1. Sarah Minson Mark Simons James Beck

2. TeleseismicStrong motionJoint km Delouis et al. (2009) Loveless et al. (2010) Seismic + Static

3. For inverse problems: PosteriorPosteriorPriorPriorDataLikelihoodDataLikelihood

4. OptimizationBayesian RegularizedNo a priori regularization required One solutionDistribution of solutions Converges to one minimumMulti-peaked solution spaces OK Limited choice of a priori constraintsGeneralized a priori constraints Error analysis hard for nonlinear problemsError analysis comes free with solution Computational efficiency is sensitive to model parameterization (model covariance leads to trade-offs) Computational efficiency is insensitive to model parameterization (if model covariance is estimated)

5. Huge numbers of samples required for high- dimensional problems “Curse of Dimensionality” Sampling can be inefficient

6. Tempering (A.K.A. Annealing) * Dynamic cooling schedule ** Resampling ** Simulation adapts to model covariance ** Simulation adapts to rejection rate *** Parallel Metropolis Cascading * Marinari and Parisi (1992) ** Ching and Chen (2007) *** Matt Muto

7. Target distribution:

8. 1.Sample P( θ ) 2.Calculate β 3.Resample 4.Metropolis algorithm in parallel 5.Collect final samples 6.Go back to Step 2, lather, rinse, and repeat until cooling is achieved

10. 1.Sample P( θ ) 2.Calculate β 3.Resample 4.Metropolis algorithm in parallel 5.Collect final samples 6.Go back to Step 2, lather, rinse, and repeat until cooling is achieved

11. Static GPS displacements 1 Hz GPS time series 6 interferograms

12. For one of our fault patches Static Posterior/ Kinematic Prior Static Posterior/ Kinematic Prior Kinematic Posterior Static Prior

14. StaticStaticKinematicKinematic

20. Fully Bayesian finite fault earthquake source modeling Resolution of the slip distribution and rupture propagation Uncertainties on derived source properties Determine which source characteristics are constrained and which are not CATMIP allows sampling high-dimensional problems Also useful for low-dimension problems with expensive forward models Wide variety of potential uses in geophysics

22. U┴U┴U┴U┴ U┴U┴U┴U┴ U║U║U║U║ U║U║U║U║ τrτrτrτr τrτrτrτr VrVrVrVr VrVrVrVr

23. VsVs VsVs