Inference for Proportions in a 2 × 2 Contingency Table: HPD or not HPD?

Summary Highest posterior density intervals are common in Bayesian inference, but as noted by Agresti and Min (2005, Biometrics 61, 515–523) they are not invariant under transformations. Agresti and Min suggested central or “tail” intervals as preferable in the context of the relative risk and odds ratio. A modification to this is proposed for extreme outcomes, as invariance is maintained when replacing central intervals by one‐sided intervals. Bayes–Laplace priors for the binomial parameters appear preferable here, compared to Jeffreys priors, contrary to Agresti and Min's suggestion based on frequentist coverage.     

Is there a star tree paradox?

Concerns have been raised that posterior probabilities on phylogenetic trees can be unreliable when the true tree is unresolved or has very short internal branches, because existing methods for Bayesian phylogenetic analysis do not explicitly evaluate unresolved trees. Two recent papers have proposed that evaluating only resolved trees results in a "star tree paradox": when the true tree is unresolved or close to it, posterior probabilities were predicted to become increasingly unpredictable as sequence length grows, resulting in inflated confidence in one resolved tree or another and an increasing risk of false-positive inferences. Here we show that this is not the case; existing Bayesian methods do not lead to an inflation of statistical confidence, provided the evolutionary model is correct and uninformative priors are assumed. Posterior probabilities do not become increasingly unpredictable with increasing sequence length, and they exhibit conservative type I error rates, leading to a low rate of false-positive inferences. With infinite data, posterior probabilities give equal support for all resolved trees, and the rate of false inferences falls to zero. We conclude that there is no star tree paradox caused by not sampling unresolved trees.     

Models for analysing species’ presence/absence data at two time points

Species’ presence/absence at two time points is a very common form of ecological data. It is the simplest type of longitudinal study and has fundamental applications in ecological succession, environmental monitoring, and climate change scenarios. Despite its widespread commonality the use of statistical regression to analyse such data has been wanting. We propose the use of the bivariate odds-ratio model to analyse these data. Seldomly used in ecology, it is argued as being suitable, especially within a constrained ordination framework. In particular, this paper presents the constrained ordination-odds ratio framework as a potentially important key in understanding the underlying processes of niche theory dynamics, e.g., local extinction and colonization probabilities can be described in terms of it. Some of the mathematical and statistical challenges associated with more ambitious extensions are highlighted. As examples, with an underlying Poisson abundance model, a complementary log-log link for the marginal probabilities is shown to be more appropriate. We then develop this model based on the zero-inflated Poisson distribution since excess absences relative to a Poisson distribution is frequent in practice. Two vegetation data sets are used for illustrative purposes.     

Uncertainty Evaluation of a Groundwater Conceptual Model by Using a Multimodel Averaging Method

ABSTRACT

A groundwater field is a complex and open system. Groundwater simulation and prediction often deviated from true values, which is attributed to the uncertainty of groundwater modeling. The conceptual model (model struture) is one of the main sources of groundwater modeling uncertianty. In this study, the mean Euclidean distance (MED) between model simulations and observations is proposed to assess the integrated likelihood value of a conceptual model in Bayesian model averaging (BMA). Moreover, this proposed BMA method is compared with the traditional generalized likelihood uncertainty estimation (GLUE) BMA method by a synthetical groundwater model, and the characteristics of these two BMA methods are summarized.     

玉米出籽率全基因组关联分析

出籽率与玉米单穗产量密切相关,其遗传机制的解析对玉米高产育种具有重要意义.本研究利用309份玉米自交系为关联群体,利用固定和随机模型交替概率统一(FarmCPU)、压缩混合线性模型(CMLM)和多位点混合线性模型(MLMM)对2017年和2019年河南新乡原阳、周口郸城、海南三亚以及最佳线性无偏估计值(BLUE)的出籽...