PEIP (version 2.0-1)

bayes: Bayes Inversion

Description

Given a linear inverse problem Gm=d, a prior mean mprior and covariance matrix covm, data d, and data covariance matrix covd, this function computes the MAP solution and the corresponding covariance matrix.

Usage

bayes(G, mprior, covm, d, covd)

Arguments

G

Design Matrix

mprior

vector, prior model

covm

vector, model covariance

d

vector, right hand side

covd

vector, data covariance

Value

vector model

References

Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.

Examples

# NOT RUN {
# }
# NOT RUN {
set.seed(2015)
G = setDesignG()
### <!-- % Setup the true model. -->
mtruem=matrix(rep(0, 16*16), ncol=16,nrow=16);

mtruem[9,9]=1; mtruem[9,10]=1; mtruem[9,11]=1;
mtruem[10,9]=1; mtruem[10,11]=1;
mtruem[11,9]=1; mtruem[11,10]=1; mtruem[11,11]=1;
mtruem[2,3]=1; mtruem[2,4]=1;
mtruem[3,3]=1; mtruem[3,4]=1;

### <!-- % reshape the true model to be a vector -->
mtruev=as.vector(mtruem);
imagesc(matrix(mtruem,16,16) , asp=1 , main="True Model" );


matrix(mtruem,16,16) , asp=1 , main="True Model" )


### <!-- % Compute the data. -->
dtrue=G %*% mtruev;

### <!-- % Add the noise. -->
d=dtrue+0.01*rnorm(length(dtrue));
covd = 0.1*diag( nrow=length(d) )
covm = 1*diag( nrow=dim(G)[2] )
# }