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The EM algorithm iterates between these two steps and converges to a local maximum of the likelihood.
The maximum of the likelihood map is searched and the corresponding 6 parameters are considered the current best estimate of vertebra pose and orientation.
Consequently, the EM algorithm with initialization vector (boldsymbol {phi }^{(0)}triangleq [0,0,0,0]) converges to the maximum of the likelihood function.
Either a global search or numerical solution of the likelihood equations will be required to identify the location of the maximum of the likelihood function.
A detailed analysis of its trajectories in a variety of real or simulated data shows the ability of P-EM to choose the most efficient paths to the global maximum of the likelihood.
Standard learning methods for such models employ a variety of heuristics applied to the expectation-maximization implementation of the maximum likelihood estimation procedure in order to find the global maximum of the likelihood function.
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The Gompertz utilized R-code used the optim R-function for finding maxima of the likelihood function.
To study these propagated numerical errors we inferred the maxima of the likelihood functions.
Subsequent maxima of the likelihood function associated with bootstrapped samples were computed by means of local optimization algorithms (e.g., downhill simplex or quasi-Newton).
The likelihood function is defined on Ω, and the relationship R in Ω that produces the maximum value of the likelihood is the maximum likelihood estimate of the true relationship, corresponding to the posterior mode with a uniform prior.
The test statistic we use is proportional to the ratio of the maximum value of the likelihood function assuming the null hypothesis is true (null likelihood) and the maximum value of the likelihood function at the estimated parameter values (full likelihood).
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