achieves a better steering performance than a conventional model predictive controller without fault detection and isolation and stabilise the overall SbW system in occurrence of actuator failure.

Prediction Error Identification Method for Continuous-time Systems Having Multiple Unknown Time Delays

This paper shows a continuous-time prediction error method for the identification of Multiple Input Single Output (MISO) Continuous-Time (CT) systems with multiple unknown time delays. The proposed algorithm entails the simultaneous estimation of both process parameters and multiple unknown time delays. Indeed, it minimizes the prediction error using the Levenberg-Marquardt (LM) optimization method with derivatives of the objective function with respect to the parameters including the multiple unknown time delays. An analysis is then presented which proves the convergence of the algorithm, and robustness issues are discussed as well. Finally, to verify the analysis and to demonstrate the feasibility of the algorithm, we present some of the simulation results which were carried out.

Determination of soil hydraulic properties and its implications for mechanistic simulations and irrigation management

Water retention θ(h) and hydraulic conductivity K(h) are mandatory soil hydraulic properties (SHP) for consistent hydrological modeling and for an efficient irrigation management. Most commonly, SHP are determined by conventional methods (CM), based on hydrostatic equilibrium and the independent measurement of saturated hydraulic conductivity, which is used as a matching point for K(h) function. Alternatively, inverse-modeling experiments allow simultaneous parameter estimation using data from transient water flow conditions. This study aims to investigate the implications of these two protocols on simulations of soil water content (θ) and crop evapotranspiration (ET), and how they affect irrigation management and scheduling for different irrigation systems and crops. The SHP obtained from CM and IM were used in simulations with the Richards equation-based SWAP hydrological model. ET and θ were simulated for passion fruit under high-frequency drip irrigation and for pasture under conventional sprinkler irrigation. The simulation performance was evaluated using measured θ and ET obtained with passion fruit under drip irrigation. Both methods (CM and IM) gave similar results in the wetter range, while in the drier soil, CM estimated higher θ than IM. These differences affected the simulated ET and irrigation scheduling. Regarding the ET and θ simulations, for the drip irrigation scenario, in which the water content in the root zone remains near saturation, both SHP determination methods produced similar results. On the other hand, for scenarios with larger irrigation intervals such as sprinkler irrigation, simulations were affected significantly, with CM likely biasing irrigation frequency and depth.

An upper bound on the number of compatible parameters in simultaneous quantum estimation

Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not necessarily achievable. There exists a necessary and sufficient condition for its achievability. It is unknown how many parameters can be estimated while satisfying this condition. In this paper, we analyse an upper bound on the number of such parameters through linear-algebraic techniques. This upper bound depends on the algebraic structure of the quantum system used as a probe. We explicitly calculate this bound for two quantum systems: single qubit and two-qubit X-states.

Global Sensitivity Analysis of the Rodgers and Rowland Model for Prediction of Tissue: Plasma Partitioning Coefficients: Assessment of the Key Physiological and Physicochemical Factors That Determine Small-Molecule Tissue Distribution.

In physiologically based pharmacokinetic (PBPK) modelling, the large number of input parameters, limited amount of available data and the structural model complexity generally hinder simultaneous estimation of uncertain and/or unknown parameters. These parameters are generally subject to estimation. However, the approaches taken for parameter estimation vary widely. Global sensitivity analyses are proposed as a method to systematically determine the most influential parameters that can be subject to estimation. Herein, a global sensitivity analysis was conducted to identify the key drug and physiological parameters influencing drug disposition in PBPK models and to potentially reduce the PBPK model dimensionality. The impact of these parameters was evaluated on the tissue-to-unbound plasma partition coefficients (Kpus) predicted by the Rodgers and Rowland model using Latin hypercube sampling combined to partial rank correlation coefficients (PRCC). For most drug classes, PRCC showed that LogP and fraction unbound in plasma (fup) were generally the most influential parameters for Kpu predictions. For strong bases, blood:plasma partitioning was one of the most influential parameter. Uncertainty in tissue composition parameters had a large impact on Kpu and Vss predictions for all classes. Among tissue composition parameters, changes in Kpu outputs were especially attributed to changes in tissue acidic phospholipid concentrations and extracellular protein tissue:plasma ratio values. In conclusion, this work demonstrates that for parameter estimation involving PBPK models and dimensionality reduction purposes, less influential parameters might be assigned fixed values depending on the parameter space, while influential parameters could be subject to parameters estimation.