In [14], maximum likelihood (ML) and minimization of classification error (MCE) learning methods were derived for the MSHMM.
We proposed an alternating minimization (AM) algorithm based on turning a maximum likelihood problem into a double minimization of I-divergence introduced by Csiszár [13].
Various parameter estimation techniques such as maximum likelihood estimation [41], prediction error minimization (PEM) [42], trust-region SQP algorithm [43] etc. have been used previously by researchers to estimate parameters of a model.
The estimation of cutpoints and slope parameters was carried out by maximum likelihood methods, by using nonlinear minimization of the appropriate binomial −2 log likelihood.
Two alternative algorithms for the calculation of the maximum likelihood fit are considered (gradient-based minimization and differential evolution).
Other regression approaches included in the analysis were maximum likelihood type robust (M) estimation (Huber 1973), minimization of robust scale (S) estimation (Rousseeuw and Yohai 1984), and high breakdown/high efficiency robust (MM) estimation (Yohai 1987).
The model was refined with PHENIX.refine (Adams et al., 2010), using gradient minimization with weight optimization, maximum likelihood targets, non-crystallographic symmetry constraints, individual B-factors, and TLS parameters.
Different reconstruction strategies on 2D hexagonal lattices are examined regarding maximum likelihood principles including maximization of obstruction effects and minimization of either local or global variance of conductances between sorption sites.
After reading many astronomy literature, I develop a notion that astronomers like to use the maximum likelihood as a robust alternative to the chi-square minimization for fitting astrophysical models with parameters.
Results confirm the success of two methods: the VFM approach which provides the "maximum likelihood solution" and the FEMU approach based on the "displacement gap" minimization.
