Table 5 List of error models. Error models (EM) and the parameters for each of the implemented error model. Noise free input data is denoted by x and the noisy output data by y. Index i refers to gene, j to array (chip), and k to biological sample specific noise. Index p refers to a specific probe within a probe set.

Model

Additive Gaussian noise is added to the data.

μ

Mean of the additive Gaussian noise. Noise is drawn from N (μ, α²)

α ²

Variance of the additive Gaussian noise.

SNR EM:

Model

Additive Gaussian noise is added to the data with given signal-to-noise ratio.

μ

Mean of the additive Gaussian noise.

SNR

Signal-to-noise ratio after the noise is added.

Dror EM [7]:

Model

y = g * (x _i * x) + f + ε

${\mu }_{x_i}$, ${\sigma }_{x_i}^2$

Binding efficiency of each probe x _i is drawn from Gaussian distribution N (${\mu }_{x_i}$, ${\sigma }_{x_i}^2$).

μ _f , ${\sigma }_f^2$

Gene specific bias f is drawn from Gaussian distribution N (μ _f , ${\sigma }_f^2$).

α _ε , β _ε

Gene and chip specific error ε is drawn from Laplace distribution L (α _ε , β _ε ).

μ _g , ${\sigma }_g^2$

Multiplicative gene and chip specific noise g is drawn from log-normal distribution LN (μ _g , ${\sigma }_g^2$).

Hartemink EM [9]:

Model

In log scale y = x + ρ _j + ε _ij

${\mu }_{p_j}$, ${\sigma }_{p_j}^2$

Chip specific bias ρ _j is drawn from Gaussian distribution N (${\mu }_{p_j}$, ${\sigma }_{p_j}^2$).

${\sigma }_{{\epsilon }_{ij}}^2$

Gene and chip specific error ε _ij is drawn from Gaussian distribution N (0, ${\sigma }_{e_{ij}}^2$).

Hierarchical EM [6]:

Model

In log scale y = X + ε, X = x + g _i + c _j , + r _ij + b _ijk

${\sigma }_{\epsilon }^2$

Independent random noise ε is drawn from zero mean Gaussian distribution N (0, ${\sigma }_{\epsilon }^2$).

${\sigma }_{g_i}^2$

Gene specific noise g _i is drawn from zero mean Gaussian distribution.N (0, ${\sigma }_{g_i}^2$).

${\sigma }_{c_j}^2$

Chip specific noise C _j is drawn from zero mean Gaussian distribution N (0, ${\sigma }_{c_j}^2$).

${\sigma }_{r_{ij}}^2$

Gene and chip specific noise r _ij is drawn from zero mean Gaussian distribution N (0, ${\sigma }_{r_{ij}}^2$).

${\sigma }_{b_{ijk}}^2$

Gene, chip and biological sample specific noise b _ijk is drawn from zero mean Gaussian distribution N (0, ${\sigma }_{b_{ijk}}^2$).

Rocke EM [8]:

Model

y = α + xeⁿ + ε

${\sigma }_n^2$

Multiplicative noise n is drawn from zero mean Gaussian distribution N (0, ${\sigma }_n^2$).

${\sigma }_{\epsilon }^2$

Additive independent noise ε is drawn from zero mean Gaussian distribution N (0, ${\sigma }_{\epsilon }^2$).

μ _α , ${\sigma }_{\alpha }^2$

Background noise (bias) α is drawn from Gaussian distribution N (μ _α , ${\sigma }_{\alpha }^2$).

Hein EM [11]:

Model

PM _ijkp ~ N(S _ijkp + H _ijkp , ${\tau }_{jk}^2$), MM _ijkp ~ N (φS _ijkp + H _ijkp , ${\tau }_{jk}^2$), where PM refers to perfect match and MM to mismatch probe.

a _k , $b_k^2$

True expression signal log(S _ijkp + 1) is drawn from truncated (realization always ≥ 0) Gaussian distribution TN (x, ${\sigma }_{ik}^2$), where variance ${\sigma }_{ik}^2$ is drawn from Gaussian distribution N (a _k , $b_k^2$) and x is the underlying expression value.

μ _λ , ${\sigma }_{\lambda }^2$, α _η , β _η

Hybridization error term log(H _ijkp + 1) is drawn from truncated Gaussian distribution TN (λ _jk , ${\eta }_{jk}^2$). Parameter λ _jk is drawn from Gaussian distribution N (μ _λ , ${\sigma }_{\lambda }^2$) and ${\eta }_{jk}^2$ is drawn from gamma distribution Γ^-1(α _τ , β _τ ).

α _τ , β _τ

Variance ${\tau }_{jk}^2$ is drawn from gamma distribution Γ^-1(α _τ , β _τ ).

φ

Fractional binding φ can be selected from interval [0, 1].