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Multinomial N-mixture models are commonly used to fit data from a removal sampling protocol. If the mixing distribution is negative binomial, the distribution of the counts does not appear to have been identified and practitioners approximate the requisite likelihood by placing an upper bound on the embedded infinite sum. In this paper, the distribution which underpins the multinomial N-mixture model with a negative binomial mixing distribution is shown to belong to the broad class of multivariate negative binomial distributions. Specifically, the likelihood can be expressed in closed form as the product of conditional and marginal likelihoods and the information matrix shown to be block diagonal. As a consequence, the nature of the maximum likelihood estimates of the unknown parameters and their attendant standard errors can be examined and tests of hypothesis of the Poisson against the negative binomial mixing distribution formulated. In addition, appropriate multinomial N-mixture models for datasets which include zero site totals can also be constructed. Two illustrative examples are provided. This article is protected by copyright. All rights reserved.
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Clustered multinomial data are prevalent in a variety of applications such as microbiome studies, where metagenomic sequencing data are summarized as multinomial counts for a large number of bacterial...
This paper describes, by the first time, a chemometric approach that combines a simple set of the UV-Vis spectra and partial least square regression (PLSR) for measuring the removal of five pharmaceut...
An experiment was established to compare composting and vermicomposting for decreasing the content of polycyclic aromatic hydrocarbons (PAHs) in biomass fly ash incorporated into organic waste mixture...
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To evaluate effectiveness of a prefixed 50% N2O- 50%O2 mixture in legal abortion under paracervical block.
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A sampling methodology using small sample sizes when conducting surveys in small geographical or population-based areas or lots.
Sampling of blood levels of the adrenocorticotropic hormone (ACTH) by withdrawal of blood from the inferior petrosal sinus. The inferior petrosal sinus arises from the cavernous sinus and runs to the internal jugular vein. Sampling of blood at this level is a valuable tool in the differential diagnosis of Cushing disease, Cushing syndrome, and other adrenocortical diseases.
A method for diagnosis of fetal diseases by sampling the cells of the placental chorionic villi for DNA analysis, presence of bacteria, concentration of metabolites, etc. The advantage over amniocentesis is that the procedure can be carried out in the first trimester.
Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.
Statistical models in which the value of a parameter for a given value of a factor is assumed to be equal to a + bx, where a and b are constants. The models predict a linear regression.