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In this stage, the decoding is accomplished by tracing the maximum likelihood path backwards through the trellis ([1] Chapter 12).
Therefore, a maximum likelihood path analysis with bootstrapped (10,000 replications) standard errors and confidence intervals for direct and indirect effects was performed.
We analyzed the maximum likelihood path model with robust standard error.
To obtain the maximum likelihood path, one only has to keep track of the values of s and f that are used to maximize each recurrence.
Subsequently, a composite-likelihood surface for the recombination parameter is calculated and, for the maximum-composite-likelihood parameter estimates, the maximum likelihood path through the HMM is calculated for each sequence (see Additional file 1).
Forming a phylogenetic tree based on FISH data involves three tasks: estimating probabilities of each type of event; using the estimated probabilities to efficiently estimate the maximum likelihood path between pairs of configurations; and finding an approximate maximum-likelihood phylogenetic tree, possibly containing Steiner nodes that represent unobserved or extinct configurations.
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First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit (epsilonrightarrow0)).
(4.5) A similar situation holds for the higher-dimensional case, except that there are now multiple maximum-likelihood paths of escape from a metastable state [27, 33].
4, we derive the basic variational principle that can be used to explore maximum-likelihood paths of escape from a metastable state, and relate the theory to the underlying Hamiltonian structure of the path-integral representation.
It is clear from the formal structure of the path integral (3.28) that each synaptic variable (u_{alpha}) has a 'conjugate momentum' (p_{alpha}) with (lambda_{0}(mathbf{u},{mathbf{p}})) the corresponding 'Hamiltonian' H. Applying steepest descents to the path integral for small ϵ yields a variational principle in which maximum-likelihood paths minimize the action (3.29).
It turns out that both classical trajectories and the maximum-likelihood paths of escape correspond to zero energy solutions of Hamilton's equations of motion; this follows from the fact that the action vanishes at fixed points of the deterministic mean-field equation.
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maximum likelihood modeling
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