Model Parameter Estimation Problem Research Articles

Diffusion kurtosis imaging with free water elimination: A bayesian estimation approach.

PurposeDiffusion kurtosis imaging (DKI) is an advanced magnetic resonance imaging modality that is known to be sensitive to changes in the underlying microstructure of the brain. Image voxels in diffusion weighted images, however, are typically relatively large making them susceptible to partial volume effects, especially when part of the voxel contains cerebrospinal fluid. In this work, we introduce the “Diffusion Kurtosis Imaging with Free Water Elimination” (DKI‐FWE) model that separates the signal contributions of free water and tissue, where the latter is modeled using DKI.Theory and MethodsA theoretical study of the DKI‐FWE model, including an optimal experiment design and an evaluation of the relative goodness of fit, is carried out. To stabilize the ill‐conditioned estimation process, a Bayesian approach with a shrinkage prior (BSP) is proposed. In subsequent steps, the DKI‐FWE model and the BSP estimation approach are evaluated in terms of estimation error, both in simulation and real data experiments.ResultsAlthough it is shown that the DKI‐FWE model parameter estimation problem is ill‐conditioned, DKI‐FWE was found to describe the data significantly better compared to the standard DKI model for a large range of free water fractions. The acquisition protocol was optimized in terms of the maximally attainable precision of the DKI‐FWE model parameters. The BSP estimator is shown to provide reliable DKI‐FWE model parameter estimates.ConclusionThe combination of the DKI‐FWE model with BSP is shown to be a feasible approach to estimate DKI parameters, while simultaneously eliminating free water partial volume effects. Magn Reson Med 80:802–813, 2018. © 2018 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Inference for Large Financial Systems

We treat the parameter estimation problem for mean-field models of large interacting financial systems such as the banking system and a pool of assets held by an institution or backing a security. We develop an asymptotic inference approach that addresses the scale and complexity of such systems. Harnessing the weak convergence results developed for mean-field financial systems in the literature, we construct an approximate likelihood for large systems. The approximate likelihood has a conditionally Gaussian structure, enabling us to design an efficient numerical method for its evaluation. We provide a representation of the corresponding approximate estimator in terms of a weighted least-squares estimator, and use it to analyze the large-system and large-sample behavior of the estimator. Numerical results for a mean-field model of systemic financial risk highlight the efficiency and accuracy of our estimator.

Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC

Cancer is one of the most fatal diseases in the world. Governments and researchers from various areas have continuously concentrated efforts to better understand the disease and propose diagnostic and treatment techniques. The use of mathematical models of tumor growth is of great importance for the development of such techniques. Due to the variety of models nowadays available in the literature, the problems of model selection and parameter estimation come into picture, aiming at suitably predicting the patient’s status of the disease. As the available data on dependent variables of existing models might not justify the use of common likelihood functions, approximate Bayesian computation (ABC) becomes a very attractive tool for model selection and model calibration (parameter estimation) in tumor growth models. In the present study, a Monte Carlo approximate Bayesian computation (ABC) algorithm is applied to select among competing models of tumor growth, with and without chemotherapy treatment. Simulated measurements are used in this work. The results obtained show that the algorithm correctly selects the model and estimates the parameters used to generate the simulated measurements.

A maximum-likelihood and moment-matching density estimator for crowd-sourcing label prediction

We deal with the parameter estimation problem for probability density models with latent variables. For this problem traditionally the expectation maximization (EM) algorithm has been broadly used. However, it suffers from bad local maxima, and the quality of the estimator is sensitive to the initial model choice. Recently, an alternative density estimator has been proposed that is based on matching the moments between sample averaged and model averaged. This moment matching estimator is typically used as the initial iterate for the EM algorithm for further refinement. However, there is actually no guarantee that the EM-refined estimator still yields the moments close enough to the sample-averaged one. Motivated by this issue, in this paper we propose a novel estimator that takes merits of both worlds: we do likelihood maximization, but the moment discrepancy score is used as a regularizer that prevents the model-averaged moments from straying away from those estimated from data. On some crowd-sourcing label prediction problems, we demonstrate that the proposed approach yields more accurate density estimates than the existing estimators.

Closed-form formulas vs. PDE based numerical solution for the FRAP data processing: Theoretical and practical comparison

Fluorescence recovery after photobleaching (FRAP) is a widely used method to analyze (usually using fluorescence microscopy) the mobility of either fluorescently tagged or autofluorescent (e.g., photosynthetic) proteins in living cells. The FRAP method resides in imaging the recovery of fluorescence intensity over time in a region of interest previously bleached by a high-intensity laser pulse. While the basic principles of FRAP are simple and the experimental setup is usually fixed, quantitative FRAP data analysis is not well developed. Different models and numerical procedures are used for the underlying model parameter estimation without knowledge of how robust the methods are, i.e., the parameter inference step is not currently well established.In this paper we rigorously formulate the inverse problem of model parameter estimation (including the sensitivity analysis), making possible the comparison of different FRAP parameter inference methods. Then, in a study on simulated data, we focus on how three different methods for inference influence the error in parameter estimation. We demonstrate both theoretically and empirically that our new method based on a solution of a general initial–boundary value problem for the Fick diffusion partial differential equation exhibits less bias and narrower confidence intervals of the estimated diffusion parameter, than two closed formula methods.

Micro-Doppler Analysis of Rigid-Body Targets via Block-Sparse Forward–Backward Time-Varying Autoregressive Model

Micro-Doppler radar signatures are capable of characterizing rich motion information of targets and have played important roles in target identification and recognition. In this letter, we develop a novel parametric time–frequency method to analyze the micro-Doppler signatures of rigid-body targets, which is referred to as the block-sparse forward–backward time-varying autoregressive (BS-FBTVAR) model. First, the basis expansion method is employed to convert the time-varying model parameter estimation problem to be time invariant. Then, by investigating the intrinsic relationship between the model parameters and the poles of rigid-body targets, block-sparsity constraints are introduced to the conventional FBTVAR model. A complex-valued block-sparse Bayesian learning algorithm is developed as the solver of the novel BS-FBTVAR model. Finally, experiments on the electromagnetic (EM) analysis data are carried out to validate the performance of the proposed method.

Parameter Estimation in Softmax Decision-Making Models With Linear Objective Functions

We contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human decision-making, we study the maximum-likelihood (ML) parameter estimation problem for softmax decision-making models with linear objective functions. We present conditions under which the likelihood function is convex. These allow us to provide sufficient conditions for convergence of the resulting ML estimator and to construct its asymptotic distribution. In the case of models with nonlinear objective functions, we show how the estimator can be applied by linearizing about a nominal parameter value. We apply the estimator to fit the stochastic Upper Credible Limit (UCL) model of human decision-making to human subject data. The fits show statistically significant differences in behavior across related, but distinct, tasks.

Image Super-Resolution Based on Structure-Modulated Sparse Representation

Sparse representation has recently attracted enormous interests in the field of image restoration. The conventional sparsity-based methods enforce sparse coding on small image patches with certain constraints. However, they neglected the characteristics of image structures both within the same scale and across the different scales for the image sparse representation. This drawback limits the modeling capability of sparsity-based super-resolution methods, especially for the recovery of the observed low-resolution images. In this paper, we propose a joint super-resolution framework of structure-modulated sparse representations to improve the performance of sparsity-based image super-resolution. The proposed algorithm formulates the constrained optimization problem for high-resolution image recovery. The multistep magnification scheme with the ridge regression is first used to exploit the multiscale redundancy for the initial estimation of the high-resolution image. Then, the gradient histogram preservation is incorporated as a regularization term in sparse modeling of the image super-resolution problem. Finally, the numerical solution is provided to solve the super-resolution problem of model parameter estimation and sparse representation. Extensive experiments on image super-resolution are carried out to validate the generality, effectiveness, and robustness of the proposed algorithm. Experimental results demonstrate that our proposed algorithm, which can recover more fine structures and details from an input low-resolution image, outperforms the state-of-the-art methods both subjectively and objectively in most cases.

A Poisson INAR(1) model with serially dependent innovations

Motivated by a certain type of infinite-patch metapopulation model, we propose an extension to the popular Poisson INAR(1) model, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the current population is large. We shall recognize that this new model forms a bridge between the Poisson INAR(1) model and the INARCH(1) model. We analyze the stochastic properties of the observations and innovations from an extended Poisson INAR(1) process, and we consider the problem of model identification and parameter estimation. A real-data example about iceberg counts shows how to benefit from the new model.

Impact of Position Errors on Path Loss Model Estimation for Device-to-Device Channels

Many wireless applications require a propagation model that describes the attenuation of the transmitted signal as a function of the distance between devices. Such channel models are derived commonly from signal strength measurements, and assume that the true distances between wireless terminals are known. In practice, however, the true distances may be unavailable or difficult to obtain, for instance in mobile scenarios or in the absence of line-of-sight. These conditions typically occur in forested environments, urban areas, etc. This paper addresses the problem of path loss model parameter estimation in presence of erroneous distance measurements, such as the ones derived from the GPS positions. We provide a model for the uncertainties, and study the impact of distance errors on the estimation of a log-distance channel model. Our main conclusion is that the path loss model can be estimated with a reasonable accuracy from unreliable distances, provided that the measurements are taken at distances beyond a few standard deviations of the GPS positioning error. In case the maximum communication range does not allow such large distances, we provide a method to correct the erroneous channel model. Real-world measurements are used in order to validate our approach.

Identification of material parameters for low bond strength masonry

This paper investigates the parameter estimation problem for masonry constitutive models and describes the development of a computational model for low bond strength masonry. The conventional method of obtaining material parameters from the results of small sample tests was thought to be problematic. Instead, material parameters were obtained from the results from the load testing of large clay brick low bond strength masonry wall panels in the laboratory. Initially, the panels were modeled computationally using UDEC software and an assumed set of material parameters. The differences between the results obtained experimentally and computationally were minimized using an optimization technique. The model was then used with the optimized parameters to predict the structural response of another wall panel that had been tested in the laboratory. Good correlation was obtained with the experimental results. The general procedure of the material parameter identification method and the numerical results are presented.

Learning a mixture model for clustering with the completed likelihood minimum message length criterion

Mixture model based clustering (also simply called model-based clustering hereinafter) consists of fitting a mixture model to data and identifying each cluster with one of its components. This paper tackles the model selection and parameter estimation problems in model-based clustering so as to improve the clustering performance on the data sets whose true kernel distribution functions are not in the family of assumed ones, as well as with inherently overlapped clusters. Being tailored to clustering applications, an effective model selection criterion is first proposed. Unlike most criteria that measure the goodness-of-fit of the model only to generate data, the proposed one also evaluates whether the candidate model provides a reasonable partition for the observed data, which enforces a model with well-separated components. Accordingly, an improved method for the estimation of mixture parameters is derived, which aims to suppress the spurious estimates by the standard expectation maximization (EM) algorithm and enforce well-supported components in the mixture model. Finally, the estimation of mixture parameters and the model selection is integrated in a single algorithm which favors a compact mixture model with both the well-supported and well-separated components. Extensive experiments on synthetic and real-world data sets are carried out to show the effectiveness of the proposed approach to the mixture model based clustering.

Comments on “Joint Bayesian Model Selection and Estimation of Noisy Sinusoids Via Reversible Jump MCMC”

Reversible jump MCMC (RJ-MCMC) sampling techniques, which allow to jointly tackle model selection and parameter estimation problems in a coherent Bayesian framework, have become increasingly popular in the signal processing literature since the seminal paper of Andrieu and Doucet [“Joint Bayesian model selection and estimation of noisy sinusoids via reversible jump MCMC,” IEEE Trans. Signal Process, vol. 47, no. 10, pp. 2667-2676, 1999]. Crucial to the implementation of any RJ-MCMC sampler is the computation of the so-called Metropolis-Hastings-Green (MHG) ratio, which determines the acceptance probability for the proposed moves. It turns out that the expression of the MHG ratio that was given in the paper of Andrieu and Doucet for “Birth-or-Death” moves is erroneous and has been reproduced in many subsequent papers dealing with RJ-MCMC sampling in the signal processing literature. This note fixes the erroneous expression and briefly discusses its cause and consequences.

Distributed Maximum Likelihood for Simultaneous Self-Localization and Tracking in Sensor Networks

We show that the sensor self-localization problem can be cast as a static parameter estimation problem for Hidden Markov Models and we implement fully decentralized versions of the Recursive Maximum Likelihood and on-line Expectation-Maximization algorithms to localize the sensor network simultaneously with target tracking. For linear Gaussian models, our algorithms can be implemented exactly using a distributed version of the Kalman filter and a novel message passing algorithm. The latter allows each node to compute the local derivatives of the likelihood or the sufficient statistics needed for Expectation-Maximization. In the non-linear case, a solution based on local linearization in the spirit of the Extended Kalman Filter is proposed. In numerical examples we demonstrate that the developed algorithms are able to learn the localization parameters.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

AbstractData assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three‐dimensional variational (3D‐Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship‐borne survey is shown to significantly improve the predictive capability of the model over a 2‐year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D‐Var data assimilation algorithm for joint state‐parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation‐based state‐parameter estimation in coastal morphodynamic modelling. Copyright © 2012 Royal Meteorological Society

Sequential State and Observation Noise Covariance Estimation Using Combined Ensemble Kalman and Particle Filters

AbstractThe authors consider the joint state and parameter estimation problem for dynamical models where the system evolution is known and where the observations are linear with additive Gaussian noise whose covariance matrix depends on unknown parameters. The form of this dependence is general, both diagonal and off-diagonal elements of the covariance matrix may depend on the unknown parameters. In this situation, the ensemble Kalman filter (EnKF) cannot be applied directly to update state and parameters simultaneously. Two novel approximate Monte Carlo methods are proposed for this purpose, which are both based on the assumption that parameters and state are approximately independent after the propagation step. The first method begins with a particle filter update of the parameters followed by an EnKF update of the state. The second method first makes an EnKF update of the state based on an approximate likelihood that does not depend on the parameters, followed by a particle filter update of the parameters with weights proportional to the ratio of the correct to the approximate likelihood. To counteract sample depletion, the authors introduce algorithmic refinements like balanced sampling, kernel resampling, and increasing the number of samples for the parameters while keeping the size of the state ensemble fixed. The performance and flexibility of these methods is demonstrated in simulations with a linear Gaussian model and with the Lorenz-96 model. Provided the EnKF with all parameters known is reasonably well calibrated, then this is also true for the state estimates in the new algorithms, and the estimated posterior distributions of the parameters are consistent with the truth.

A novel P systems based optimization algorithm for parameter estimation of proton exchange membrane fuel cell model

Accurate kinetic models are of great significance for the simulation and analysis for hydrogen fuel cells. The proton exchange membrane (PEM) fuel cell is a complex nonlinear, multi-variable system. The mathematical modeling of PEM fuel cell usually leads to nonlinear parameter estimation problems which often contain more than one minimum. In this paper, a novel bio-inspired P systems based optimization algorithm, named BIPOA, is proposed to solve PEM fuel cell model parameter estimation problems. In BIPOA, the nested membrane structure and new rules such as adaptive mutation rule, partial migration rule and autophagy rule are combined to improve the algorithm's global search capacities and convergence accuracy. Studies on some benchmark test functions indicate that the BIPOA outperforms the other two methods (PSOPS and GAs) in both convergence speed and accuracy. In addition, experimental results reveal that the model predictive outputs are in better agreement with the actual experimental data. Therefore, the BIPOA is a helpful and reliable technique for estimating the PEM fuel cell model parameters and is available to other complex parameter estimation problems of fuel cell models.

Bayesian Variable Selection for the Seemingly Unrelated Regression Models with a Large Number of Predictors

Computationally efficient methods for Bayesian analysis of Seemingly Unrelated Regression (SUR) models with a large number of predictors are developed. One of the most crucial problems in Bayesian modeling of SUR models is how to determine the optimal combination of predictors. In this paper, under a Bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis functions, the regression coefficients, the variance matrix of the errors, and a set of predictors to be included in the model are estimated simultaneously. Usually the Bayesian model estimation problem is solved using Markov Chain Monte Carlo (MCMC) techniques. Herein we show how a direct Monte Carlo (DMC) technique can be employed to solve the variable selection and model parameter estimation problems more efficiently.

How the signal‐to‐noise ratio influences hyperpolarized 13C dynamic MRS data fitting and parameter estimation

MRS of hyperpolarized (13) C-labeled compounds represents a promising technique for in vivo metabolic studies. However, robust quantification and metabolic modeling are still important areas of investigation. In particular, time and spatial resolution constraints may lead to the analysis of MRS signals with low signal-to-noise ratio (SNR). The relationship between SNR and the precision of quantitative analysis for the evaluation of the in vivo kinetic behavior of metabolites is unknown. In this article, this topic is addressed by Monte Carlo simulations, covering the problem of MRS signal model parameter estimation, with strong emphasis on the peak amplitude and kinetic model parameters. The results of Monte Carlo simulation were confirmed by in vivo experiments on medium-sized animals injected with hyperpolarized [1-(13) C]pyruvate. The results of this study may be useful for the establishment of experimental planning and for the optimization of kinetic model estimation as a function of the SNR value.

Bayesian mixture of AR models for time series clustering

In this paper, we propose a Bayesian framework for estimation of parameters of a mixture of autoregressive models for time series clustering. The proposed approach is based on variational principles and provides a tractable approximation to the true posterior density that minimizes Kullback---Liebler (KL) divergence with respect to prior distribution. This method simultaneously addresses the model complexity and parameter estimation problems. The proposed approach is applied both on simulated and real-world time series datasets. It is found to be useful in exploring and finding the true number of underlying clusters, starting from an arbitrarily large number of clusters.