Maximum likelihood expectation maximization

In closing this section, we should note that many other estimation methods have been developed through the years, including maximum likelihood and maximization expectation (Mendel 1995 McLachlan 8c Krishnan 1999), Bayesian estimation (Carlin 8c Louis 1997), and iterative gradient-based methods (Haykin 1994 Ljung 1999) that cannot be detailed here in the interest of space. 

The training problem determines the set of model parameters given above for an observed set of wavelet coefficients. In other words, one first obtains the wavelet coefficients for the time series data that we are interested in and then, the model parameters that best explain the observed data are found by using the maximum likelihood principle. The expectation maximization (EM) approach that jointly estimates the model parameters and the hidden state probabilities is used. This is essentially an upward and downward EM method, which is extended from the Baum-Welch method developed for the chain structure HMM [43, 286]. 

Population pharmacokinetics offered as a feature of a broader PK/PD application within an Enterprise (end-to-end, LIMS to report) solution population approach uses a parametric expectation-maximization (EM) algorithm to compute maximum likelihood estimates... 

Maximum-likelihood haplotype frequencies are estimated from the observed data using an expectation-maximization (EM) algorithm and standardized linkage disequilibrium values (D = D/D ax). and D values are shown as graphic maps (http // www.weU.ox.ac.uk/asthma/GOLD/docs/ldmax.html) and HAPLOVIEW program. 

Stanley and Guichon [151] have recently proposed the expectation-maximization (EM) method for numerical estimation of adsorption energy distributions. This method does not require prior knowledge of the distribution function or any analytical equation for the total isotherm. Moreover, it requires no smoothing of the adsorption isotherm data and coverages with high stability toward the maximum-likelihood estimate. 

The adjustable parameters in the model are Z and P(Q for i = 1,..., K. These parameters are fit by maximum likelihood (i.e. to maximize p(x) on the training data vectors jc) via the well-known expectation-maximization (EM) algorithm (McLachlan and Krishnan, 1997). The EM algorithm is initialized using the very efficient T-means algorithm, and it typically converges in 20-100 iterations. 

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