Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models

The problem of evaluating the goodness of the predictive distributionsof hierarchical Bayesian and empirical Bayes models is investigated.A Bayesian predictive information criterion is proposed as anestimator of the posterior mean of the expected loglikelihoodof the predictive distribution when the specified family ofprobability distributions does not contain the true distribution.The proposed criterion is developed by correcting the asymptoticbias of the posterior mean of the loglikelihood as an estimatorof its expected loglikelihood. In the evaluation of hierarchicalBayesian models with random effects, regardless of our parametricfocus, the proposed criterion considers the bias correctionof the posterior mean of the marginal loglikelihood becauseit requires a consistent parameter estimator. The use of thebootstrap in model evaluation is also discussed.     

Scaling of long bones in ruminants with respect to the scapula

The significance of the scapula for locomotion is becoming more and more established. Studies of locomotion in small and medium‐sized mammals show a considerable amplitude of the scapula and a large contribution to step length. Taking this into account, long bone studies of forelimb movement restricted to the ‘arm’ miss one important segment. A regression model (reduced major axis) was used for analysis of a sample of 77 species of ruminants. This sample was divided according to (1) phylogenetic relationships and (2) habitat. The proximal elements of the limbs, scapula and humerus in the anterior extremity, femur in the hindlimb, show a similar scaling in the different analyses. The changes to limb proportions in the different subsamples are caused by the variability of the distal segments. The anterior extremity scales with a higher coefficient than the hindlimb in all analyses. Concepts like elastic or geometric similarity are inadequate for long bone scaling when the full range of body size in the sample is used. Taking all analyses into account, the differences in limb proportions are due more to phylogenetic relationships than to habitat.     

An empirical assessment of tree branching networks and implications for plant allometric scaling models

Several theories predict whole‐tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self‐similar within trees. However, differences among scaling exponents calculated at node‐ and whole‐tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.     

Semiparametric mixed-scale models using shared Bayesian forests

This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semicontinuous responses. In this paper, we present a methodology which allows for information to be shared nonparametrically across various model components using Bayesian sum-of-tree models. Our simulation results demonstrate that sharing of information across related model components is often very beneficial, particularly in sparse high-dimensional problems in which variable selection must be conducted. We illustrate our methodology by analyzing medical expenditure data from the Medical Expenditure Panel Survey (MEPS). To facilitate the Bayesian nonparametric regression analysis, we develop two novel models for analyzing the MEPS data using Bayesian additive regression trees—a heteroskedastic log-normal hurdle model with a “shrink-toward-homoskedasticity” prior and a gamma hurdle model.     

Digging through model complexity: using hierarchical models to uncover evolutionary processes in the wild

The growing interest for studying questions in the wild requires acknowledging that eco-evolutionary processes are complex, hierarchically structured and often partially observed or with measurement error. These issues have long been ignored in evolutionary biology, which might have led to flawed inference when addressing evolutionary questions. Hierarchical modelling (HM) has been proposed as a generic statistical framework to deal with complexity in ecological data and account for uncertainty. However, to date, HM has seldom been used to investigate evolutionary mechanisms possibly underlying observed patterns. Here, we contend the HM approach offers a relevant approach for the study of eco-evolutionary processes in the wild by confronting formal theories to empirical data through proper statistical inference. Studying eco-evolutionary processes requires considering the complete and often complex life histories of organisms. We show how this can be achieved by combining sequentially all life-history components and all available sources of information through HM. We demonstrate how eco-evolutionary processes may be poorly inferred or even missed without using the full potential of HM. As a case study, we use the Atlantic salmon and data on wild marked juveniles. We assess a reaction norm for migration and two potential trade-offs for survival. Overall, HM has a great potential to address evolutionary questions and investigate important processes that could not previously be assessed in laboratory or short time-scale studies.     

Quantifying the effects of temperature and flow regime on the abundance of 0+ cyprinids in the upper River Rhone using Bayesian hierarchical modelling

1. Assuming that recruitment variation is one of the main sources of fish population and assemblage changes, it is necessary to understand how natural variations in the environment influence 0+ fish abundance. Temperature regimes play an important role in enhancing both spawning activity and survival during early larval fish development. Flow regime variation, which is a powerful source of stream disturbance, is another factor to be taken into account. 2. Responses to these variables need to be assessed using long‐term datasets, since standard statistical approaches fail to provide a causal structure or to quantify the different effects. We therefore used a 26‐year dataset to evaluate the respective effects of seven derived independent variables describing the effects of temperature and flow regimes on the 0+ juvenile abundance of eight fish species in the River Rhone. 3. A clustering procedure using the Kendall tau rank correlation coefficient was implemented and identified three groups of fish according to their synchronic variations in juvenile abundance; i.e. varying with decreasing juvenile abundance, slightly increasing juvenile abundance and increasing juvenile abundance. These clusters provided the basis for building hierarchical log‐Poisson generalized linear models. The Bayesian paradigm gives a reliable framework for model selection, and the best model was determined using the Bayes Factor. 4. The posterior distribution of the regression parameters was coherent with what was expected based on knowledge of the biology of the different species. It indicates that temperature regime drives 0+ juvenile abundance but that flow regime also plays an important regulating role. The models thus detected evidence of the consequences of specific flow events such as larval drift and an increase in available habitat during higher flow discharges. 5. Our study illustrates the advantages of using a hierarchical modelling approach to quantify ecological effects by improving discrimination between the different sources of uncertainty, leading to better precision when estimating regression parameters.