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which is equivalent to maximizing the log of p(r ; x).
These spatial and temporal hyperparameters λ and τ were estimated by approximately maximizing the log likelihood of the system (Additional file 4) (Kitagawa and Gersch 1996; McGuire and Segall 2003).
Parameters that best describe P can be obtained by maximizing the log likelihood with respect to the Gaussian mixture models (GMM) for all the frames of the speech [2].
We seek the optimal solution of hyperparameters by maximizing the log marginal likelihood (see [27] for details): log p ( Ψ ′ | s, θ ) = − 1 2 Ψ ′ T K Ψ ′ − 1 Ψ ′ − 1 2 log | K Ψ ′ | − n 2 log 2 Π, (11).
Now, by maximizing the log marginal likelihood and then differentiating with respect to Ξ j and ξ 0 and setting to zero yields (boldsymbol{Xi}_{j})^{new}=frac{J-boldsymbol{Xi}_{j} sum_{j=1}^{J} boldsymbol{Sigma}^{n}_{c^,c^,i,j}}{sum_{j=1}^{J}left(boldsymbol{mu}^{n}_{c^,c^,i,j}right)^{2}}, (29).
For maximizing the log likelihood function and determining a numerically approximated information matrix for calculation of the standard errors of the estimates, we use the BFGS algorithm as implemented in R. The approximated values are in line with results from simulation of datasets and subsequent re-estimation of the parameters.
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The most likely set of parameters is found by maximizing the log-likelihood function using an iterative approach related to expectation-maximization.
A class of predictive densities is derived by weighting the observed samples in maximizing the log-likelihood function.
By maximizing the log-likelihood function, we estimate the parameters.3.3
Maximizing the log-likelihood function of given, results in the following ML decision rule: (2).
The MLE is obtained by maximizing the log-likelihood function shown in (11).
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