Applied Bayesian Modelling

Congdon, Peter

doi:10.1002/0470867159

Cited by 532 publications

(297 citation statements)

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“…A standard approach is to model the logarithm of the mean of the Poisson distribution as a linear function of the explanatory variables, adding normally distributed random effects if needed to account for variability in the observations (Congdon, 2003). However, for our data, we found no transformation that satisfied the assumptions of equal variances, normally distributed errors, and a linear relationship between the Poisson means and the explanatory variables.…”

Section: Analysis Of Queen Fecunditymentioning

confidence: 87%

“…We used Bayesian methods for statistical inference (Congdon, 2003;Gelman et al, 2004) because this approach makes it particularly easy to estimate hierarchical models (Clark, 2005). Bayesian analyses produce easily interpreted posterior probability distributions for estimated quantities, which can be summarized by means and 95 % credibility intervals.…”

Section: Hierarchical Regressionsmentioning

confidence: 99%

“…We also estimated a standard Poisson regression (model 4), in which the logarithm of the Poisson mean was assumed to have a linear relationship with the logarithm of weight. This model included a normally distributed error with a mean of 0 and an unknown standard deviation added to the Poisson mean, a typical Poisson regression model for overdispersed data (Congdon, 2003). Table 2 presents the DIC values for the alternative models.…”

Section: Analysis Of Queen Fecunditymentioning

confidence: 99%

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Queen fecundity and reproductive skew in the termite Nasutitermes corniger

Adams

Atkinson²

2007

Insect. Soc.

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A major goal of studies on social animals is to understand variation in reproduction within and between groups. We used hierarchical regressions to analyze oviposition rates in the neotropical termite Nasutitermes corniger, a species with both monogynous and polygynous colonies. Queen fecundity was a non-linear, saturating function of queen weight. Greater queen weight was associated with larger nest size and with lower numbers of queens per nest, suggesting competition among queens for resources acquired by the colony. The collective egglaying rate of pairs of queens exceeded that of single queens, but further increases in queen number did not raise total fecundity. Skew in oviposition rates, as quantified by Morisitas index I d , averaged 1.2, indicating inequalities in reproductive rates that are only moderately greater than expected for random apportionment. The leveling off of oviposition with increasing queen weight suggests that it is costly for individual females to produce eggs at high rates, which could favor tolerance of reproduction by other females, reducing reproductive skew. We hypothesize that the incentive to tolerate reproduction by other females is especially pronounced for heavier queens, because these queens are close to the limit of their own reproductive capacity. Consistent with this hypothesis, skew in oviposition rates was inversely related to the mean weight of queens within a nest.

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Section: Analysis Of Queen Fecunditymentioning

confidence: 87%

Section: Hierarchical Regressionsmentioning

confidence: 99%

Section: Analysis Of Queen Fecunditymentioning

confidence: 99%

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Queen fecundity and reproductive skew in the termite Nasutitermes corniger

Adams

Atkinson²

2007

Insect. Soc.

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“…A finite mixture distribution has the form of where , are called the mixture components, are the mixture probabilities and are the parameters to be estimated. In what follows, we focus on a mixture of two normal populations with possibly different mean and variance parameters and, following the approach of Congdon (2003) <v14n2/datasets.aerts.html#Congdon2003> we formulate the mixture model in terms of an hierarchical model using a latent indicator variable.…”

Section: A Second Analysis: Normal Mixturesmentioning

confidence: 99%

“…The following code was used for the model with the unknown mixture probabilities Nsub is the number of euro coins and Nmix is the number of components in the mixture). For a more elaborate discussion on hierarchical mixture models, we refer to Congdon (2003) <v14n2/datasets.aerts.html#Congdon2003>. The skew-normal distributions were fitted using the S-PLUS library sn, which is available on Professor Azzalini's website azzalini.stat.unipd.it/SN/index.html#lib-sn <v14n2/datasets.aerts_link1.html>.…”

Section: Getting the Datamentioning

confidence: 99%

The Weight of Euro Coins: Its Distribution Might Not Be As Normal As You Would Expect

Shkedy

Aerts

Callaert

2006

Journal of Statistics Education

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Classical regression models, ANOVA models and linear mixed models are just three examples (out of many) in which the normal distribution of the response is an essential assumption of the model. In this paper we use a dataset of 2000 euro coins containing information (up to the milligram) about the weight of each coin, to illustrate that the normality assumption might be incorrect. As the physical coin production process is subject to a multitude of (very small) variability sources, it seems reasonable to expect that the empirical distribution of the weight of euro coins does agree with the normal distribution. Goodness of fit tests however show that this is not the case. Moreover, some outliers complicate the analysis. As alternative approaches, mixtures of normal distributions and skew normal distributions are fitted to the data and reveal that the distribution of the weight of euro coins is not as normal as expected.

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