# bayes: Bayes Inversion In PEIP: Geophysical Inverse Theory and Optimization

## 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

 `1` ```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

vector model

## Author(s)

Jonathan M. Lees<[email protected]>

## References

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

## 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 29``` ```## 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 Jan. 20, 2018, 9:03 a.m.