Table 1.

Definitions of Notations Used Throughout the Paper^a

variable	meaning
$s^{(l)}$	indices of peaks in a fragmentation spectrum l
$m_i^{(l)}\text{for}i\in s^{(l)}$	m/z of peak i in spectrum $s^{(l)}$
$p_i^{(l)}\text{for}i\in s^{(l)}$	intensity of the peak at m/z in spectrum $s^{(l)}$
$D^{(l)}$	set of s(l), m(l), and $p_i^{(l)}$ for spectrum l
$m_j^{(l)}-m_i^{(l)}\text{for}i\in s^{(l)},j\in s^{(l)}$	m/z difference between two peaks in spectrum s(l)
Δ1, Δ2, Δ3, ..., Δd	alphabet of size d (units are mass, not m/z)
Є	maximum allowed error tolerance in m/z; if two m/z values are approximately equal, then the absolute value of their difference must be ≤Є.
$E_{z,i,j,k}^{(l)}\text{for}i\in s^{(l)},j\in s^{(l)},k\in \{1,2,\cdot \cdot \cdot ,d\}$	peaks i and j in spectrum s(l) can be connected by difference Δk using charge z; i.e., $\left|m_j^{(l)}-m_i^{(l)}-\frac{{\Delta }_k}{z}\right|\le \mathrm{Є}$ for some charge state
$E_z^{(l)}$	all edges for spectrum l that use charge state z
$g\left(E_z^{(l)}\right)=\left\{e_1,e_2,\dots \right\}$	collection of edges in the connected components of the graph defined by $E_z^{(l)}$
θ	hyperparameter that can be tuned to influence the acceptance rate; θ = 0 will accept all proposed changes; θ = ∞ will only accept changes that improve the likelihood

^aIn each spectrum $s^{(l)}$, a peak $i\in s^{(l)}$ has an m/z value $m_i^{(l)}$, with machine tolerance Є and intensity $p_i^{(l)}$. The set of $s^{(l)}$, $m_i^{(l)}$, and $p_i^{(l)}$ for all peaks in spectrum l forms $D^{(l)}$. The alphabet of size d, Δ₁, Δ₂, Δ₃, ..., Δ_d, is used to form a set of edges, $E_z^{(l)}$, for charge state z, and the set of edges forms connected components, $g(E_z^{(l)})=\{e_1,e_2,\dots \}$, of the graph defined by $E_z^{(l)}$.