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Likewise, forward values for preceding rows are not affected, since they depend only on the states preceding them, which are unchanged.
So, provided we are at a particular sequence position and in a particular state, we can sample the state at the previous sequence position, if we know all forward values for the previous sequence position.
(S2) If we have a close look at the description of the stochastic back-tracing algorithm, in particular the sampling step in Equation (4), we observe that the sampling of a previous state only requires the forward values for the current and the previous sequence position.
As this stochastic back-tracing procedure requires the entire matrix of forward values for all states and all sequence positions, the above algorithm for sampling a state path requires O (ML) memory and O (MT max L) time in order to first calculate the matrix of forward values and then O (L) memory and O (LT max ) time for sampling a single state path from the matrix.
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Walking backward was examined in a study and as for walking forward; values were lower in water than land-based [ 27].
BW [ 37] iteratively improves the parameters of the distributions in Equations 1 and 2. The utility of the algorithm relies on an efficient recursive formula for calculating the "forward" values α τ (h τ ) = ℙ(d τ, h τ | Θ), where the notation d τ denotes the first τ elements (e.g. residues) of observed sequence, and Θ are the parameters of the HMM.
We analyzed the data, carrying forward baseline values for these missing outcomes, assuming that any weight lost during the study was regained.
Table 4 summarizes the backward and forward linkage multiplier values for the six regions across the sectors.
Carrying forward baseline HbA1c values for those 283 participants with missing follow-up data, participants who were food insecure continued to have a 0.21% decrease in HbA1c over time (P = 0.02), whereas participants who were food secure had a nonsignificant decrease of 0.01%.
Although comparing AMOVA results across studies is not straight-forward, this value for these 4 islands is unsurpassed in the mtDNA literature for among-population variation within entire continents.
When a predicted value is at odds with the observations, we analyse which variables were responsible for the expectation failure these form a conflict and continue forward simulation considering different values for these variables.
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