"MAP estimate estimate"

[gusl]

(That's not a typo)

Standard Bayesian setting: suppose you have a large space of parameter values, one of which is the MAP estimate. While you search, you keep track of the best one found so far. This incumbent may be called the "MAP estimate estimate". The first "estimate" derives from sampling noise (which goes away with infinite data), and the second "estimate" from "search noise" (which goes away with infinite computation time).

I think the first usage should take precedence... so what's a good word for the second kind of "estimate", due to "search noise"?

Comments

[stepleton.livejournal.com]

Why not say "approximate MAP estimate" or "approximate MAP estimate"?

[gustavolacerda.livejournal.com]

In this case, we are also interested in near-MAP parameter values, i.e. those whose probability is within a constant factor of the MAP's probability.

"approximate MAP" sounds too close to "near-MAP".

[the-locster.livejournal.com]

meta estimate?

[bhudson.livejournal.com]

what's a good word for the second kind of "estimate", due to "search noise"?

Approximation.

[gustavolacerda.livejournal.com]

But there are no guarantees at any point... also, the incumbent value can start at a random place. At that point it's not an approximation in any sense.

See also my response to stepleton.

[bhudson.livejournal.com]

So your algorithm is:

best-so-far = infinity
for each parameter value v, 
  best-so-far = min(best-so-far, compute MAP-estimate(v))

and you want a name for the variable I imaginatively called "best-so-far" ?

[gustavolacerda.livejournal.com]

yup... except we traverse the parameter values according to a heuristic.

"best-so-far" is usually called "incumbent".

How about "incumbent MAP estimate"?

[bhudson.livejournal.com]

It makes me want to support the opposition party, but it certainly doesn't clash with any computer science term I've seen used. In fact, I might start using it.

[stepleton.livejournal.com]

I also like "incumbent". Good call!