As a result, determining the most probable lineage becomes a trans-dimensional model selection problem.
RJMCMC is an extension to standard MCMC methods that are often used in trans-dimensional model selection problems such as variable selection, mixture models and factor analysis (Green 1995).
For scenarios with colored noise, we present our proposed multi-dimensional model order selection technique called closed-form PARAFAC-based model order selection (CFP-MOS) scheme [3, 5].
Under certain conditions on the number of variables n, the number of nodes p and the maximum neighborhood size, the ℓ1 -penalized logistic regression for high-dimensional binary graphical model selection gives consistent neighborhood selection [ 24, 25].
In multi-dimensional model order selection schemes, forward-backward averaging is incorporated by replacing the data tensor in (11) by.
Besides the global eigenvalues-based schemes, we also propose a tensor data-based multi-dimensional model order selection scheme.
In this section, the multi-dimensional model order selection schemes are proposed based on the global eigenvalues, the R-D subspace, or tensor-based data model.
Multi-dimensional model order selection (MOS) techniques achieve an improved accuracy, reliability, and robustness, since they consider all dimensions jointly during the estimation of parameters.
The article by da Costa, Roemer, Haardt, and de Sousa entitled, "Multi-Dimensional Model Order Selection," considers the fundamental problem of deciding how many parameters are actually relevant to the model.
In this section, we evaluate the performance, in terms of the probability of correct detection (PoD), of all multi-dimensional model order selection techniques presented previously via Monte Carlo simulations considering different scenarios.
Therefore, as a first important contribution, we have proposed in [1, 2] the one-dimensional model order selection scheme called Modified Exponential Fitting Test (M-EFT), which outperforms all the other schemes for scenarios involving white Gaussian noise.
