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However when the landscape of likelihood function has several local minima, gradient based optimization might end up with local convergence.
logarithm of likelihood function.
However, MLE has some shortcomings; its expressions of likelihood function are not explicitly computable.
A common problem of this approach is that the numerical method used in the optimisation process may fail to give a reasonable solution due to the complexity of likelihood function.
The new CSS scheme is superior to the classical one, obviously, since precise estimation of CSI can ensure the accuracy of likelihood function ratio between two hypotheses H 1 and H 0 (Fig. 7).
where L is the maximized value of likelihood function for the estimated model, n is the number of data points, k is the number of free parameters to be estimated and λ is the penalty factor assumed 1 in our case.
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Future models could incorporate a wider variety of likelihood functions, or even learn the global functional form from the data.
Unfortunately, only a small set of likelihood functions can easily be used without resorting to multi-hypothesis filtering methods.
In particular, assuming conditional independence of the different sensor measurements given the state vector, a distributed particle filter (PF) normally requires the computation of a product of likelihood functions that depend on local data only[8].
By running R × D consecutive minimum consensus iterations[12] for each particle q, it is possible (see details in[11]) to build an identical ordered list of likelihood functions λ r, n ( q ) ( x n ( q ) ), r ∈ R, at all nodes.
Other features include an SBML parser for automated generation of likelihood functions (Liepe et al., 2010) and plotting tools.
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