Specifically, as shown in Table 4, CRM2 took in average 10 times more the average solution time taken by CRM1 to solve instances having 10 SNPs, reaching a maximum
Some sufficient conditions are presented to determine its optimal solution in terms of the maximum solution or the minimal solutions of its feasible domain.
Errors corresponding to the range from about 10-2 of the maximum solution value, down to about 10-7 or even smaller, can be easily obtained at a modest computational cost.
Moreover, when (S A,mathbf{b})) is nonempty, the principal solution (hat{mathbf{x}}) becomes the maximum solution and (S A,mathbf{b})) can be determined by the maximum solution and a finite number of minimal solutions.
This process is made robust to corruption by weighting out its effect with the opacity values of the maximum likelihood solution of BTBR-S.
The maximum likelihood solution of unknown parameter α is regarded as the estimated value, and then, we sample the bimodal PDF p(x).
This method is derived from the interpretation of PCA as the maximum likelihood solution of a probabilistic factor analysis model (Tipping and Bishop, 1999) into which the technical variance is integrated as an additional term (for the detailed derivation, see Sanguinetti et al., 2005).
Therefore, we translate the cost function and constraints into a joint likelihood function of a probabilistic graphical model and apply a belief propagation algorithm to find a (approximate) maximum-likelihood solution of the model.
Classically, the maximum principle states that the maximum of the solution of a second-order elliptic or parabolic equation in a domain is to be found on the boundary of that domain.
This method develops a dynamic programming algorithm, which is theoretically guaranteed to find exact maximum likelihood solutions of the variable order Markov chain model for haplotype inference problem within linear running time.
