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

Yamada, Sakutarō; Zenitani, Hiromu

doi:10.1111/j.1444-2906.2004.00873.x

Cited by 1 publication

(8 citation statements)

References 11 publications

(22 reference statements)

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“…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.…”

Section: Resultsmentioning

confidence: 99%

“…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…”

Section: Resultsmentioning

confidence: 99%

“…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:…”

Section: Models and Methodsmentioning

confidence: 99%

“…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.…”

Section: Models and Methodsmentioning

confidence: 99%

“…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 …”

Section: Introductionmentioning

confidence: 99%

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

Yamada

Zenitani²

2005

Fisheries Sci

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Statistical properties of estimators relating to the mean abundance of fish eggs were investigated using the data from the presence-absence sampling (PAS) and counting sampling (CS). PAS, which focuses on the presence-absence of eggs in a sample, is more cost-effective yet is unlikely to give more precise estimates than CS, which counts the number of eggs. But when limitations are given on the sampling cost and number of sampling stations, PAS may have advantages. This study shows that the mean square error (MSE) of the maximum likelihood estimator (MLE) based on PAS may become smaller than the MSE of the MLE based on counting data when the number of observations for PAS becomes larger. The observation number for PAS is determined, which minimizes the MSE of a combined estimator from the two MLE under a restriction of the total cost of observation. A dual problem is also solved. It is shown that MSE of the MLE in PAS is a monotone increasing function of the oversight probability. PAS becomes more informative as the distribution of the number of eggs is more aggregated.KEY WORDS: counting sampling, estimation of fish egg abundance, Fisher information, mean square error, presence-absence sampling, relative efficiency, sampling cost.

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Section: Resultsmentioning

confidence: 99%

“…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…”

Section: Resultsmentioning

confidence: 99%

Section: Models and Methodsmentioning

confidence: 99%

Section: Models and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%