A negative binomial model with varying element sizes

Bissell, A. F.

doi:10.1093/biomet/59.2.435

Cited by 42 publications

(18 citation statements)

References 5 publications

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“…The robust variance estimates are given in the second line in each row of Table IV. Example 2: Bissell [14] collected data on 32 rolls of textile fabric. The response variable is the number of faults y in a bolt of fabric of length l. The data were analysed by Lee and Nelder [15].…”

Section: Real Examplesmentioning

confidence: 99%

A simple and exploratory way to determine the mean–variance relationship in generalized linear models

Tsou¹

2006

Statistics in Medicine

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This paper introduces an exploratory way to determine how variance relates to the mean in generalized linear models. This novel method employs the robust likelihood technique introduced by Royall and Tsou.A urinary data set collected by Ginsberg et al. and the fabric data set analysed by Lee and Nelder are considered to demonstrate the applicability and simplicity of the proposed technique. Application of the proposed method could easily reveal a mean-variance relationship that would generally be left unnoticed, or that would require more complex modelling to detect.

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Section: Real Examplesmentioning

confidence: 99%

A simple and exploratory way to determine the mean–variance relationship in generalized linear models

Tsou¹

2006

Statistics in Medicine

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“…As usual we combine this with ℓ(θ) to compute r * (ψ). For a numerical illustration of these calculations, we take the data from Bissell (1972) on the numbers of faults, y, in lengths of cloth, x (m×10 2 ). We suppose that y i follows the two parameter negative binomial distribution (15), where now µ = µ i = βx i , and we take the common shape parameter, ν, to be the parameter of interest.…”

Section: A More Complex Modelmentioning

confidence: 99%

Improved Likelihood Inference for Discrete Data

Davison

Fraser

Reid

2006

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary. Discrete data, particularly count and contingency table data, are typically analyzed using methods that are accurate to first order, such as normal approximations for maximum likelihood estimators. By contrast continuous data can quite generally be analyzed using third order procedures, with major improvements in accuracy and with intrinsic separation of information concerning parameter components. This paper extends these higher order results to discrete data, yielding a methodology that is widely applicable and accurate to second order. The extension can be described in terms of an approximating exponential model expressed in terms of a score variable. The development is outlined and the flexibility of the approach illustrated by examples.

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“…Anscombe 1948Anscombe , 1950Taylor 1953;Sampford 1956;Bliss and Owen 1958;Bissell 1972;Pielou 1977;Taylor et al 1979;Ripley 1981;Zweifel and Smith 1981;Diggle 1983;Dennis and Patil 1984). It also has limitations.…”

Section: Models For Egg and Larval Distributionmentioning

confidence: 99%

Presence-Absence Sampling for Fisheries Management

Mangel¹,

Smith²

1990

Can. J. Fish. Aquat. Sci.

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Mangel, M., and P. E. Smith. 1990. Presence-absence sampling for fisheries management. Can. I. Fish. Aquat.Sci. 47:1875-1887.It i s often important to estimate the abundance of a fish stock when the stock is somewhat depleted. For pelagic species this presents great operational difficulties, because adult surveys may be prohibitively expensive and time consuming. Here we introduce a method for estimating the spawning biomass of a stock by means of egg or larval surveys. In particular, we develop a series of models for presence-absence sampling of eggs or larvae and show how presence-absence data can be used to estimate adult spawning biomass. The models are based on an underlying probabilistic description of the aggregation of eggs or larvae, a search process, and a description of habitat structure. Methodologies are given for estimating the distribution of the size of the spawning biomass from presence-absence data. A case study of sardine is used to justify a number of the assumptions. The methods are applied to a 1985 survey for sardine eggs and are compared to an alternative method based on egg production.Dans bon nombre de cas, il est important d'estimer I'abondance d'un stock de poissons lorsque ses effectifs sont quelque peu rauits. Pour les esp&es Nlagiques, cela entraine des difficult& op6rationnelles majeures, car le denombrement des adultes peut Ctre excessivement coirteux et long. Les auteurs ont mis au point une methode permettant d'estimer la biomasse des geniteurs d'un stock par la presence ou I'absence de leurs oeufs ou de leurs larves. A cette fin, ils ont 6labor6 une serie de modeles et demontrent comment I'on peut se servir de donnks relatives a la presence ou a I'absence des wufs ou des larves de poisson pour estimer la biomasse des geniteurs adultes. Les modeles reposent sur un calcul probabiliste du rassemblement des oeufs ou des larves, une methode de recherche et une description de la structure de I'habitat. Les auteurs donnent des techniques pour estimer la repartition de la biomasse des gkniteurs d'apr&s les donnees sur la presence et I'absence des oeufs ou des larves. ery often, fisheries managers must estimate the adult biomass of pelagic stocks. When the stocks are depleted, V direct assessment of adult population levels is not only difficult, but may be highly inaccurate (Hewitt et al. 1984). In such situations, an alternative is the survey of egg or larval populations as a means of estimating adult biomass (Lasker 1981). The interpretation of data from egg or larval surveys, called plankton surveys in this paper, is complicated by the patchy and highly aggregated nature of eggs and larvae (Smith 1978). A method based on egg production (Santander et al. 1982; Hewitt 1984; Hewitt et al. 1984; Lasker 1985;Wolf and Smith 1985;Wolf et al. 1987) has been proposed as a means of relating the data from egg surveys to adult biomass. The objective of this paper is to introduce another set of tools which can be used by the fisheries scientist or manager who is involved in egg or larval surve...

show abstract

A negative binomial model with varying element sizes

Cited by 42 publications

References 5 publications

A simple and exploratory way to determine the mean–variance relationship in generalized linear models

A simple and exploratory way to determine the mean–variance relationship in generalized linear models

Improved Likelihood Inference for Discrete Data

Presence-Absence Sampling for Fisheries Management

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