For each step k, once an observation vector is received, the corresponding likelihood denoted as a weighting coefficient for each hypothesis can be obtained from one formula derived as follows.
Given : X_{i+k} = X_{i+k-1}=\cdots=X_i, \, we get : D_{i+k}(\theta) = D_{i+k-1}(\theta) = \cdots = D_{i+1}(\theta) = 0. \, When the ties are due to multiple observations, the repeated spacings (those that would otherwise be zero) should be replaced by the corresponding likelihood.
The total probability is the weighted average of the various conditional probabilities calculated as Total Probability = SUM [(Prior Probability) i × (Likelihood) i] Where (Prior Probability)I is the ith prior probability and (Likelihood)I is the corresponding ith likelihood.
In our method, the angles are deterministically biased towards the preferred direction, and the scattered photon packets are weighted by the corresponding likelihood ratio that eliminates any residual statistical bias.
Therefore, here, the spatial regression takes into account proximity among geographical units through the weight matrix W. Both spatial error and spatial lag models are estimated by maximizing the corresponding likelihood functions discussed further by Anselin et al. (2006).
The corresponding likelihood is relatively low (P = 0.059), suggesting that these pairs may be not subject to off-target cross-reaction and that the minimum length may be more than 25 nt.
The corresponding likelihood was computed by a beta function according to equation (4): where when The second part P oi|ri, qi) would be very easy to calculate if the real states ri were known.
To remove the dependence on initial states, the corresponding likelihood is further maximized and realized iteratively.
Suboptimal estimate can be computed, with weights given by the corresponding likelihood functions, from Equation 9. (9).
Based on running two alternative models, Models 1 and 2, we found that migrants with high work stress had 1.75 times the likelihood of being current smokers as those with low work stress, and the corresponding likelihood for life stress was 1.45 times.
