bayes: Bayes Inversion

In PEIP: Geophysical Inverse Theory and Optimization

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

Author(s)

Jonathan M. Lees<[e-mail]>

References

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

Examples

## Not run: 
set.seed(2015)
G = setDesignG()
### 
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;

### 
mtruev=as.vector(mtruem);
imagesc(matrix(mtruem,16,16) , asp=1 , main="True Model" );


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


### 
dtrue=G %*% mtruev;

### 
d=dtrue+0.01*rnorm(length(dtrue));
covd = 0.1*diag( nrow=length(d) )
covm = 1*diag( nrow=dim(G)[2] )

## End(Not run)

PEIP documentation built on Aug. 21, 2023, 9:10 a.m.