QuoteOriginally posted by: alphaquantumrralph, your methods remind me about similar problem: you have a tiger in the field, and you have to capture it. Describe how would you do that. 1) Shoot it. Any method works fine - gun, rocket, grenade etc. (not an elegant math solution )2) WLOG assume that the field is a square. Divide into 2 equal parts. Locate where the tiger is. Dived that one in two equal parts, and so on. Eventually (read Cantor), you will capture the tiger. 3) Draw a big circle that contains the tiger. Draw another one, smaller, comparable to tiger's size. Make an inverse transformation (symmetric reflection) of big circle into small circle. The tiger will be inside of the small one. you name other methods. Quantyst, are you looking for theoretical methods, or practical ones? While RRalph's method works fine in theory, in practice to sample randomly fishes is almost nonsense. Admit, you have to fish first to understand that Tiger in a field:1) Why not use a tranqualiser? I am happy to kill fish in the persuit of science, but killing a Tiger with a rocket launcher seems a little messy (it wouldn't leave you with much of a trophy either)2) If you have a method for finding the tiger, then why not just throw a net over it. I'm sure a sturdy net would be cheaper than all those fences (Tigers are good climbers, so presumably you would have to electrify them too).3) Again, a lot of fences, people or machinary would be needed to form the perimeter and move it. A large hunk of meat suspended over a camoflaged pit would be much cheaper.Fish:I agree that randomly sampling fish is not easy, but certainly not impossible. As with al good statistical problems a good amount of hand waving and talking about "first order approximations" (or is that physics, maybe stats is "correct sampling methodologies") should take care of that. If that doesn't work, then just stick some large error bands around your final estimate and you can't go wrong.
Last edited by rralph
on December 14th, 2008, 11:00 pm, edited 1 time in total.