From: A new Bayesian piecewise linear regression model for dynamic network reconstruction
Symbol | Description | Prior distribution |
---|---|---|
N | Total number of nodes (genes) | – |
n | Number of potential parent nodes, here \(n=N-1\) | – |
h | Data segment h | – |
H | Total number of data segments | – |
k | Number of covariates in covariate set | – |
t | Data point t | – |
\(\sigma ^2\) | Noise variance parameter | \(\sigma ^{-2}\sim GAM(\alpha _{\sigma },\beta _{\sigma })\) |
\(\lambda _c\) | Coupling strength parameter, \(h>1\) | \(\lambda _c^{-1}\sim GAM(\alpha _{c},\beta _{c})\) |
\(\lambda _u\) | SNR parameter, \(h=1\) | \(\lambda _u^{-1}\sim GAM(\alpha _{u},\beta _{u})\) |
\(\lambda _h\) | hth coupling strength parameter (M4 model) | \(\lambda _h^{-1}\sim GAM(\alpha _{c},\beta _{c})\) |
\(\delta _h\) | hth coupling indicator variable (M3 model) | \(\delta _h\sim BER(\text{ p})\), \(\text{ p }\sim BETA(a,b)\) |
T | Total number of data points | – |
\(T_h\) | Number of data points in segment h | – |
\(D_i\) | ith data point | – |
\(Z_i\) | ith network node | – |
\({\varvec{\pi }_{i}}\) | Parent (covariate) set of ith node, \(Z_i\) | \(p(|\varvec{\pi }|<=3)=c\), \(p(|\varvec{\pi }|>3)=0\) |
\(\varvec{\tau }\) | Changepoint set | \(p(\varvec{\tau }) = (1-p)^{(T-1)-(H-1)} \cdot p^{H-1}\) |
\(\tau _h\) | Changepoint h | – |
\(X_i\) | ith covariate | – |
\(\mathbf{X }_{h}\) | Design matrix of segment h | – |
\(\mathbf{y }_{h}\) | Response vector of segment h | \(\mathbf{y }_{h}|(\varvec{{w}}_{h},\sigma ^2) \sim \mathcal {N}(\mathbf{X }_{h} \varvec{{w}}_{h} , \sigma ^2 \mathbf{I })\) |
\(\varvec{{w}}_{h}\) | Regression coefficient vector of segment h | \(\varvec{{w}}_{h}|(\varvec{\mu }_h,\varvec{\Sigma }_h,\sigma ^2) \sim \mathcal {N}(\varvec{\mu }_h, \sigma ^2 \varvec{\Sigma }_h )\) |
\(\tilde{\varvec{{w}}_{h-1}}\) | Posterior expectation of \(\varvec{{w}}_{h-1}\) | – |