Example Of Parameter Estimation Research Articles

Generalized moment estimation of multi-dimensional uncertain differential equations

Multi-dimensional uncertain differential equations (MUDEs) are often used to describe complex systems that vary with time. In this paper, the generalized moment estimation method is employed to estimate the MUDEs’ unknown parameters. A method to optimize parameters with multiple estimation results is proposed. The hypothesis test and α-path are proposed to verify the feasibility of the parameter results. Several examples of parameter estimation for MUDEs are given, as well as two numerical examples to verify the feasibility of the method.

Single-spacecraft techniques for shock parameters estimation: A systematic approach

Spacecraft missions provide the unique opportunity to study the properties of collisionless shocks utilising in situ measurements. In the past years, several diagnostics have been developed to address key shock parameters using time series of magnetic field (and plasma) data collected by a single spacecraft crossing a shock front. A critical aspect of such diagnostics is the averaging process involved in the evaluation of upstream/downstream quantities. In this work, we discuss several of these techniques, with a particular focus on the shock obliquity (defined as the angle between the upstream magnetic field and the shock normal vector) estimation. We introduce a systematic variation of the upstream/downstream averaging windows, yielding to an ensemble of shock parameters, which is a useful tool to address the robustness of their estimation. This approach is first tested with a synthetic shock dataset compliant with the Rankine-Hugoniot jump conditions for a shock, including the presence of noise and disturbances. We then employ self-consistent, hybrid kinetic shock simulations to apply the diagnostics to virtual spacecraft crossing the shock front at various stages of its evolution, highlighting the role of shock-induced fluctuations in the parameters’ estimation. This approach has the strong advantage of retaining some important properties of collisionless shock (such as, for example, the shock front microstructure) while being able to set a known, nominal set of shock parameters. Finally, two recent observations of interplanetary shocks from the Solar Orbiter spacecraft are presented, to demonstrate the use of this systematic approach to real events of shock crossings. The approach is also tested on an interplanetary shock measured by the four spacecraft of the Magnetospheric Multiscale (MMS) mission. All the Python software developed and used for the diagnostics (SerPyShock) is made available for the public, including an example of parameter estimation for a shock wave recently observed in-situ by the Solar Orbiter spacecraft.

The parameter estimation of logistic regression with maximum likelihood method and score function modification

The maximum likelihood parameter estimation method with Newton Raphson iteration is used in general to estimate the parameters of the logistic regression model. Parameter estimation using the maximum likelihood method cannot be used if the sample size and proportion of successful events are small, since the iteration process will not yield a convergent result. Therefore, the maximum likelihood method cannot be used to estimate the parameters. One way to resolve this un-convergence problem is using the score function modification. This modification is used to obtain the parameters estimate of logistic regression model. An example of parameter estimation, using maximum likelihood method with small sample size and proportion of successful events equals 0.1, showed that the iteration process is not convergent. This non-convergence can be solved with modifications on a score function. Modification on score function is to change a score function, a matrix of the first derivative of the log likelihood function, to the first derivative matrix itself minus multiplication of information matrix and biased vector. The modification of the score function can quickly yield values of parameter estimates, especially when the sample sizes are larger, and convergence was reached before the 10th iteration.

A time-frequency-shift invariant parameter estimator for oscillating transient functions using the matched window reassignment

In this paper we present the matched window reassignment method, generalizing the results to complex valued signals in multiple dimensions. For an oscillating transient signal with an envelope shape described by an arbitrary twice differentiable function, the reassigned spectrogram, with a matched window, concentrates all energy into one single time-frequency point. An estimator for the parameters of the envelope, in multiple dimensions, is constructed using the above property where the concentration is measured using the Rényi entropy. Furthermore, we present a classification scheme, where an observation is classified based on the concentration when reassigning with a set of model functions. Finally, two examples of parameter estimation from real-world measurements are shown, a one-dimensional time series of a single dolphin click and a two-dimensional time-series of seismic data.

Model reduction of aerobic bioprocess models for efficient simulation

Owing to the increasing demand for large scale and high efficiency in manufacturing processes, computer aided tools for process operation and control are rapidly gaining popularity. An important state variable in aerobic processes is the dissolved oxygen, which can be easily measured online and is an important indicator of the metabolic activity. However, due to the fast kinetics of the oxygen transfer, dynamical models describing aerobic bioprocesses tend to be highly stiff. This can lead to significant numerical problems hampering its use for fixed step discretization methods and computationally costly applications such as computer fluid dynamics. In this work we use the slow-motion invariant manifold and the quasi steady state assumption methods to eliminate the differential equation describing the dissolved oxygen (the fast mode). By doing this, the tractability of the model is significantly increased with a neglectable loss in description power. The reduced model is also useful for simplifying the observer design problems, which is demonstrated by a state and parameter estimation example at the end of the work.

Statistical applications of optimization methods and mathematical programming

Abstract Optimization techniques perform an important role in different domains of statistic. Examples of parameter estimation of different distributions, correlation analysis (parametric and nonparametric), regression analysis, optimal allocation of resources in partial research, exploration of response surfaces, design of experiments, efficiency tests, reliability theory, survival analysis are the most known methods of statistical analysis in which we find optimization techniques. The paper contains a synthetic presentation of the main statistical methods using classical optimization techniques, numerical optimization methods, linear and nonlinear programming, variational calculus techniques. Also, an example of applying the “simplex” algorithm in making a decision to invest an amount on the stock exchange, using a prediction model..

PENAKSIRAN PARAMETER ANALISIS REGRESI COX DAN ANALISIS SURVIVAL BAYESIAN

In the theory of estimation, there are two approaches, namely the classical statistical approach and global statistical approach (Bayesian). Classical statistics are statistics in which the procedure is the decision based only on the data samples taken from the population. While Bayesian statistics in making decisions based on new information from the observed data (sample) and prior knowledge. At this writing Cox Regression Analysis will be taken as an example of parameter estimation by the classical statistical approach Survival Analysis and Bayesian statistical approach as an example of global (Bayesian). Survival Bayesial parameter estimation using MCMC algorithms for model complex / complicated and difficult to resolve while the Cox regression models using the method of partial likelihood. Results of the parameter estimates do not close form that needs to be done by the method of Newton-Raphson iteration.

Inference for time-varying signals using locally stationary processes

Abstract Locally Stationary Processes (LSPs) in Silverman’s sense, defined by the modulation in time of a stationary covariance function, are valuable in stochastic modelling of time-varying signals. However, for practical applications, methods to conduct reliable parameter inference from measured data are required. In this paper, we address the lack of suitable methods for estimating the parameters of the LSP model, by proposing a novel inference method. The proposed method is based on the separation of the two factors defining the LSP covariance function, in order to take advantage of their individual structure and divide the inference problem into two simpler sub-problems. The method’s performance is tested in a simulation study and compared with traditional sample covariance based estimation. An illustrative example of parameter estimation from EEG data, measured during a memory encoding task, is provided.

Component-wise conditionally unbiased widely linear MMSE estimation

Biased estimators can outperform unbiased ones in terms of the mean square error (MSE). The best linear unbiased estimator (BLUE) fulfills the so called global conditional unbiased constraint when treated in the Bayesian framework. Recently, the component-wise conditionally unbiased linear minimum mean square error (CWCU LMMSE) estimator has been introduced. This estimator preserves a quite strong (namely the CWCU) unbiased condition which in effect sufficiently represents the intuitive view of unbiasedness. Generally, it is global conditionally biased and outperforms the BLUE in a Bayesian MSE sense. In this work we briefly recapitulate CWCU LMMSE estimation under linear model assumptions, and additionally derive the CWCU LMMSE estimator under the (only) assumption of jointly Gaussian parameters and measurements. The main intent of this work, however, is the extension of the theory of CWCU estimation to CWCU widely linear estimators. We derive the CWCU WLMMSE estimator for different model assumptions and address the analytical relationships between CWCU WLMMSE and WLMMSE estimators. The properties of the CWCU WLMMSE estimator are deduced analytically, and compared by simulation to global conditionally unbiased as well as WLMMSE counterparts with the help of a parameter estimation example and a data estimation/channel equalization application.

Time-domain compressive dictionary of attributed scattering center model for sparse representation

Parameter estimation of the attributed scattering center (ASC) model is significant for automatic target recognition (ATR). Sparse representation based parameter estimation methods have developed rapidly. Construction of the separable dictionary is a key issue for sparse representation technology. A compressive time-domain dictionary (TD) for ASC model is presented. Two-dimensional frequency domain responses of the ASC are produced and transformed into the time domain. Then these time domain responses are cutoff and stacked into vectors. These vectored time-domain responses are amalgamated to form the TD. Compared with the traditional frequency-domain dictionary (FD), the TD is a matrix that is quite spare and can markedly reduce the data size of the dictionary. Based on the basic TD construction method, we present four extended TD construction methods, which are available for different applications. In the experiments, the performance of the TD, including the basic model and the extended models, has been firstly analyzed in comparison with the FD. Secondly, an example of parameter estimation from SAR synthetic aperture radar (SAR) measurements of a target collected in an anechoic room is exhibited. Finally, a sparse image reconstruction example is from two apart apertures. Experimental results demonstrate the effectiveness and efficiency of the proposed TD.

Adaptive initial step size selection for Simultaneous Perturbation Stochastic Approximation.

A difficulty in using Simultaneous Perturbation Stochastics Approximation (SPSA) is its performance sensitivity to the step sizes chosen at the initial stage of the iteration. If the step size is too large, the solution estimate may fail to converge. The proposed adaptive stepping method automatically reduces the initial step size of the SPSA so that reduction of the objective function value occurs more reliably. Ten mathematical functions each with three different noise levels were used to empirically show the effectiveness of the proposed idea. A parameter estimation example of a nonlinear dynamical system is also included.

Cross model validation and optimisation of bilinear regression models

Whenever regression models are optimised, it is important that all optimisation steps are properly validated. Variable selection is one example of parameter estimation that will give overly optimistic models if not included in the validation. There are many examples of reported work where the validation is performed posterior to variable selection, and many have correctly noted that these models are optimistically biased. However, if the availability of samples is limited, separation of the data into a training and validation set may decrease the quality of both the calibration model and the validation. Cross model validation is designed to validate the optimisation by including the variable selection in an extra layer of cross-validation. This means that all available samples are utilised both in the training and for estimating the residual error of the model. Cross model validation poses challenging questions both conceptually and algorithmically, and a presentation of the full work-flow is needed. We present a complete framework including optimisation, validation and calibration of bilinear regression models with variable selection. Several issues are addressed that are important for each separate stage of the analysis, and suggestions for improvements are proposed. The method is validated on a gene expression data set with a low signal-to-noise ratio and a small number of samples. It is shown that many replicates are needed to model these data properly, and that cross model validated variable selection improves both the final calibration model and the associated error estimates. A Matlab toolbox (Mathworks Inc, USA) is available from www.specmod.org.

Probability estimation when some observations are grouped

This paper considers the use of additional questions for decreasing survey non-response rates and an approach for estimating a probability based on the results obtained. In a survey, the respondents are asked to answer an original question and follow-up questions, where the answers for the follow-up questions are grouped answers for the original question. For example, respondents are asked to provide an exact number of incidents, but in cases of 'Do not know' or 'Refuse' responses, they are subsequently asked to pick an answer from a less specific categorical scale. The new estimator obtains smaller variance asymptotically and does not depend on a distribution family. This method is applied to income questions in a survey regarding injury prevention and behaviours. Another application is survey data on intimate partner violence, where some amendments were applied for incorporating post-stratification weights and for using non-random grouping. For additional illustration, an example of parameter estimation on artificially generated data is presented.

Simulation of conditioned diffusion and application to parameter estimation

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on a terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of another diffusion which is easy for simulation, and the formula for the density is given explicitly. An example of parameter estimation for a Duffing–Van der Pol oscillator is given as an application.

On minimal representation of heterogeneous mass transfer for simulation and parameter estimation: Application to breakthrough curves exploitation

This paper deals with the problem of mass transfer representation within heterogeneous systems. For the purpose of their modelling from material balances, it is emphasised the existence of a well-suited change of state variables which leads to a representation containing a minimal number of parameters. The benefits of the proposed approach are illustrated by an example of parameter estimation performed from experimental breakthrough curves in chromatography. Experimental data concerning the adsorption of p-nitrophenol onto granular activated carbon are taken from [Chern, J., Chien, Y. (2002). Adsorption of nitrophenol onto activated carbon: isotherms and breakthrough curves. Water Research 36, 647–655]. This representation has several advantages: from a numerical point of view for simulation and also for parameter estimation since the number of parameter groups (macro-parameters) is minimal. In order to confirm the relevance of the change of coordinates that we propose, a structural identifiability study is also performed in some cases.

ESTIMA – an integrated software tool for nonlinear parameter estimation

System identification is an iterative model building process to obtain an accurate mathematical description from measured system responses. It involves two characteristically different aspects, the first being the choice of computationally intensive parameter estimation procedure and the second being the mandatory tasks such as preparation of experimental data, statistical analysis of residuals and model validation through time history plots and system analysis. In the first case, a variety of efficient parameter estimation algorithms is necessary to cover the broad spectrum of applications. The second aspect requires availability of user friendly pre- and post-processing graphical tools to rapidly determine the model quality. ESTIMA, an integrated software tool developed at the DLR Institute of Flight Systems, provides a well proven developmental environment to researchers and engineers to accelerate efficient model development process. This paper highlights the capabilities of this universally applicable package for system identification and simulation of general nonlinear dynamic systems. A few typical examples of parameter estimation and post-processing capabilities are demonstrated. A short description of related software tools KONVERT and MeDaLib for format conversion and preparation of measured data is presented.

On the use of constraints in least squares estimation and control

In this article, we examine the effect of constraints on estimation and control methods based on quadratic penalty functions. We begin with estimation theory and analyze how constraints alter the statistical properties of the least squares estimates. It is shown that constraints can be used to formulate maximum likelihood (MLE) and maximum a posteriori (MAP) estimators for a variety of unimodal distributions. This provides greater flexibility over the assumption of normality inherent in the MLE and MAP interpretation of traditional least squares. We discuss how these ideas apply to state space models of dynamic systems. Possible applications for controllers that handle constraints are also discussed. A parameter estimation example is given to demonstrate the potential for improved performance over unconstrained least squares.

Worst case Cramer-Rao bounds for parametric estimation of superimposed signals with applications

The problem of parameter estimation of superimposed signals in white Gaussian noise is considered. The effect of the correlation structure of the signals on the Cramer-Rao bounds is studied for both the single and multiple experiment cases. The best and worst conditions are found using various criteria. The results are applied to the example of parameter estimation of superimposed sinusoids, or plane-wave direction finding in white Gaussian noise, and best and worst conditions on the correlation structure and relative phase of the sinusoids are found. This provides useful information on the limits of the resolvability of sinusoid signals in time series analysis or of plane waves in array processing. The conditions are also useful for designing worst-case simulation studies of estimation algorithms, and for the design of minimax signal acquisition and estimation procedures, as demonstrated by an example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Combined Parameter and Function Estimation in Heat Transfer With Application to Contact Conductance

This paper discusses parameter estimation, function estimation, and a combination of the two. An example of parameter estimation is the determination of thermal conductivity of solids from transient temperature measurements. An example of function estimation is the inverse heat conduction problem, which uses transient temperature measurements to determine the surface heat flux history. The examples used herein involve the determination of the thermal contact conductance. Two sets of very good data are analyzed. One set of steady-state data was obtained by Antonetti and Eid (1987). The other set was obtained by Moses and Johnson (1986) under transient conditions for periodic contact. Both sets of data are used to illustrate parameter, function, and combined estimation. It is demonstrated that the proposed methods are more powerful then commonly accepted methods. Many other heat transfer problems can be treated using the proposed techniques.