Maximum-likelihood and maximum-a-posteriori estimates of human-observer templates

2001 ◽  
Author(s):  
Craig K. Abbey ◽  
Miguel P. Eckstein
Keyword(s):  
Maximum Likelihood ◽  
Maximum A Posteriori ◽  
Human Observer ◽  
A Posteriori ◽  
A Posteriori Estimates

scholarly journals Score-Based Measurement Invariance Checks for Bayesian Maximum-a-Posteriori Estimates in Item Response Theory

2020 ◽  
Author(s):  
Rudolf Debelak ◽  
Samuel Pawel ◽  
Carolin Strobl ◽  
Edgar C. Merkle
Keyword(s):  
Maximum Likelihood ◽  
Item Response Theory ◽  
Item Response ◽  
Statistical Tests ◽  
Maximum A Posteriori ◽  
Model Parameters ◽  
A Posteriori ◽  
Response Theory ◽  
Simulation Based ◽  
A Posteriori Estimates

A family of score-based tests has been proposed in the past years for assessing the invariance of model parameters in several models of item response theory. These tests were originally developed in a maximum likelihood framework. This study aims to extend the theoretical framework of these tests to Bayesian maximum-a-posteriori estimates and to multiple group IRT models. We propose two families of statistical tests, which are based on a) an approximation using a pooled variance method, or b) a simulation-based approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be practically useful with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

A method for approximating the density of maximum-likelihood and maximum a posteriori estimates under a Gaussian noise model

1998 ◽  
Vol 2 (4) ◽  
pp. 395-403 ◽  
Author(s):  
Craig K. Abbey ◽  
Eric Clarkson ◽  
Harrison H. Barrett ◽  
Stefan P. Müller ◽  
Frank J. Rybicki
Keyword(s):  
Maximum Likelihood ◽  
Gaussian Noise ◽  
Noise Model ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
A Posteriori Estimates

scholarly journals Theoretical Analysis of the Relationship Between the Boundary Problem and Irregular Standard Errors in Diagnostic Classification Models

2021 ◽  
Author(s):  
Kazuhiro Yamaguchi
Keyword(s):  
Maximum Likelihood ◽  
Boundary Problem ◽  
Diagnostic Classification ◽  
Maximum A Posteriori ◽  
Standard Errors ◽  
Classification Models ◽  
A Posteriori ◽  
Diagnostic Classification Models ◽  
A Posteriori Estimates ◽  
The Relationship

In diagnostic classification models, parameter estimation sometimes provides estimates that stick to the boundaries of the parameter space, which is called the boundary problem, and it may lead to extreme values of standard errors. However, the relationship between the boundary problem and irregular standard errors has not been analytically explored. In addition, prior research has not shown how maximum a posteriori estimates avoid the boundary problem and affect the standard errors of estimates. To analyze these relationships, the expectation-maximization algorithm for maximum a posteriori estimates and a complete data Fisher information matrix are explicitly derived for a mixture formulation of saturated diagnostic classification models. Theoretical considerations show that the emptiness of attribute mastery patterns causes both the boundary problem and the inaccurate standard error estimates. Furthermore, unfortunate boundary problem without emptiness causes shorter standard errors. A simulation study shows that the maximum a posteriori method prevents boundary problems and improves standard error estimates more than maximum likelihood estimates do. The effect is sometimes radical, and the results show that the maximum a posteriori method is more appropriate than the maximum likelihood method.

scholarly journals The Onsager–Machlup functional for data assimilation

2017 ◽  
Author(s):  
Nozomi Sugiura
Keyword(s):  
Data Assimilation ◽  
Sampling Methods ◽  
Time Discretization ◽  
Model Error ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Discrete Form ◽  
Drift Term ◽  
A Posteriori Estimates ◽  
Large Systems

Abstract. When taking the model error into account in data assimilation, one needs to evaluate the prior distribution represented by the Onsager–Machlup functional. Numerical experiments have clarified how one should put it into discrete form in the maximum a posteriori estimates and in the assignment of probability to each path. In the maximum a posteriori estimates, the divergence of the drift term is essential, but for the path probability assignments in combination with the Euler time-discretization scheme, it is not necessary. The latter property will help simplify the implementation of nonlinear data assimilation for large systems with sampling methods such as the Metropolis-adjusted Langevin algorithm.

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