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Table 3 Distribution type for each variable of the SRM acquisition chain

From: Variance component analysis to assess protein quantification in biomarker validation: application to selected reaction monitoring-mass spectrometry

Hierarchical level Variable Analytic expression distributiona Distribution type
Transition Noise \( {\displaystyle \begin{array}{c}p\left(\boldsymbol{I}|\boldsymbol{\kappa}, \boldsymbol{\xi}, \boldsymbol{\tau}, \boldsymbol{\lambda}, \gamma \right)\sim \prod \limits_{l=1}^L\mathit{\exp}\left(-\frac{1}{2}{\gamma}_n{\left\Vert {I}_l-{G}_l\left(\kappa, \xi, \tau, \lambda \right)\right\Vert}^2\right)\\ {}p\left({I}^{\ast }|\boldsymbol{\kappa}, \boldsymbol{\xi}, {\boldsymbol{\phi}}^{\ast},\boldsymbol{\tau}, \boldsymbol{\lambda}, {\gamma}^{\ast}\right)\sim \prod \limits_{l=1}^L\mathit{\exp}\left(-\frac{1}{2}{\gamma}_n^{\ast }{\left\Vert {I}_l^{\ast }-{G}_l^{\ast}\left(\kappa, \xi, {\phi}^{\ast },\tau, \lambda \right)\right\Vert}^2\right)\end{array}} \) Normal
Peptide Peptide to fragment gain \( p\left(\boldsymbol{\xi} \right)\sim \prod \limits_{i=1}^S\mathit{\exp}\left(-\frac{1}{2}{\gamma}_{\xi}^i{\left({\xi}_i-{m}_{\xi_i}\right)}^2\right) \) Normal
Peptide to fragment gain correction factor \( p\left({\boldsymbol{\phi}}^{\ast}\right)\sim \prod \limits_{i=1}^S\mathit{\exp}\left(-\frac{1}{2}{\gamma}_{\phi}^{\ast }{\left({\phi}_i^{\ast }-1\right)}^2\right) \) Normal
Noise inverse variance \( {\displaystyle \begin{array}{c}p\left({\gamma}_n\right)\sim \frac{\gamma_n^{\alpha_n-1}}{\beta_n^{\alpha_n}\Gamma \left({\alpha}_n\right)}\mathit{\exp}\left(-\frac{\gamma_n}{\beta_n}\right)\\ {}p\left({\gamma}_n^{\ast}\right)\sim \frac{\gamma_n^{\ast \left({\alpha}_n-1\right)}}{\beta_n^{\alpha_n}\Gamma \left({\alpha}_n\right)}\mathit{\exp}\left(-\frac{\gamma_n^{\ast }}{\beta_n}\right)\end{array}} \) Gamma
Peak retention time \( p\left(\boldsymbol{\tau} \right)\sim \prod \limits_{i=1}^SU\left({\tau}_i;{\tau}_i^m,{\tau}_i^M\ \right) \) Uniform
Peak width \( p\left(\boldsymbol{\lambda} \right)\sim \prod \limits_{i=1}^SU\left({\lambda}_i;{\lambda}_i^m,{\lambda}_i^M\ \right) \) Uniform
Peptide concentration \( p\left(\boldsymbol{\kappa} |\boldsymbol{y}\right)\sim \prod \limits_{i=1}^S\mathit{\exp}\left(-\frac{1}{2}{\gamma}_{\kappa }{\left({\kappa}_i-{H}_i(y)\right)}^2\right) \) Normal
Protein Protein concentration \( p\left(\boldsymbol{y}\right)\sim \prod \limits_{p=1}^P\mathit{\exp}\left(-\frac{1}{2}{\gamma}_x^p{\left({y}_p-{m}_{y_p}\right)}^2\right) \) Normal
Digestion yield \( p\left(\boldsymbol{g}\right)\sim \prod \limits_{i=1}^S\prod \limits_{p=1}^P\mathit{\exp}\left(-\frac{1}{2}{\gamma}_g{\left({g}_{ip}-{m}_g\right)}^2\right) \) Normal
  1. aBold notation stands for vectors