I am studying Bayesian inversion and try to write a code for Bayesian inversion and MCMC/RJMCMC. The inversion I intend is simple linear system Ax=b, I have used steepest descent and conjugate gradient algorithms.
Do you have matlab/python code for Ax=b using Bayesian inversion and MCMC/RJMCMC.
And also, I have heard about stochastic steepest descent method, Do any one provide the codes.
Thank you
https://inv-conj-geophy.sciencesconf.org/conference/inv-conj-geophy/talkJointInversionCoutant.pdf
x = ( ATA )-1ATy
To add on Jerry Decker Answer, you can take the inverse by using Sherman-Morrison formula in O(n^2) provided it is invertible (to ensure invertibility you might want to add a regularisation term see ridge regression). In contrast, MATLAB/python inv function takes O(n^3).
A very helpful overview of several techniques to establish this inversion and appropriate regularisation can be found in a Paper by Bouchet:
L. Bouchet, A comparative study of deconvolution methods for gamma-
ray spectra, Astron. Astrophys. Suppl. Ser. 113 (1995) 167–183
He compares several approaches, while focusing an application scenario from the Gamma-spectroscopy.
Best regards,
Marcus
- Badges
- Science topic
- Similar topics
- Computer Science and Engineering
- Programming Languages
- Python