scholarly journals Maximum a posteriori estimates in linear inverse problems with log-concave priors are proper Bayes estimators

2014 ◽  
Vol 30 (11) ◽  
pp. 114004 ◽  
Author(s):  
Martin Burger ◽  
Felix Lucka
Keyword(s):  
Inverse Problems ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Bayes Estimators ◽  
Linear Inverse Problems ◽  
A Posteriori Estimates

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.

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 Maximum a posteriori estimators as a limit of Bayes estimators

2018 ◽  
Vol 174 (1-2) ◽  
pp. 129-144 ◽  
Author(s):  
Robert Bassett ◽  
Julio Deride
Keyword(s):  
Maximum A Posteriori ◽  
A Posteriori ◽  
Bayes Estimators

scholarly journals A BAYESIAN APPROACH FOR THE SOLUTION OF INVERSE PROBLEMS TO ESTIMATE RADIATIVE PROPERTIES

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
Cairo Martins Da Silva ◽  
Gustavo Antunes Guedes ◽  
Luiz Alberto da Silva Abreu ◽  
Diego Campos Knupp ◽  
Antônio José Da Silva Neto
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Inverse Problems ◽  
Optical Thickness ◽  
Radiative Heat ◽  
Single Scattering ◽  
Radiative Properties ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Numerical Application

The main objective of the present work is related to the formulation and solutionof inverse problems in radiative heat transfer phenomena. The analysis consists in estimating parameters and functions of a participanting medium, such as optical thickness, single scattering albedo, diffusive reflectivities and phase function coefficients. It is performed with the numerical application of a Bayesian framework, which includes “Maximum a Posteriori” (MAP) and "Markov Chains Monte Carlo"(MCMC), within the Metropolis-Hastings procedure. These methodologiesproved to be effective for solving such problems.

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