(i) How does one go about with the random selection leading to a sample while studying a particular resource especially when the frame is impossible to construct?
(ii)Are we justified in terming fish samples taken from time to time as random samples?
(iii)Can we consider catches from various gears as independent random samples?
The answers would be serving better if they satisfy both a statistician and a biologist.
I feel that assuming a countably infinite population as a large population will be proper. The issue of drawing random samples whereby each unit has a probablility of getting included (not necessarily same) or the inclusion probability (pi) has been dealt with in much detail. As the sampling frame which is not per se tangible in the case of any fish population, the selection process can be viewed as random so far as the fish selected does not deprive the selection of the rest n-1 units. Or on a Monte Carlo plan the selection can be made at random on a two dimensional grid which can loosely fit the geographic spread of the population. So far as inclusion probability is not affected the scheme is bound to be valid for inferences. As regards catches sampled from time to time, the population should give the cue. If the population is defined as a grand assemblage at a given point of time, then these samples should necessarily be considered as random. In the probability parlance, the sample getting selected at time t should not vitiate the probability of another sample getting selected at time t+1. As regards catches caught by different gear at the same time- they are necessarily random, but conditionally independent. The probability of the sample getting selected should be a combination of the unit getting selected by the gear at the given point of time (which may vary) and the probability that the particular gear would be used at the first instance.
ReplyDeleteThose interested in "Sampling fish populations", a fairly good place to visit:
ReplyDeletehttp://www.fao.org/DOCREP/003/AA044E/AA044E13.htm
It is an easy read for biologists and statisticians.