Parameter estimation for complex physical problems often suffers from finding ‘solutions’ that are not physically realistic. The PEUQSE software provides tools for finding physically realistic parameter estimates, graphs of the parameter estimate positions within parameter space, and plots of the final simulation results.
How to solve the case of filtering multiple chains for an ensemble of walkers:
If we want the final filtered chains to have the same length:
OPTION 1 -- replace the fitlered values.
Assumption 1:
the low probability points are a small part of the overall # of points when doing Ensemble Samplings (ESS or EJS), for a good sampled distribution
Assumption 2:
if we replace the low probability points with other low probability points we will not distort the posterior distribution significantly
Assumption 3:
for a convergnce test with an adequate window size it will not matter if a few points are moved around (that is, it doesn't matter if the 'walker' jumps around randomly) therefor even if we replace that point with a parameter set that is far away in the walking, it should not affect the convergence diagnostic in the limit of a converged window.
First have to make a set of points between 1 order magnitude lower than our cutoff and then sample from those when replacing.
OPTION 2 -- just cut the chains shorter
After filtering, find out which chain is the shortest, then cut all of the chains to that length.
However, option 2 only works if there is (for example) as single mode posterior that all of the chains are on.
If one of the chains has gone to a low probability mode, then this won't work because it would cut all of the chains to being a very short length.
How to solve the case of filtering multiple chains for an ensemble of walkers:
If we want the final filtered chains to have the same length:
OPTION 1 -- replace the fitlered values. Assumption 1: the low probability points are a small part of the overall # of points when doing Ensemble Samplings (ESS or EJS), for a good sampled distribution
Assumption 2: if we replace the low probability points with other low probability points we will not distort the posterior distribution significantly
Assumption 3: for a convergnce test with an adequate window size it will not matter if a few points are moved around (that is, it doesn't matter if the 'walker' jumps around randomly) therefor even if we replace that point with a parameter set that is far away in the walking, it should not affect the convergence diagnostic in the limit of a converged window.
First have to make a set of points between 1 order magnitude lower than our cutoff and then sample from those when replacing.
OPTION 2 -- just cut the chains shorter After filtering, find out which chain is the shortest, then cut all of the chains to that length. However, option 2 only works if there is (for example) as single mode posterior that all of the chains are on. If one of the chains has gone to a low probability mode, then this won't work because it would cut all of the chains to being a very short length.