Parameter Estimation via Gaussian Processes and Maximum Likelihood Estimation
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Computer models usually have a variety of parameters that can (and need to) be tuned so that the model better reflects reality. This problem is called calibration and is an inverse problem. We assume that we have a set of observed responses to given inputs in a physical system and a computer model that depends on parameters that models the physical system being studied. It is often the case that many more simulations can be run than experiments conducted, so we typically have many more simulation results (at various parameter values) than experimental results (at the “true” parameter value). In this paper, we use Maximum Likelihood Estimation (MLE) to calibrate model parameters. We assume that the response data is vector-valued, e.g. a response is given as a function of time. We approximate the underlying models with Gaussian Processes (GPs) and fit the parameters of the GPs with MLE. Specifically, we propose a decomposition approach to identify the basis vectors that allows for efficient calculation of the parameters. Experimental data is then used to calibrate the model parameters. This approach is demonstrated on one test problem.The Bock and Aitkin (1981) Marginal Maximum Likelihood/EM approach to item parameter estimation is an alternative to the classical joint maximum likelihood procedure of item response theory. Unfortunately , the complexity of the underlying mathematics and the terse nature of the existing literature has made understanding of the approach difficult. To make the approach accessible to a wider audience, the present didactic paper provides the essential mathematical details of a marginal maximum likelihood/EM solution and shows how it can be used to obtain consistent item parameter estimates. For pedagogical purposes, a short BASIC computer program is used to illustrate the underlying simplicity of the method.
Simplicity
Marginal likelihood
Restricted maximum likelihood
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Maximum likelihood sequence estimation is seen as the superior algorithm for electronic equalization at the receiver. We report about the first implementation of a 10.7 Gb/s optical receiver using maximum likelihood sequence estimation.
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Using the maximum likelihood method to carry on parameter estimation is to avoid the traditional optimization algorithms'shortcomings.This article uses the evolutional strategy algorithm and the maximum likelihood parameter estimation method for parameter estimation not to be affected by the initial value,but obtain a globally optimal solution.Finally parameter estimation is carried out based on the Weibulls'three parameter distribution.The results indicate this method has the merits of high solution precision and fast convergence speed,and the evolution strategy algorithm can be better applied in mathematical statistics.
Value (mathematics)
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The easy slighting problems in maximum likelihood estimation teaching are summarized in this paper. Also the authors illustrated the special conditions in maximum likelihood estimation. Finally,the authors pointed out that not all of parameters exist maximum likelihood estimation.
Restricted maximum likelihood
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It is shown that maximum likelihood estimation of unknown parameters of a linear system with singular observations in general results in the maximization of a likelihood function subject to equality constraints.
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Restricted maximum likelihood
Likelihood principle
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This paper introduces a new realization for maximum likelihood parameter and time-delay estimation using two channels. We obtain the result by using coupled Karhunen-Loeve expansions to derive the likelihood function. The new realization illuminates the analytical relationship between maximum likelihood time-delay estimation and other methods. Experimental results that support the theoretical findings are included.
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In this paper, we present a new method for two-dimensional spectral estimation. This method is based on the extension of the relationship that exists between the maximum likelihood method and the maximum entropy method for one-dimensional signals to two-dimensional signals. This method has a computational requirement similar to that of the maximum likelihood method, but has a resolution property which is considerably better than that of the maximum likelihood method. Examples are shown to illustrate the performance of the new algorithm.
Maximum entropy method
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