Parameter reduction for the compound Gauss-Markov model

Undirected graphical models such as Markov random fields or Boltzmann machines prove useful in many signal processing and machine learning tasks. However, parameter estimation in these models is difficult due to the intractable normalising constant in their probability density functions. One powerful technique for parameter estimation in such models is score matching. This technique makes use of an objective function which is independent of the normalising constant and constitutes locally consistent estimators for the parameters of such models. However, score matching is only applicable to fully-observed models. In this paper, we extend the applicability of score matching to models with latent variables. Our estimators are unbiased, based on Monte Carlo integration. Unbiased gradient estimators open the way to optimisation through stochastic approximation. We demonstrate the performance of our methodology on two synthetic problems.

A methodology is proposed to aid parameter estimation in fundamental models of pharmaceutical processes. This methodology addresses situations with insufficient data to reliably estimate all parameters, when the estimation is complicated by uncertain independent variables. The proposed method uses an augmented sensitivity matrix to rank the combined set of parameters and uncertain inputs from most estimable to least estimable. An updated mean‐squared‐error criterion is then used to determine the appropriate parameters and inputs that should be estimated, based on the ranked list. A model for one step in a batch pharmaceutical production process with an uncertain initial reactant concentration is used to illustrate the method, revealing that the initial reactant concentration in each batch should be estimated along with three out of six model parameters. Non‐estimable parameters are fixed at their initial values to prevent overfitting. The method will aid error‐in‐variables parameter estimation in many situations involving limited data.

Electron beam evaporation with hot filament and magnetic field—Computer control and parameter estimation

Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.

The paper presents the two-dimensional, field-circuit model of a high power synchronous generator verified by measurements. The model enables determining the waveforms of electromagnetic quantities in steady and transient states. Verification of the model was based on comparison of the measured and calculated waveforms after a disturbance in the voltage regulation system of a TWW-200-2 generator operating in Połaniec Power Plant. There are also presented the field methods for determining electromagnetic parameters (synchronous reactances and time constants) when using the distributions of static and quasi-static, magnetic and electromagnetic fields calculated by the finite element method (FEM). The set of these parameters was used as the starting parameters of the optimization algorithm for estimation of electromagnetic parameters of the synchronous generator circuit model. The dynamic waveforms under the generator load conditions calculated by the finite element method are the basis of parameter estimation. The parameter estimation of the generator model was performed with the use of the least squares method.

When model-based controllers are used for carrying out precise tasks, the estimation of model parameters is key for a better trajectory tracking performance. We consider the scenario of a free-flying space robot with limited actuation that has grasped an object of unknown properties. The inertial parameters - mass, centre of mass and the inertia tensor - of the robot-object system are to be determined. In our previous works, we used a parameter estimation algorithm where truncated Fourier series were used to represent both the reference excitation trajectory and the executed one. That algorithm is the focus of this paper, along with a study of the factors that could contribute to a loss of accuracy in the obtained estimates. Simulation results with the Space CoBot free-flyer robot are used to find the causes of the latter: first, a modified version of the minimum condition number criterion is used to generate feasible excitatory trajectories. The results are compared with those given by the maximum information criterion to check for better excitation. Next, an appropriate number of harmonics has to be found for the Fourier series, which will be used to fit the measured data. This is done autonomously, based on the least squares residual. Finally, the relation between input saturation while executing the excitation trajectory and the errors in the resulting parameter estimates is studied.

High Range Resolution (HRR) -based Automatic Target Recognition (ATR) has attracted increasing attention due to a number of potential advantages over alternative radar techniques in moving target identification. Most current HRR-based ATR studies have been conducted using 1D HRR signatures. However, these 1D HRR signatures are generally plagued by scintillation effects, and thus demonstrate highly irregular behavior that dramatically degrades the performance and robustness of algorithms based on these signatures. In order to circumvent this difficulty, an alternative HRR radar data representation and processing technique is presented in this paper. This technique models and extracts the target characteristics directly, based on the 2D HRR raw data. In this paper, we first derive a general, but complex HRR radar model, and then simplify this model by instantiating a set of real-world radar and target parameters for the model. This simplification process produces two HRR radar models with different degrees of simplicity. After establishing this set of models, the typical HRR data processes, such as feature extraction and clutter suppression, are reduced to one problem, which is model-parameter estimation. Based upon the most simplified HRR model we proposed, we devise two model- parameter estimation algorithms. One is a scatterer extraction algorithm based on available 1D Parameter Estimation (1DPE), while the other is based on 2D discrete Fourier Transform (2DFT). In order to examine the performance of these two algorithms a set of simulations are conducted. The experimental results are presented, and the performance comparison between 1DPE and 2DFT is presented.

Data 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

Fast and robust parameter estimation for statistical partial volume models in brain MRI.

In order to solve the problem of parameter estimation of nonlinear model in chemical engineering, a novel heuristic optimization approach is presented. The proposed approach develops and employs particle swarm optimization (PSO) technique to search for optimal solution of the parameter estimation. Firstly, the proposed approach converts the problem of parameter estimation of nonlinear model into an equation solving problem that is prone to be optimized. Secondly, two extrema of PSO are used as the target, and all the particles synchronously move through the solution space roundly and efficiently to find the optimum parameter estimation. The feasibility of the proposed method is demonstrated by the parameter estimation example of the pyrolysis model for fir.

Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

Beyond the basics: A deep dive into parameter estimation for advanced PBPK and QSP models

Parameter estimation in blood flow models from measured velocity data—as e.g. velocity-encoded MRI—is a key step for patient-specific hemodynamic analysis. However, velocity encoding suffers from competing noise and aliasing artifacts, which negatively impact the parameter estimation results. The aim of this work is to propose a new inverse problem formulation capable of tackling aliased and noisy velocity MRI measurements in parameter estimation in flows. The formulation is based on a modification of the quadratic cost function for velocity measurements. This allows for a correct parameter estimation when they have influence on the whole measurement domain, in spite of aliasing artifacts. The new inverse problem can be solved numerically using any standard solver, and we show how a popular sequential approach can be applied. Numerical results in an aortic flow show robust parameter estimation for velocity encoding ranges until 30% of the maximal velocity of the problem, while the standard inverse problem fails already for any encoding velocity smaller than the true one. Moreover, the parameter estimation results are even improved for reduced velocity encoding ranges when using the new cost function. The presented approach allows therefore for great flexibility in personalization of blood flows models from MRI data commonly encountered in the clinical context.

Accurate parameter estimation for photovoltaic (PV) cell or module models is crucial for enhancing the performance of PV systems through simulation, evaluation, and control. However, due to the nonlinear and multi-modal nature of PV models, parameter extraction remains a challenging task. To address this issue, this study proposes an improved mayfly optimization algorithm (MOA) for PV cell parameter estimation using measured current–voltage data. To strengthen the algorithm’s global search capability, Lévy-distributed random numbers are introduced to replace uniformly distributed numbers in the mayflies’ position updates. The heavy-tailed property of Lévy flight enables a broader search range, effectively preventing the algorithm from converging to local optima. Furthermore, a chaotic local search operator is incorporated into MOA to refine its local exploitation ability. The proposed algorithm, termed LFC-MOA (Lévy Flight and Chaos-based Mayfly Optimization Algorithm), is rigorously evaluated on three benchmark PV cell datasets. Experimental results demonstrate its effectiveness in accurately identifying PV cell parameters.

The primary challenge of software reliability growth model is to find the unknown model parameters that are used to validate on software failure dataset. Though, numerical estimation technique plays a vital role in parameter estimation of software reliability growth models, they are not optimal as they suffer from constraints sucha as sample size, biasing, and initialisation of parameters. In this study, a parameter estimation of software reliability growth model that utilises a variant of harmony search is proposed. Extensive experiments are conducted on seven different software datasets of varying complexity. A robust experimental setup is developed employing an orthogonal array and Taguchi method. Two‐fold performance comparisons are performed. First, the authors tested their proposed approach against Cuckoo search and numerical method (least square estimation) considering mean square error and Theil's statistics as a quality measure. Second, the authors applied statistical tests are performed that demonstrate the superiority of their approach over the others. The underlying motivation to conduct this study is to motivate researchers to utilise their approach for a better estimation of model parameters.