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Final segmentation is obtained by combining a likelihood modification technique and the mixture foreground model.
The hyperparameter α rj ( t + 1 ) is sampled according to a conditional posterior distribution which is obtained by combining a likelihood function of [Ar] i j and an exponential prior density of α r j with parameter λ α rj.
The sampling of LSM parameter γ rj ( t + 1 ) is performed by using the conditional posterior distribution which is derived by combining a likelihood function of λ r j and an exponential prior density of γ r j with parameter λ γ rj.
The hyperparameter β rj ( t + 1 ) is sampled according to a conditional posterior distribution which is obtained by combining a likelihood function of [Ar] i j and a gamma prior density of β r j with parameters { α β rj, β β rj }, i.e., p ( β rj ∣ [ A r ( t + 1 ) ] ij, α rj ( t + 1 ) ) ∝ ( β rj ) D r α rj ( t + 1 ) × exp − β rj ∑ j = 1 D r [ A r ( t + 1 ) ] ij G ( β rj | α β rj, β β rj ).
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We show that this can be done in linear-time by combining a state machine with a Viterbi algorithm to find the nucleotide sequence that maximizes the likelihood of the observed flowgram.
We have taken the maximum likelihood approach to parameter estimation by combining an approximation of the population likelihood together with an extended Kalman filter for state estimation.
The current study aimed at identifying cortical areas consistently involved in action observation and imitation by combining activation likelihood estimation (ALE) meta-analysis with probabilistic cytoarchitectonic maps.
By combining likelihood function of (17) and gamma prior p ( [ A r ] ij | Φ A rij ( t ) ) of (11), the conditional posterior distribution in (16) is derived in a form of [ A r ] ij α rj ( t ) − 1 exp − ( [ A r ] ij − μ A rij post ) 2 2 [ σ A rij post ] 2 I [ 0, + ∞ [ ( [ A r ] ij ) (18).
We find these tree distances by fitting the tree to the empirical network data combining a maximum-likelihood approach with a Monte Carlo sampling method that explores the space of all possible dendrograms (see Methods).
Provided that they are independent, it is possible to account for other information by combining likelihood ratios for any additional test with that produced by the model.
In all three cases both curves are fitted using the growth model of Eqs. 1 and (2) and the likelihood function is given by combining the individual likelihoods for the two curves (from Eq. 4).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com