getRePara: Parameter Reparameterization

In eLNNpaired: Model-Based Gene Clustering for Genomics Data from Paired/Matched Designs

Description

Parameter reparameterization.

Usage

getRePara(
  mu1, 
  k1, 
  alpha1, 
  beta1, 
  mu2, 
  k2, 
  alpha2, 
  beta2, 
  alpha3, 
  beta3, 
  c1 = qnorm(0.95), 
  c2 = qnorm(0.05))

Arguments

mu1	mean of the mean expression levels for gene probes in cluster 1 (over-expressed probes).
k1	scalar in the variance of the mean expression levles for gene probes in cluster 1 (over-expressed probes).
alpha1	shape parameter of the distribution of the variance of gene expression levels for gene probes in cluster 1 (over-expressed probes).
beta1	rate parameter of the distribution of the variance of gene expression levels for gene probes in cluster 1 (over-expressed probes).
mu2	mean of the mean expression levels for gene probes in cluster 2 (under-expressed probes).
k2	scalar in the variance of the mean expression levles for gene probes in cluster 2 (under-expressed probes).
alpha2	shape parameter of the distribution of the variance of gene expression levels for gene probes in cluster 2 (under-expressed probes).
beta2	rate parameter of the distribution of the variance of gene expression levels for gene probes in cluster 2 (under-expressed probes).
alpha3	shape parameter of the distribution of the variance of gene expression levels for gene probes in cluster 3 (non-differentially expressed probes).
beta3	rate parameter of the distribution of the variance of gene expression levels for gene probes in cluster 3 (non-differentially expressed probes).
c1	the lower bound for mu_g/sqrt(tau_g^{-1}) for cluster 1 (over-expressed probes). By default c_1=Phi^{-1}(0.95).
c2	the upper bound for mu_g/sqrt(tau_g^{-1}) for cluster 2 (under-expressed probes). By default c_2=Phi^{-1}(0.05).

Details

We assume the following the Bayesian hierarchical models for the 3 clusters of gene probes.

For cluster 1 (over-expressed gene probes):

d_{gl} | (mu_g, tau_g) ~ N(mu_g, tau_g^{-1}),\ mu_g | tau_g ~ N(mu_1, k_1 tau_g^{-1}),\ tau_g ~ Gamma(alpha_1, beta_1).

For cluster 2 (under-expressed gene probes):

d_{gl} | (mu_g, tau_g) ~ N(mu_g, tau_g^{-1}),\ mu_g | tau_g ~ N(mu_2, k_2 tau_g^{-1}),\ tau_g ~ Gamma(alpha_2, beta_2).

For cluster 3 (non-differentially-expressed gene probes):

d_{gl} | (mu_g, tau_g) ~ N(0m, tau_g^{-1}),\ tau_g ~ Gamma(alpha_3, beta_3).

For cluster 1, we add one constraint

alpha_1>1+beta_1( (c_1-Phi^{-1}(0.05)sqrt{k_1})/mu_1 \right)^2

based on

Pr(mu_g/tau_g^{-1} <= c_1 | tau_g^{-1})<0.05,

where c_1=Phi^{-1}(0.05) and Phi is the cumulative distribution function of the standard normal distribution.

For cluster 2, we add one constraint

alpha_2>1+beta_2( (c_2-Phi^{-1}(0.95)sqrt{k_2})/mu_2 \right)^2

based on

Pr(mu_g/tau_g^{-1} >= c_2 | tau_g^{-1})<0.05,

where c_2=Phi^{-1}(0.95) and Phi is the cumulative distribution function of the standard normal distribution.

To do unconstraint numerical optimization, we do parameter reparameterization:

mu_1=exp(delta_1), k_1=Phi(xi_1), beta_1=exp(nu_1),\ alpha_1=exp(lambda_1)+1+beta_1left( frac{c_1-Phi^{-1}(0.05)sqrt{k_1}}{mu_1} right)^2,\ mu_2= -exp(delta_2), k_2=Phi(xi_2), beta_2=exp(nu_2),\ alpha_2=exp(lambda_2)+1+beta_2left( frac{c_2-Phi^{-1}(0.95)sqrt{k_2}}{mu_2} right)^2,\ beta_3=exp(nu_3), alpha_3=exp(lambda_3).

Value

A 10x1 vector of reparameterized parameters: delta_1, xi_1, lambda_1, nu_1, delta_2, xi_2, lambda_2, nu_2, lambda_3, nu_3.

Author(s)

Yunfeng Li <[e-mail]> and Weiliang Qiu <[e-mail]>

References

Li Y, Morrow J, Raby B, Tantisira K, Weiss ST, Huang W, Qiu W. (2017), <doi:10.1371/journal.pone.0174602>

See Also

See Also as getPara.orig

Examples

getRePara(
  mu1 = 5.015045e-01, 
  k1 = 2.756702e-13, 
  alpha1 = 2.192323e+00, 
  beta1 = 1.108378e-01,
  mu2 = -8.448602e-01, 
  k2 = 5.034642e-01, 
  alpha2 = 1.766274e+00, 
  beta2 = 6.917261e-02,
  alpha3 = 1.392992e+00, 
  beta3 = 9.636037e-02,
  c1 = qnorm(0.95),
  c2 = qnorm(0.05)
)

eLNNpaired documentation built on May 29, 2017, 12:04 p.m.