This is all very interesting .... too bad it'll probably all be moved to the private forums soon.
I studied a bit of Paul Glimcher's lab work on "vision & risk/decisionmaking" in the brain, if you are interested in how the brain's vision system addresses these exact kinds of issues ... in particular I studied eye saccades, which is a kind of search routine. It sounds very familiar to the way Malcolm was explaining it, relative-weighted areas of the vision area getting updated as evidence comes in ... (well, more complicated, as you could imagine ... You could just google Paul Glimcher, vision, and NYU to find his papers if you want more detail on how LIP, the brain area he studies, does it).
The one major element it adds to what you were saying is that it isn't just "likelihood" alone, but (likelihood of a hit) * (expected payoff, if it's a hit) ... in effect, relative expected utility of a hit (REU = L*P). You've already thought about likelihood well (shadows before well lit areas, heard sounds+, etc), so I don't need to really discuss it. And you've also got a system where the weights are relative to one another built into the hierarchy of choice based on weight, so I don't really need to talk about that, either.
As for payoff, in most cases the expected payoff is probably the same -- a "hit" will be the same thief every time; there he is. It's not like some shadows are more likely to carry more thieves than other shadows so go to those first (the traditional way P works). If the task is just to find that one guy, then that's it. So it might not apply so well.
But just so I don't make a completely irrelevant point, another possible way to think about payoff is the same thief in different situations. E.g., there might be situations where the guard has a better chance of catching the thief by surprise or at least off-guard ... that's a higher payoff for the guard. ... So you might tweak the scales a little so that certain evidence that indicates coming from a certain direction might catch the thief off guard (e.g., coming from behind the thief rather than in front of him) will bump up the P factor in the weight just a little more than usual for that direction relative to the other direction (of course, the L factor might still outweigh for the other direction). Or an approach which better cuts off the thief's exit.
Or, vice versa, things that lessen the expected payoff for the guard might get bumped down, e.g., if the direction puts the guard in a particularly vulnerable position if he catches the thief, relative to catching him from another position. Or, e.g., distance/work to get to the spot might also tweak the payoff, insofar as it leaves him more vulnerable to fight vs. another approach (need to think about that; if fatigue were a factor it definitely would, but I don't think you'll have that, or some approaches making fighting easier or harder for him, not sure.)The point is
that these wouldn't be independent factors affecting the weighting, but a multiplier to the factors you already have (which are most all, in effect, "likelihood" factors), that have the potential to tweak a little in either direction with the right evidence, otherwise it's just set at "1". Although maybe this graduated-approach you have to weighting--bits of evidence tweak the amount this way or that--amounts to the same thing in effect.
My examples are just me thinking on the fly, take them with a grain of salt. You need to think the idea through. You might think it might be better to have a hit at all than worry about the relative value of that hit when it happens (well, really this is about a hit from one place relative to the same hit from another place; but from a more/less advantageous position for the guard, coming from the Thief's behind, or cutting off his exit, etc).
But anyway, because so much of the literature always has this equation of REU = L*P for rational saccade/search behavior, it's worth spending a little time thinking about how the P (expected payoff) factor might work for you, as well as the L factor that you've been working with ... maybe in a much different way than my examples. Since there's just one hit, maybe it's not all that important as it would be in other situations (e.g., where there are other potential hits at play), but it might come up in other ways like I was trying to think out. It's just worth thinking about, that's all I'm saying, outsider that I am.
Edited by demagogue, 07 June 2007 - 02:19 PM.