A probabilistic solution to the MEG inverse problem via MCMC methods: the reversible jump and parallel tempering algorithms

2001 ◽  
Vol 48 (5) ◽  
pp. 533-542 ◽  
Author(s):  
C. Bertrand ◽  
M. Ohmi ◽  
R. Suzuki ◽  
H. Kado
Keyword(s):  
Inverse Problem ◽  
Parallel Tempering ◽  
Mcmc Methods ◽  
Reversible Jump ◽  
Meg Inverse Problem ◽  
Probabilistic Solution

Gaussian mixture prior distribution on artifactual current for MEG inverse problem

2010 ◽  
Vol 68 ◽  
pp. e332
Author(s):  
Taku Yoshioka ◽  
Ken-ichi Morishige ◽  
Mitsuo Kawato ◽  
Masa-aki Sato
Keyword(s):  
Inverse Problem ◽  
Prior Distribution ◽  
Gaussian Mixture ◽  
Meg Inverse Problem ◽  
Mixture Prior

Solving the MEG Inverse Problem: A Robust Two-Way Regularization Method

Technometrics ◽  
2015 ◽  
Vol 57 (1) ◽  
pp. 123-137
Author(s):  
Siva Tian ◽  
Jianhua Z. Huang ◽  
Haipeng Shen
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Meg Inverse Problem

Finite Mixture Models

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Dirichlet Process ◽  
Bayesian Method ◽  
Finite Mixture Models ◽  
Finite Mixture ◽  
Maximum A Posteriori ◽  
Mcmc Methods ◽  
Reversible Jump ◽  
Posterior Distributions ◽  
A Posteriori ◽  
Point Estimates

Fitting a finite mixture model when the number of components, k, is unknown can be carried out using the maximum likelihood (ML) method though it is non-standard. Two well-known Bayesian Markov chain Monte Carlo (MCMC) methods are reviewed and compared with ML: the reversible jump method and one using an approximating Dirichlet process. Another Bayesian method, to be called MAPIS, is examined that first obtains point estimates for the component parameters by the maximum a posteriori method for different k and then estimates posterior distributions, including that for k, using importance sampling. MAPIS is compared with ML and the MCMC methods. The MCMC methods produce multimodal posterior parameter distributions in overfitted models. This results in the posterior distribution of k being biased towards high k. It is shown that MAPIS does not suffer from this problem. A simple numerical example is discussed.

A verifiable solution to the MEG inverse problem

NeuroImage ◽  
2006 ◽  
Vol 31 (2) ◽  
pp. 623-626 ◽  
Author(s):  
Gareth R. Barnes ◽  
Paul L. Furlong ◽  
Krish D. Singh ◽  
Arjan Hillebrand
Keyword(s):  
Inverse Problem ◽  
Meg Inverse Problem
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