PEIP: bayes – R documentation

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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

Author(s)

Jonathan M. Lees<jonathan.lees@unc.edu>

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

Geophysical Inverse Theory and Optimization

v2.2-3

GPL (>= 2)

Authors

Jonathan M. Lees [aut, cre]

Initial release

2020-08-28