array9

Likelihood versus maximum likelihood

There is no firm foundation for maximum likelihood estimates for parameters in a statistical model.  There are likelihoods of an outcome associated with parameters, and that is it.  There is rarely a probabilistic model for the parameters.

This can be seen simply by noting that it is sensitive to a transformation of a continuous parameter.  It makes more sense for discrete parameters.

This is not really a paradox, in that points are still just the same points after transformation.

There seems to be something quantum in this.  But I am not sure what.

One wonders if evolution might have a view on this?  Might there be decision processes that go for the maximum likelihood.  Does one assume a rustle is a tiger?

The example I like to think about is smell, where individual molecules trigger or do not trigger a set of sensor cells.  Given an observation, it decides what the smell is and gets the brain to do the rest.

Perhaps this could only happen in a digital world.

Martinw