Sensitivity computation is required for computing the Hessian matrix in the Gauss Newton and LM algorithms (Gill et al. 1981; Nocedal and Wright 2006; Griva et al. 2009).
A benchmark is required for computing this relative risk-adjusted measure.
Parameters for mass error and peak intensity can be chosen individually for each dataset, and are required for computing the likelihood of the data.
In contrast, hyperparameters are only estimated once for the SIRIUS 3 method, and are not retrained for a new dataset; they are required for computing the prior probability of a FT. Mass accuracy parameters (sigma _{text{m}}, MA, m_{ MA }) and noise intensity parameters (x_{text{i}}, alpha _{text{i}}) can be determined individually for each dataset.
For complex models encountered in applications, efficient computational tools robust to the number of uncertain parameters in the problem are required for computing the posterior statistics, which can generally be formulated as a multi-dimensional integral over the space of the uncertain parameters.
This enables us to compute the conditional entropy, which is required for computing the mutual information.
If a linear relationship, which is required for computing Pearson's r, could not be confirmed by pre-testing with scatter plots, Spearman's rho was used instead.
Additional O(d u ) operations are required for computing the term for row 1 and the row i such that v i = x∗, and therefore the total number of operations for computing the term for all d u entries in column j of H u, u ′ is O(d u ).
However, baseline estimation is required for computing predicted risk-free probability to estimate Brier score, and different methods used could result in different Brier scores.
Shortest paths algorithms are well-known from graph theory (e.g. Dijkstra algorithm [ 23]), however, interaction graphs are signed directed graphs and a special procedure is required for computing the length of the shortest positive and of the shortest negative path from a node i to a node k, denoted with Pik and Nik, respectively.
