The "MVN" Class
Description
The MVN
class is a tool used to generate gene expressions that
follow multivariate normal distribution.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13  MVN(mu, Sigma, tol = 1e06)
covar(object)
correl(object)
## S4 method for signature 'MVN'
alterMean(object, TRANSFORM, ...)
## S4 method for signature 'MVN'
alterSD(object, TRANSFORM, ...)
## S4 method for signature 'MVN'
nrow(x)
## S4 method for signature 'MVN'
rand(object, n, ...)
## S4 method for signature 'MVN'
summary(object, ...)

Arguments
mu 
numeric vector representing kdimensional means 
Sigma 
numeric kbyk covariance matrix containing the measurement of the linear coupling between every pair of random vectors 
tol 
numeric scalar roundoff error that will be tolerated when assessing the singularity of the covariance matrix 
object, x 
object of class 
TRANSFORM 
function that takes a vector of mean expression or standard deviation and returns a transformed vector that can be used to alter the appropriate slot of the object. 
n 
numeric scalar representing number of samples to be simulated 
... 
extra arguments for generic or plotting routines 
Details
The implementation of MVN
class is designed for efficiency when
generating new samples, since we expect to do this several times.
Basically, this class separates the mvrnorm
function from the
MASS package into several steps. The computationally expensive step
(when the dimension is large) is the eigenvector decomposition of the
covariance matrix. This step is performed at construction and the
pieces are stored in the object. The rand
method for MVN
objects contains the second half of the mvrnorm
function.
Note that we typically work on expression value with its logarithm to some appropriate base. That is, the multivariate normal should be used on the logarithmic scale in order to contruct engine.
alterMean
for an MVN
simply replaces the appropriate slot by
the transformed vector. alterSD
for an MVN
is trickier,
because of the way the data is stored. In order to have some hope of getting
this correct, we work in the space of the covariance matrix, Sigma.
If we let R denote the correlation matrix and let Delta be the
diagonal matrix whose entries are the individual standard deviations, then
Sigma = Delta \%*\% R \%*\% Delta.
So, we can change the standard deviations by replacing Delta in this
product. We then construct a new MVN
object with the old mean vector
and the new covariance matrix.
covar
and correl
functions calculate the covariance matrix
and correlation matrix underlies the covariance matrix for the objects of
class MVN
, respectively. We have four assertions as shown below,
and will be tested in the examples section:

covar
should return the same matrix that was used in the function call to construct theMVN
object. After applying an
alterMean
method, the covariance matrix is unchanged.The diagonal of correlation matrix consists of all ones.
After applying an
alterMean
or analterSD
method, the correlation matrix is unchanged.
Objects from the Class
Although objects of the class can be created by a direct call to
new, the preferred method is to use the
MVN
generator function.
Slots
mu
:numeric vector containing the kdimentional means
lambda
:numeric vector containing the square roots of eigenvalues of the covariance matrix
half
:numeric matrix with k*k dimensions whose columns contain the eigenvectors of the covariance matrix
Methods
 alterMean(object, TRANSFORM, ...)
Takes an object of class
MVN
, loops over themu
slot, alters the mean as defined by TRANSFORM function, and returns an object of classMVN
with alteredmu
. alterSD(object, TRANSFORM, ...)
Takes an object of class
MVN
, works on the diagonal matrix of the covariance matrix, alters the standard deviation as defined by TRANSFORM function, and reconstructs an object of classMVN
with the oldmu
and reconstructed covariance matrix. nrow(x)
Returns the number of genes (i.e, the length of the
mu
vector). rand(object, n, ...)
Generates nrow(MVN)*n matrix representing gene expressions of
n
samples following the multivariate normal distribution captured in the object ofMVN
. summary(object, ...)
Prints out the number of multivariate normal random variables in the object of
MVN
. covar(object)
Returns the covariance matrix of the object of class
MVN
. correl(object)
Returns the correlation matrix of the object of class
MVN
.
Author(s)
Kevin R. Coombes krc@silicovore.com, Jiexin Zhang jiexinzhang@mdanderson.org, P. Roebuck proebuck@mdanderson.org
References
OOMPA
See Also
Engine
,
IndependentNormal
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  showClass("MVN")
## Not run:
tolerance < 1e10
## Create a random orthogonal 2x2 matrix
a < runif(1)
b < sqrt(1a^2)
X < matrix(c(a, b, b, a), 2, 2)
## Now choose random positive squaredeigenvalues
Lambda2 < diag(rev(sort(rexp(2))), 2)
## Construct a covariance matrix
Y < t(X)
## Use the MVN constructor
marvin < MVN(c(0,0), Y)
## Check the four assertions
print(paste('Tolerance for assertion checking:', tolerance))
print(paste('Covar assertion 1:',
all(abs(covar(marvin)  Y) < tolerance)))
mar2 < alterMean(marvin, normalOffset, delta=3)
print(paste('Covar assertion 2:',
all(abs(covar(marvin)  covar(mar2)) < tolerance)))
print(paste('Correl assertion 1:',
all(abs(diag(correl(marvin))  1) < tolerance)))
mar3 < alterSD(marvin, function(x) 2*x)
print(paste('Correl assertion 1:',
all(abs(correl(marvin)  correl(mar2)) < tolerance)))
rm(a, b, X, Lambda2, Y, marvin, mar2, mar3)
## End(Not run)
