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Introduction
Published in Bin Jia, Ming Xin, Grid-based Nonlinear Estimation and Its Applications, 2019
An estimator is a procedure that processes measurement to deduce an estimate of the state or parameters of a system from the prior (deterministic or statistic) knowledge of the system, measurement, and initial conditions. The estimation is usually obtained by minimizing the estimation error in a well-defined statistical sense. Three types of estimation problems have been extensively investigated based on the times at which the measurement is obtained and estimation is processed. When an estimate is obtained at the same time as the last measurement point, it is a filtering problem; when the estimation takes place within the time interval of available measurement data, it is a smoothing problem; and when the estimation is processed at the time after the last available measurement, it is a prediction problem. This book will cover all these three estimation problems with relatively more attention to the first one since a large spectrum of estimation applications is the filtering problem.
Computational Modeling of Nanoparticles
Published in Sarhan M. Musa, ®, 2018
Elastic properties are not deterministic in the thin film that contains a small number of grains because the orientation of each grain is stochastic. In this case, multiple simulations should be performed to obtain the elastic properties. However, the number of simulations should be determined before the simulations. Without assuming normality, we need more than 30 simulations (samples) to construct an approximate 95% confidence interval (CI) for the mean elastic properties of a specific size polysilicon thin film (population). The CI is a formula that tells us how to use sample data to determine an interval that estimates a population parameter [44]. The confidence level (i.e., 95%) is the probability that an interval estimator encloses the population parameter. To determine the actual number of simulations, the following equation is used: () n=[(Za/2s0de)2]
Main Statements of Statistical Estimation Theory
Published in Vyacheslav Tuzlukov, Signal Processing in Radar Systems, 2017
In theory, for statistical parameter estimation, two types of estimates are used: the interval estimations based on the definition of confidence interval, and the point estimation, that is, the estimate defined at the point. Employing the interval estimations, we need to indicate the interval, within the limits of which there is the true value of unknown random process parameter with the probability that is not less than the predetermined value. This predetermined probability is called the confidence factor and the indicated interval of possible values of estimated random process parameter is called the confidence interval. The upper and lower bounds of the confidence interval, which are called the confidence limits, and the confidence interval are the functions to be considered during digital signal processing (a discretization) or during analog signal processing (continuous function). of the received realization x (t). In the case of point estimation, we assign one parameter value to the unknown parameter from the interval of possible parameter values; that is, some value is obtained based on the analysis of the received realization x (t) and we use this value as the true value of the evaluated parameters.
Inferential-Statistical Reevaluation of Spent Fuel Zircaloy Cladding Integrity
Published in Nuclear Technology, 2023
A confidence coefficient expresses the theoretical fraction of interval estimates that would contain the true value of an unknown population parameter, generated in a long series of repeated random samples under identical conditions.20 The confidence coefficient states as a decimal fraction the same quantity the confidence level states as a percentage. The confidence coefficient is sometimes called “confidence” and represented symbolically by the expression , as in Refs. 20 and 21. In early pioneering work on tolerance intervals,17 Wilks employed the symbol to denote the confidence coefficient. At the time, statistical vocabulary had not matured to the state of specificity and precision of definition it currently possesses, and therefore Wilks referred to as a “probability level.”
Learning attack-defense response in continuous-time discrete-states Stackelberg Security Markov games
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2022
The likelihood of observations is conceptualised as the probability to jump from state to at time , continued by a jump from state to at time , etc. The maximum-likelihood estimator is a method for estimating the parameters of a probability distribution by maximising a likelihood function. The objective is to obtain the values of the model parameters that maximise the likelihood function over the parameter space as follows
Maximum Likelihood Finite-Element Model Updating of Civil Engineering Structures Using Nature-Inspired Computational Algorithms
Published in Structural Engineering International, 2021
Javier Fernando Jiménez-Alonso, Javier Naranjo-Perez, Aleksandar Pavic, Andrés Sáez
Thus, given that one of the main objectives of FE model updating is to indirectly estimate the values of some relevant physical parameters of the structure, the updating process may be formulated as a parameter identification problem,7 where appropriate estimators need to be employed.8 Generally speaking, estimators may be classified into two categories:9,10 (1) Point estimators, which return the expected value of each considered design parameter; and (2) Interval estimators, which determine either an interval in which the value of each parameter lies or a probability density function for each parameter. Among the interval estimators, the Bayesian method11 has prevailed, since the determination of the probabilistic density function of the design parameters is relevant when performing subsequent structural reliability analyses.12 Meanwhile, among the point estimators, the maximum likelihood method (MLM) has been widely implemented due to its proved efficiency and accuracy when tackling model updating.8