Bayesian experimental design for nonlinear mixed-effects models with application to HIV dynamics

Bayesian experimental design is investigated for Bayesian analysis of nonlinear mixed-effects models. Existence of the posterior risk for parameter estimation is shown. When the same prior distribution is used for both design and inference, existence of the preposterior risk for design is also proven. If the prior distribution used in design is different from that used for inference, sufficient conditions are established for existence of the preposterior risk for design. A case study of design for an experiment in population HIV dynamics is provided.     

Cutpoint selection for categorizing a continuous predictor

This article presents a new approach for choosing the number of categories and the location of category cutpoints when a continuous exposure variable needs to be categorized to obtain tabular summaries of the exposure effect. The optimum categorization is defined as the partition that minimizes a measure of distance between the true expected value of the outcome for each subject and the estimated average outcome among subjects in the same exposure category. To estimate the optimum partition, an efficient nonparametric estimate of the unknown regression function is substituted into a formula for the asymptotically optimum categorization. This new approach is easy to implement and it outperforms existing cutpoint selection methods.     

Methods for the statistical analysis of binary data in split-cluster designs

Split-cluster designs are frequently used in the health sciences when naturally occurring clusters such as multiple sites or organs in the same subject are assigned to different treatments. However, statistical methods for the analysis of binary data arising from such designs are not well developed. The purpose of this article is to propose and evaluate a new procedure for testing the equality of event rates in a design dividing each of k clusters into two segments having multiple sites (e.g., teeth, lesions). The test statistic proposed is a generalization of a previously published procedure based on adjusting the standard Pearson chi-square statistic, but can also be derived as a score test using the approach of generalized estimating equations.     

环境污染下基于最优捕获策略的近海-远海捕鱼模型的动力学性质(英文)

近年来,由于人类的过度开发,使得海洋资源(尤其是近海海洋资源)急剧下降,加上日益严重的海洋污染,给海洋资源管理带来很大的困难.为了更好的管理和利用海洋资源,本文考虑到环境污染中脉冲扩散对种群的影响,建立了一个近海-远海渔业模型,给出了正周期解存在性及平凡周期解和正周期解全局渐近稳定性的充分条件.进一步,在环境污染的情况下,给出了最优捕获策略,得到了最大持续产量和相应的捕获努力量.最后,通过数值模拟证实了我们所得的结论的正确性.     

Optimal investment across different aspects of anti-predator defences

We present a simple model of investment across a suite of different anti-predatory defences. Defences can incur an initial construction cost and and/or may be costly each time they are utilised. Our aim is to use a simple, but general, mathematical model to explore when prey that face a single predatory threat where each attack is of the same nature should invest only in a single defence, and when they should spread their investment across more than one defence. This should help to explain the observed variety of defences that a single prey individual may employ during repeated attacks of a similar nature or even at different stages during one attack. Previous verbal reasoning suggested that prey should specialise in investment in defences that can be utilised early in the predation sequence. Our quantitative model predicts that (depending of the relatively properties of different defences), there may be concentrated investment in early acting, or in late-acting defences, or a spread of investment across both defence types. This variety of predictions is in agreement with the variation in defences shown by natural organisms subjected to repeated predatory attack.     

The Predatory Mite Phytoseiulus persimilis Adjusts Patch-leaving to Own and Progeny Prey Needs

Integration of optimal foraging and optimal oviposition theories suggests that predator females should adjust patch leaving to own and progeny prey needs to maximize current and future reproductive success. We tested this hypothesis in the predatory mite Phytoseiulus persimilis and its patchily distributed prey, the two-spotted spider mite Tetranychus urticae. In three separate experiments we assessed (1) the minimum number of prey needed to complete juvenile development, (2) the minimum number of prey needed to produce an egg, and (3) the ratio between eggs laid and spider mites left when a gravid P. persimilis female leaves a patch. Experiments (1) and (2) were the pre-requirements to assess the fitness costs associated with staying or leaving a prey patch. Immature P. persimilis needed at least 7 and on average 14±3.6 (SD) T. urticae eggs to reach adulthood. Gravid females needed at least 5 and on average 8.5±3.1 (SD) T. urticae eggs to produce an egg. Most females left the initial patch before spider mite extinction, leaving prey for progeny to develop to adulthood. Females placed in a low density patch left 5.6±6.1 (SD) eggs per egg laid, whereas those placed in a high density patch left 15.8±13.7 (SD) eggs per egg laid. The three experiments in concert suggest that gravid P. persimilis females are able to balance the trade off between optimal foraging and optimal oviposition and adjust patch-leaving to own and progeny prey needs.     

Optimal movement between patches under incomplete information about the spatial distribution of food items

If the food distribution contains spatial pattern, the food density in a particular patch provides a forager with information about nearby patches. Foragers might use this information to exploit patchily distributed resources profitably. We model the decision on how far to move to the next patch in linear environments with different spatial patterns in the food distribution (clumped, random, and regular) for foragers that differ in their degree of information. An ignorant forager is uninformed and therefore always moves to the nearest patch (be it empty or filled). In contrast, a prescient forager is fully informed and only exploits filled patches, skipping all empty patches. A Bayesian assessor has prior knowledge about the content of patches (i.e. it knows the characteristics of the spatial pattern) and may skip neighbouring patches accordingly by moving to the patch where the highest gain rate is expected. In most clumped and regular distributions there is a benefit of assessment, i.e. Bayesian assessors achieve substantially higher long-term gain rates than ignorant foragers. However, this is not the case in distributions with less strong spatial pattern, despite the fact that there is a large potential benefit from a sophisticated movement rule (i.e. a large penalty of ignorance). Bayesian assessors do also not achieve substantially higher gain rates in environments that are relatively rich or poor in food. These results underline that an incompletely informed forager that is sensitive to spatial pattern should not always respond to existing pattern. Furthermore, we show that an assessing forager can enhance its long-term gain rate in highly clumped and some specific near-regular food distributions, by sampling the environment in slightly larger spatial units.