Using MCMC. Separating MCMC from Bayesian Inference? Line fitting revisited A toy equaliser problem Some lessons A problem in film restoration/retouching. Articulate Probabilities [Bayesian Inference]. Try to see if you can integrate out nuisances. Derive the Posterior.
Try to see if you can
integrate out nuisances
Derive the PosteriorMCMC is (just) a tool
Choose a Model
Need better model
If solution not ok
Direct, CG, Steepest Descent etc
Manipulate Random Samples
To get one answer
(if you want)
Gives you one answer
Can always design single parameter-at-a-time schemes. So iterations can be very low complexity
Simple iterations = long convergence
Gives you a picture of alternate answers
Do you really need alternate answers?
Will always allow you to get to “best” solution
Iterations can be high complexity?
Convergence can be rapid (e.g. CG) for well defined problems
Gives you just one answer
Can give local minimum for non-linear problemsGood, Bad
See Matlab demo
because we can draw samples directly
All pole System
Identify the system coefficients
AND recover the original signal
Comms, Deblurring, Overshoot Cancellation
Now more latex
P(1) = 0.3, p(2) = 0.25,
P(3) = 0.2, p(4) = 0.25
71 points evaluated
Back to Latex
X 20 !