Oversight probability in presence-absence sampling for detection of fish eggs

Abstract

Presence-absence sampling (PAS) is a sampling technique that observes only the presence or absence of objects, such as eggs, in sampling units. The purpose of the present paper was to study the oversight probability in a PAS study for detecting fish eggs in connection with the spatial distribution of eggs. It was shown that the oversight probability of presence of eggs under noeggs observation is a monotone decreasing function of the parameter of the degree of contagion.KEY WORDS: contagious distribution, detection function, negative binomial distribution, oversight probability, parameter of degree of contagion, presence-absence sampling.

Efficiency of presence-absence sampling used to estimate the mean abundance of fish eggs

“…It is difficult to compare two estimators from the two sampling methods for the same estimation problem without any assumption on a relationship between the respective detection functions. The assumption that equation 23 6 or p = a (1 − e –b ) is one of the assumed relationships which would be understood intuitively and is often used below.…”

“…under the assumptions that n = N – n and p = ω, 6 where MSE () a =1 indicates the MSE of under a = 1. Naturally it holds that…”

“…In a station, if a PAS is used it means, as in the previous paper, 6 observing a random variable U whose conditional distribution given the number of eggs in the station, X (it is also assumed to be a random variable) = x , is the following Bernoulli (1[presence] and 0 [non‐presence]) distribution:…”

“…which is proved using the moment generating function of B ( m , k ). If a CS in a station is taken, it means that a random variable Y whose conditional distribution given X = x is assumed to be the binomial distribution B N ( x , p ) as in the previous paper (Yamada and Zenitani 6 ) is observed. Hence, the unconditional distribution of Y is NB ( mp , k ), as is easily shown.…”

“…The cost problem of sampling has been well examined in the literature, including Kuno's book 5 . Yamada and Zenitani investigated the oversight probability of PAS related to the parameters of the spatial distribution of eggs in the spawning ground, including the mean abundance per station, and to the parameters in the detection function 6 …”