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Given a hereditary property of graphs $\mathcal{H}$ and a $p\in [0,1]$ , the edit distance function $\textrm{ed}_{\mathcal{H}}(p)$ is asymptotically the maximum proportion of edge additions plus edge deletions applied to a graph of edge density p sufficient to ensure that the resulting graph satisfies $\mathcal{H}$ . The edit distance function is directly related to other well-studied quantities such as the speed function for $\mathcal{H}$ and the $\mathcal{H}$ -chromatic number of a random graph.Let $\mathcal{H}$ be the property of forbidding an Erdős–Rényi random graph $F\sim \mathbb{G}(n_0,p_0)$ , and let $\varphi$ represent the golden ratio. In this paper, we show that if $p_0\in [1-1/\varphi,1/\varphi]$ , then a.a.s. as $n_0\to\infty$ , \begin{align*} {\textrm{ed}}_{\mathcal{H}}(p) = (1+o(1))\,\frac{2\log n_0}{n_0} \cdot\min\left\{ \frac{p}{-\log(1-p_0)}, \frac{1-p}{-\log p_0} \right\}. \end{align*} Moreover, this holds for $p\in [1/3,2/3]$ for any $p_0\in (0,1)$ .A primary tool in the proof is the categorization of p-core coloured regularity graphs in the range $p\in[1-1/\varphi,1/\varphi]$ . Such coloured regularity graphs must have the property that the non-grey edges form vertex-disjoint cliques.

The classical credibility theory is a cornerstone of experience rating, especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly robust in the sense that it retains the credibility estimator’s freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.

Cities are often hotter and drier compared with nearby undeveloped areas, but how organisms respond to these multifarious stressors associated with urban heat islands is largely unknown. Terrestrial isopods are especially susceptible to temperature and aridity stress as they have retained highly permeable gills from their aquatic ancestors. We performed a two temperature common garden experiment with urban and rural populations of the terrestrial isopod, Oniscus asellus, to uncover evidence for plastic and evolutionary responses to urban heat islands. We focused on physiological tolerance traits including tolerance of heat, cold, and desiccation. We also examined body size responses to urban heat islands, as size can modulate physiological tolerances. We found that different mechanisms underlie responses to urban heat islands. While evidence suggests urban isopods may have evolved higher heat tolerance, urban and rural isopods had statistically indistinguishable cold and desiccation tolerances. In both populations, plasticity to warmer rearing temperature diminished cold tolerance. Although field‐collected urban and rural isopods were the same size, rearing temperature positively affected body size. Finally, larger size improved desiccation tolerance, which itself was influenced by rearing temperature. Our study demonstrates how multifarious changes associated with urban heat islands will not necessarily contribute to contemporary evolution in each of the corresponding physiological traits.

An individual’s early-life environment and phenotype often influence its traits and performance as an adult. We investigated whether such ‘carryover effects’ are associated with alternative, environmentally-induced phenotypes (‘polyphenism’), and, if so, whether they influence the evolution of polyphenism. To do so, we studied Mexican spadefoot toads, Spea multiplicata, which have evolved a polyphenism consisting of two, dramatically different forms: a carnivore morph and an omnivore morph. We sampled both morphs from a fast-drying and a slow-drying pond and reared them to sexual maturity. Larval environment (pond) strongly influenced survival as well as age and size at metamorphosis and sexual maturity; i.e. environment-dependent carryover effects were present. By contrast, larval phenotype (morph) did not affect life-history traits at sexual maturity; i.e. phenotype-dependent carryover effects were absent. These results are consistent with theory, which suggests that by amplifying selective trade-offs in heterogenous environments, environment-dependent carryover effects might foster the evolution of polyphenism. At the same time, by freeing selection to refine a novel phenotype without altering the existing form, the absence of phenotype-dependent carryover effects might enable polyphenism to evolve in the first place. Generally, carryover effects might play an underappreciated role in the evolution of polyphenism.

In the context of predicting future claims, a fully Bayesian analysis --- one that specifies a statistical model, prior distribution, and updates using Bayes's formula --- is often viewed as the gold-standard, while Buhlmann's credibility estimator serves as a simple approximation. But those desirable properties that give the Bayesian solution its elevated status depend critically on the posited model being correctly specified. Here we investigate the asymptotic behavior of Bayesian posterior distributions under a misspecified model, and our conclusion is that misspecification bias generally has damaging effects that can lead to inaccurate inference and prediction. The credibility estimator, on the other hand, is not sensitive at all to model misspecification, giving it an advantage over the Bayesian solution in those practically relevant cases where the model is uncertain. This begs the question: does robustness to model misspecification require that we abandon uncertainty quantification based on a posterior distribution? Our answer to this question is No, and we offer an alternative Gibbs posterior construction. Furthermore, we argue that this Gibbs perspective provides a new characterization of Buhlmann's credibility estimator.

A common assumption in plant physiological ecology is that variation in functional traits reflects the adaptation of organisms to their abiotic environment. This assumption can be tested by estimat...

Understanding complex responses of multiple character suites (e.g. behaviour, life history, morphology) across multifarious environments is a challenging task. Here we use a multivariate approach (partial least squares structural equation modelling) to disentangle environmental drivers (i.e. predation, resource availability and population demographics) of population divergence in life history and morphology. We further employ a two‐block partial least squares analysis in a novel approach to uncovering integrated and independent aspects of divergence in correlated character suites. Examining Bahamas mosquitofish Gambusia hubbsi inhabiting blue holes, we found phenotypic divergence mainly resulted from differences in predation regimes, but demography and resources also proved important in particular aspects of divergence. We uncovered significant covariation among life histories and morphologies, and revealed that phenotypic divergence between predation regimes involved both integrated and independent responses. For instance, female life histories strongly diverged independently of morphology, while some morphological shifts (abdominal distension) resulted from changes in fecundity; males showed strong morphological divergence independent of life history, but much of their life‐history shifts reflected joint morphological changes (lean weight and body shape). Our study illustrates the utility of gathering disparate data types from multiple populations/species to better understand the causes and nature of phenotypic divergence in the wild.

Although studies increasingly disentangle phenotypic plasticity from evolutionary responses to environmental change, few test for transgenerational plasticity in this context. Here, we evaluate whether phenotypic divergence of acorn ants in response to urbanization is driven by transgenerational plasticity rather than evolution. F2 generation worker ants (offspring of laboratory‐born queens) exhibited similar divergence among urban and rural populations as field‐born worker ants, suggesting that evolutionary divergence rather than transgenerational plasticity was primarily responsible for shifts toward higher heat tolerance and diminished cold tolerance in urban acorn ants. Hybrid offspring from matings between urban and rural populations also indicated that evolutionary divergence was likely the primary mechanism underlying population differences in thermal tolerance. Specifically, thermal tolerance traits were not inherited either maternally or paternally in the hybrid pairings as would be expected for strong parental or grandparental effects mediated through a single sex. Urban–rural hybrid offspring provided further insight into the genetic architecture of thermal adaptation. Heat tolerance of hybrids more resembled the urban–urban pure type, whereas cold tolerance of hybrids more resembled the rural–rural pure type. As a consequence, thermal tolerance traits in this system appear to be influenced by dominance rather than being purely additive traits, and heat and cold tolerance might be determined by separate genes. Though transgenerational plasticity does not appear to explain divergence of acorn ant thermal tolerance, its role in divergence of other traits and across other urbanization gradients merits further study.

An advantage of methods that base inference on a posterior distribution is that credible regions are readily obtained. Except in well-specified situations, however, there is no guarantee that such regions will achieve the nominal frequentist coverage probability, even approximately. To overcome this difficulty, we propose a general strategy that introduces an additional scalar tuning parameter to control the posterior spread, and we develop an algorithm that chooses this parameter so that the corresponding credible region achieves the nominal coverage probability., Comment: 15 pages, including supplementary material; 2 figures, 3 tables

Although natural selection often fluctuates across ontogeny, it remains unclear what conditions enable selection in one life-cycle stage to shape evolution in others. Organisms that undergo metamorphosis are useful for addressing this topic because their highly specialized life-cycle stages cannot always evolve independently despite their dramatic life-history transition. Using a comparative study of dragonflies, we examined three conditions that are hypothesized to allow selection in one stage to affect evolution in others. First, we tested whether lineages with less dramatic metamorphosis (e.g., hemimetabolous insects) lack the capacity for stage-specific evolution. Rejecting this hypothesis, we found that larval body shape evolves independently from selection on adult shape. Next, we evaluated whether stage-specific evolution is limited for homologous and/or coadapted structures. Indeed, we found that selection for larger wings is associated with the evolution of coadapted larval sheaths that store developing wing tissue. Finally, we assessed whether stage-specific evolution is restricted for traits linked to a single biochemical pathway. Supporting this hypothesis, we found that species with more wing melanization in the adult stage have evolved weaker melanin immune defenses in the larval stage. Thus, our results collectively show that natural selection in one stage imposes trait-dependent constraints on evolution in others.

New technology noninvasively monitors cerebral blood flow index and brain function in adult humans., Cerebral blood flow (CBF) is essential for brain function, and CBF-related signals can inform us about brain activity. Yet currently, high-end medical instrumentation is needed to perform a CBF measurement in adult humans. Here, we describe functional interferometric diffusing wave spectroscopy (fiDWS), which introduces and collects near-infrared light via the scalp, using inexpensive detector arrays to rapidly monitor coherent light fluctuations that encode brain blood flow index (BFI), a surrogate for CBF. Compared to other functional optical approaches, fiDWS measures BFI faster and deeper while also providing continuous wave absorption signals. Achieving clear pulsatile BFI waveforms at source-collector separations of 3.5 cm, we confirm that optical BFI, not absorption, shows a graded hypercapnic response consistent with human cerebrovascular physiology, and that BFI has a better contrast-to-noise ratio than absorption during brain activation. By providing high-throughput measurements of optical BFI at low cost, fiDWS will expand access to CBF.

Cities are emerging as a new venue to overcome the challenges of obtaining data on compensatory responses to climatic warming through phenotypic plasticity and evolutionary change. In this Review, we highlight how cities can be used to explore physiological trait responses to experimental warming, and also how cities can be used as human-made space-for-time substitutions. We assessed the current literature and found evidence for significant plasticity and evolution in thermal tolerance trait responses to urban heat islands. For those studies that reported both plastic and evolved components of thermal tolerance, we found evidence that both mechanisms contributed to phenotypic shifts in thermal tolerance, rather than plastic responses precluding or limiting evolved responses. Interestingly though, for a broader range of studies, we found that the magnitude of evolved shifts in thermal tolerance was not significantly different from the magnitude of shift in those studies that only reported phenotypic results, which could be a product of evolution, plasticity, or both. Regardless, the magnitude of shifts in urban thermal tolerance phenotypes was comparable to more traditional space-for-time substitutions across latitudinal and altitudinal clines in environmental temperature. We conclude by considering how urban-derived estimates of plasticity and evolution of thermal tolerance traits can be used to improve forecasting methods, including macrophysiological models and species distribution modelling approaches. Finally, we consider areas for further exploration including sub-lethal performance traits and thermal performance curves, assessing the adaptive nature of trait shifts, and taking full advantage of the environmental thermal variation that cities generate.

Detection of an image boundary when the pixel intensities are measured with noise is an important problem in image segmentation, with numerous applications in medical imaging and engineering. From a statistical point of view, the challenge is that likelihood-based methods require modeling the pixel intensities inside and outside the image boundary, even though these are typically of no practical interest. Since misspecification of the pixel intensity models can negatively affect inference on the image boundary, it would be desirable to avoid this modeling step altogether. Towards this, we develop a robust Gibbs approach that constructs a posterior distribution for the image boundary directly, without modeling the pixel intensities. We prove that, for a suitable prior on the image boundary, the Gibbs posterior concentrates asymptotically at the minimax optimal rate, adaptive to the boundary smoothness. Monte Carlo computation of the Gibbs posterior is straightforward, and simulation experiments show that the corresponding inference is more accurate than that based on existing Bayesian methodology., 19 pages, 1 figure, 2 tables

Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use prediction regions and predictive distributions, respectively, with the latter believed to be more informative because it can perform other prediction-related tasks. The standard notion of validity, what we refer to here as Type-1 validity, focuses on coverage probability of prediction regions, while a notion of validity relevant to the other prediction-related tasks performed by predictive distributions is lacking. Here we present a new notion, called Type-2 validity, relevant to these other prediction tasks. We establish connections between Type-2 validity and coherence properties, and show that imprecise probability considerations are required in order to achieve it. We go on to show that both types of prediction validity can be achieved by interpreting the conformal prediction output as the contour function of a consonant plausibility measure. We also offer an alternative characterization of conformal prediction, based on a new nonparametric inferential model construction, wherein the appearance of consonance is natural, and prove its validity., 34 pages, 2 figures, 2 tables. Comments welcome at https://www.researchers.one/article/2020-01-12

Bayesian and other likelihood-based methods require specification of a statistical model and may not be fully satisfactory for inference on quantities, such as quantiles, that are not naturally defined as model parameters. In this paper, we construct a direct and model-free Gibbs posterior distribution for multivariate quantiles. Being model-free means that inferences drawn from the Gibbs posterior are not subject to model misspecification bias, and being direct means that no priors for or marginalization over nuisance parameters are required. We show here that the Gibbs posterior enjoys a root-$n$ convergence rate and a Bernstein--von Mises property, i.e., for large n, the Gibbs posterior distribution can be approximated by a Gaussian. Moreover, we present numerical results showing the validity and efficiency of credible sets derived from a suitably scaled Gibbs posterior., Comment: 24 pages, 3 figures, 2 tables

The subdivision of samples into stationary sets is one of the first decisions in a resource modeling workflow where geologically and statistically related samples are grouped for further geostatistical modeling. Unsupervised learning algorithms (clustering) with modifications to consider spatial correlation have several benefits in the decision of stationarity, they are: automatic and repeatable; assess uncertainty; and provide a framework for checking existing groupings. However, subjective parameterization remains a critical limitation for the application of spatial clustering in geostatistical workflows. In this work, two main extensions to the current state of research are proposed: 1) a combined spatial-multivariate metric that describes cluster quality in both multivariate and Cartesian space by measuring multivariate compactness and spatial contiguity; and 2) a novel random-path spatial-multivariate ensemble clustering algorithm to reduce the reliance on subjective clustering parameterization. The metrics developed in this work quantify clustering quality based multivariate and spatial properties. Moreover, the proposed clustering algorithm allows the user to control the spatial contiguity and multivariate compactness of the final clusters by modifying a single parameter. The clustering algorithm is introduced and demonstrated on a synthetic test dataset, then further application to more complex datasets are explored to demonstrate the clustering properties and simplicity of tuning the algorithm to prefer spatially contiguous clusters or multivariate compactness. The proposed algorithm outperforms other clustering algorithms for the datasets tested based on the metrics developed.

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are not satisfied. In this paper, I first develop a new prior designed specifically to satisfy an empirical version of the prior concentration property, and then I give sufficient conditions on the prior inputs such that the corresponding empirical Bayes posterior concentrates around the true monotone density at nearly the optimal minimax rate. Numerical illustrations also reveal the practical benefits of the proposed empirical Bayes approach compared to Dirichlet process mixtures., 14 pages; 3 figures; 2 tables

An iterative algorithm has been conjectured to converge to the nonparametric MLE of the mixing distribution. We give a rigorous proof of this conjecture and discuss the use of this algorithm for producing smooth mixing densities as near-MLEs.

In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm and convergence properties are known under certain conditions, but we provide a simpler convergence proof without requiring the restrictive conditions that have previously been needed. Several examples of independent interest are given, including mixing density estimation and a first passage time density function involving Brownian motion. We also develop the basic algorithm to include functions which are not necessarily non-negative and, again, present illustrations.

Incorporating locally varying anisotropy (LVA) in geostatistical modeling improves estimates for structurally complex domains where a single set of anisotropic parameters modeled globally do not account for all geological features. In this work, the properties of two LVA-geostatistical modeling frameworks are explored through application to a complexly folded gold deposit in Ghana. The inference of necessary parameters is a significant requirement of geostatistical modeling with LVA; this work focuses on the case where LVA orientations, derived from expert geological interpretation, are used to improve the grade estimates. The different methodologies for inferring the required parameters in this context are explored. The results of considering different estimation frameworks and alternate methods of parameterization are evaluated with a cross-validation study, as well as visual inspection of grade continuity along select cross sections. Results show that stationary methodologies are outperformed by all LVA techniques, even when the LVA framework has minimal guidance on parameterization. Findings also show that additional improvements are gained by considering parameter inference where the LVA orientations and point data are used to infer the local range of anisotropy. Considering LVA for geostatistical modeling of the deposit considered in this work results in better reproduction of curvilinear geological features.

The inferential model (IM) approach, like fiducial and its generalizations, depends on a representation of the data-generating process. Here, a particular variation on the IM construction is considered, one based on generalized associations. The resulting generalized IM is more flexible than the basic IM in that it does not require a complete specification of the data-generating process and is provably valid under mild conditions. Computation and marginalization strategies are discussed, and two applications of this generalized IM approach are presented., Comment: 18 pages, 4 figures

Bayesian analysis requires prior distributions for all model parameters, whether of interest or not. This can be a burden, for a number of reasons, especially when the nuisance parameters are high- or infinite-dimensional, so there is motivation to find a way around this without completely abandoning the Bayesian approach. Here we consider a general strategy of working with a purposely misspecified model to avoid dealing directly with nuisance parameters. We focus this investigation on an interesting and challenging problem of inference on the volatility of a jump diffusion process based on discrete observations. If we simply ignore the jumps, we can work out precisely the asymptotic behavior of the Bayesian posterior distribution based on the misspecified model. This result suggests some simple adjustments to correct for the effects of misspecification, and we demonstrate that a suitably corrected version of our purposely misspecified posterior leads to inference on the volatility that is asymptotically optimal.

Insurance regulation often dictates that insurers monitor their solvency risk in real time and take appropriate actions whenever the risk exceeds their tolerance level. Bayesian methods are appealing for prediction problems thanks to their ability to naturally incorporate both sample variability and parameter uncertainty into a predictive distribution. However, handling data arriving in real time requires a flexible non-parametric model, and the Monte Carlo methods necessary to evaluate the predictive distribution in such cases are not recursive and can be too expensive to rerun each time new data arrives. In this paper, we apply a recently developed alternative perspective on Bayesian prediction based on copulas. This approach facilitates recursive Bayesian prediction without computing a posterior, allowing insurers to perform real-time updating of risk measures to assess solvency risk, and providing them with a tool for carrying out dynamic risk management strategies in today’s “big data” era.

A graphic sequence $\pi$ is potentially $H$-graphic if there is some realization of $\pi$ that contains $H$ as a subgraph. The Erd\H{o}s-Jacobson-Lehel problem asks to determine $\sigma(H,n)$, the minimum even integer such that any $n$-term graphic sequence $\pi$ with sum at least $\sigma(H,n)$ is potentially $H$-graphic. The parameter $\sigma(H,n)$ is known as the potential function of $H$, and can be viewed as a degree sequence variant of the classical extremal function ${\rm ex}(n,H)$. Recently, Ferrara, LeSaulnier, Moffatt and Wenger [On the sum necessary to ensure that a degree sequence is potentially $H$-graphic, Combinatorica 36 (2016), 687--702] determined $\sigma(H,n)$ asymptotically for all $H$, which is analogous to the Erd\H{o}s-Stone-Simonovits Theorem that determines ${\rm ex}(n,H)$ asymptotically for nonbipartite $H$. In this paper, we investigate a stability concept for the potential number, inspired by Simonovits' classical result on the stability of the extremal function. We first define a notion of stability for the potential number that is a natural analogue to the stability given by Simonovits. However, under this definition, many families of graphs are not $\sigma$-stable, establishing a stark contrast between the extremal and potential functions. We then give a sufficient condition for a graph $H$ to be stable with respect to the potential function, and characterize the stability of those graphs $H$ that contain an induced subgraph of order $\alpha(H)+1$ with exactly one edge., Comment: 20 pages, 3 figures

Geological domains contain non-stationary features that cannot be described by a single direction of continuity. Non-stationary estimation frameworks generate more realistic curvilinear interpretations of subsurface geometries. A radial basis function (RBF) based implicit modeling framework using domain decomposition is developed that permits introduction of locally varying orientations and magnitudes of anisotropy for boundary models to better account for the local variability of complex geological deposits. The interpolation framework is paired with a method to automatically infer the locally predominant orientations, which results in a rapid and robust iterative non-stationary boundary modeling technique that can refine locally anisotropic geological shapes automatically from the sample data. The method also permits quantification of the volumetric uncertainty associated with the boundary modeling. The methodology is demonstrated on a porphyry dataset and shows improved local geological features. Partition of Unity is used to model non-stationary implicit geological shapes.Iterative refinements automatically extract non-stationary geological features.Complex geological modeling is improved considering local anisotropy.

Organisms with complex life cycles commonly exhibit adaptive plasticity in the timing of transitions between life stages. While the threat of predation is predicted to induce earlier transitions, empirical support has been equivocal. When predation risk affects both the propensity to transition to the next life stage and the ability to reach the energetic thresholds necessary to complete the transition, only those individuals in the best physiological condition may be able to accelerate development and emerge earlier. To test this hypothesis, we followed uniquely marked dragonfly larvae (Pachydiplax longipennis) through emergence in pools where we factorially manipulated the presence of a large heterospecific predator (Anax junius) and cannibalism risk via conspecific size variation. Consistent with our hypothesis, high-condition larvae were more likely to emerge in the presence of the heterospecific predator than in its absence, and low-condition larvae were more likely to emerge in its absence than in its presence. Moreover, high-condition larvae emerged earlier when cannibalism risk was high than when it was low. Predation risk therefore has condition-dependent effects on emergence. As predation risk frequently affects resource accumulation, similar mechanisms across taxa could commonly underlie the incongruence between empirical results and theoretical expectations for predator-induced life-history variation. This article is protected by copyright. All rights reserved.

In the recent insurance literature, a variety of finite-dimensional parametric models have been proposed for analyzing the hump-shaped, heavy-tailed, and highly skewed loss data often encountered in applications. These parametric models are relatively simple, but they lack flexibility in the sense that an actuary analyzing a new data set cannot be sure that any one of these parametric models will be appropriate. As a consequence, the actuary must make a non-trivial choice among a collection of candidate models, putting him/herself at risk for various model misspecification biases. In this paper, we argue that, at least in cases where prediction of future insurance losses is the ultimate goal, there is reason to consider a single but more flexible nonparametric model. We focus here on Dirichlet process mixture models, and we reanalyze several of the standard insurance data sets to support our claim that model misspecification biases can be avoided by taking a nonparametric approach, with little to no cost, compared to existing parametric approaches.

Although many selection estimates have been published, the environmental factors that cause selection to vary in space and time have rarely been identified. One way to identify these factors is by experimentally manipulating the environment and measuring selection in each treatment. We compiled and analyzed selection estimates from experimental studies. First, we tested whether the effect of manipulating the environment on selection gradients depends on taxon, trait type, or fitness component. We found that the effect of manipulating the environment was larger when selection was measured on life-history traits or via survival. Second, we tested two predictions about the environmental factors that cause variation in selection. We found support for the prediction that variation in selection is more likely to be caused by environmental factors that have a large effect on mean fitness but not for the prediction that variation is more likely to be caused by biotic factors. Third, we compared selection gradients from experimental and observational studies. We found that selection varied more among treatments in experimental studies than among spatial and temporal replicates in observational studies, suggesting that experimental studies can detect relationships between environmental factors and selection that would not be apparent in observational studies.

IIt is known that a statistically significant treatment may not be clinically significant. A quantity that can be used to assess clinical significance is called the minimum clinically important difference (MCID), and inference on the MCID is an important and challenging problem. Modeling for the purpose of inference on the MCID is non-trivial, and concerns about bias from a misspecified parametric model or inefficiency from a nonparametric model motivate an alternative approach to balance robustness and efficiency. In particular, a recently proposed representation of the MCID as the minimizer of a suitable risk function makes it possible to construct a Gibbs posterior distribution for the MCID without specifying a model. We establish the posterior convergence rate and show, numerically, that an appropriately scaled version of this Gibbs posterior yields interval estimates for the MCID which are both valid and efficient even for relatively small sample sizes., Comment: 17 pages, 1 figure, 2 tables

Over the last two decades, Bayesian methods have been widely used in general insurance applications, ranging from credibility theory to loss-reserves estimation, but this literature rarely addresses questions about the method’s asymptotic properties. In this paper, we review the Bayesian’s notion of posterior consistency in both parametric and nonparametric models and its implication on the sensitivity of the posterior to the actuary’s choice of prior. We review some of the techniques for proving posterior consistency and, for illustration, we apply these results to investigate the asymptotic properties of several recently proposed Bayesian methods in general insurance.

Accurate prediction of future claims is a fundamentally important problem in insurance. The Bayesian approach is natural in this context, as it provides a complete predictive distribution for future claims. The classical credibility theory provides a simple approximation to the mean of that predictive distribution as a point predictor, but this approach ignores other features of the predictive distribution, such as spread, that would be useful for decision making. In this article, we propose a Dirichlet process mixture of log-normals model and discuss the theoretical properties and computation of the corresponding predictive distribution. Numerical examples demonstrate the benefit of our model compared to some existing insurance loss models, and an R code implementation of the proposed method is also provided.

Although there is considerable optimism surrounding adaptive evolutionary responses to global change, relatively little attention has been paid to maladaptation in this context. In this review, we consider how global change might lead populations to become maladapted. We further consider how populations can evolve to new optima, fail to evolve and therefore remain maladapted, or become further maladapted through trait-driven or eco-evo-driven mechanisms after being displaced from their fitness optima. Our goal is to stimulate thinking about evolution as a "double-edged sword" that comprises both adaptive and maladaptive responses, rather than as a "silver bullet" or a purely adaptive mechanism to combat global change. We conclude by discussing how a better appreciation of environmentally driven maladaptation and maladaptive responses might improve our current understanding of population responses to global change and our ability to forecast future responses.

The area under the receiver operating characteristic curve (AUC) serves as a summary of a binary classifier's performance. Methods for estimating the AUC have been developed under a binormality assumption which restricts the distribution of the score produced by the classifier. However, this assumption introduces an infinite-dimensional nuisance parameter and can be inappropriate, especially in the context of machine learning. This motivates us to adopt a model-free Gibbs posterior distribution for the AUC. We present the asymptotic Gibbs posterior concentration rate, and a strategy for tuning the learning rate so that the corresponding credible intervals achieve the nominal frequentist coverage probability. Simulation experiments and a real data analysis demonstrate the Gibbs posterior's strong performance compared to existing methods based on a rank likelihood., 19 pages, 3 figures, 5 tables

The environment experienced early in life often affects the traits that are developed after an individual has transitioned into new life stages and environments. Because the phenotypes induced by earlier environments are then screened by later ones, these 'carry-over effects' influence fitness outcomes across the entire life cycle. While the last two decades have witnessed an explosion of studies documenting the occurrence of carry-over effects, little attention has been given to how they adapt and diversify. To aid future research in this area, we present a framework for the evolution of carry-over effects. Carry-over effects can evolve in two ways. First, the expression of traits later in life may become more or less dependent on the developmental processes of earlier stages (e.g., 'adaptive decoupling'). Genetic correlations between life stages then either strengthen or weaken. Alternatively, those influential developmental processes that begin early in life may become more or less sensitive to that earlier environment. Here, plasticity changes in all the traits that share those developmental pathways across the whole life cycle. Adaptive evolution of a carry-over effect is governed by selection on the induced phenotypes in the later stage, and also by selection on any developmentally linked traits in the earlier life stage. When these selective pressures conflict, the evolution of the carry-over effect will be biased towards maximizing performance in the life stage with stronger selection. Because life stages often contribute unequally to total fitness, the strength of selection in any one stage depends on: (a) the relationship between the traits and the stage-specific fitness components (e.g., juvenile survival, adult mating success), and (b) the reproductive value of the life stage. Considering the evolution of carry-over effects reveals several intriguing features of the evolution of life histories and phenotypic plasticity more generally. For instance, carry-over effects that manifest as maladaptive plasticity in one life stage may represent an adaptive strategy for maximizing fitness in stages with stronger selection. Additionally, adaptation to novel environments encountered early in the life cycle may be faster in the presence of carry-over effects that influence sexually selected traits.

Inferential challenges that arise when data are censored have been extensively studied under the classical frameworks. In this paper, we provide an alternative generalized inferential model approach whose output is a data-dependent plausibility function. This construction is driven by an association between the distribution of the relative likelihood function at the interest parameter and an unobserved auxiliary variable. The plausibility function emerges from the distribution of a suitably calibrated random set designed to predict that unobserved auxiliary variable. The evaluation of this plausibility function requires a novel use of the classical Kaplan--Meier estimator to estimate the censoring rather than the event distribution. We prove that the proposed method provides valid inference, at least approximately, and our real- and simulated-data examples demonstrate its superior performance compared to existing methods., Comment: 20 pages, 8 figures

Bias resulting from model misspecification is a concern when predicting insurance claims. Indeed, this bias puts the insurer at risk of making invalid or unreliable predictions. A method that could provide provably valid predictions uniformly across a large class of possible distributions would effectively eliminate the risk of model misspecification bias. Conformal prediction is one such method that can meet this need, and here we tailor that approach to the typical insurance application and show that the predictions are not only valid but also efficient across a wide range of settings.

Given a finite poset $\mathcal{P}$, a family $\mathcal{F}$ of elements in the Boolean lattice is induced-$\mathcal{P}$-saturated if $\mathcal{F}$ contains no copy of $\mathcal{P}$ as an induced subposet but every proper superset of $\mathcal{F}$ contains a copy of $\mathcal{P}$ as an induced subposet. The minimum size of an induced-$\mathcal{P}$-saturated family in the $n$-dimensional Boolean lattice, denoted $\mathrm{sat}^*(n,\mathcal{P})$, was first studied by Ferrara et al. (2017). Our work focuses on strengthening lower bounds. For the 4-point poset known as the diamond, we prove $\mathrm{sat}^*(n,\Diamond)\geq\sqrt{n}$, improving upon a logarithmic lower bound. For the antichain with $k+1$ elements, we prove $$\mathrm{sat}^*(n,\mathcal{A}_{k+1})\geq \left(1-\frac{1}{\log_2k}\right)\frac{kn}{\log_2 k}$$ for $n$ sufficiently large, improving upon a lower bound of $3n-1$ for $k\geq 3$.

Simulating from a gamma distribution with small shape parameter is a challenging problem. Towards an efficient method, we obtain a limiting distribution for a suitably normalized gamma distribution when the shape parameter tends to zero. Then this limiting distribution provides insight to the construction of a new, simple, and highly efficient acceptance---rejection algorithm. The proposed method is fast and comparisons based on acceptance rates show that it is more efficient than existing acceptance---rejection methods.

Sexual signalling is predicted to shape the evolution of sex-specific ornamentation, and establishing the costs and benefits of ornamentation and the information that ornamentation provides to receivers is necessary to evaluating this adaptive function. Here, we assessed the adaptive function of a common colour ornament in insects, melanin wing ornamentation, using the dragonfly Pachydiplax longipennis. We hypothesized that greater ornamentation would improve territory-holding success by decreasing aggression that males receive from territorial rivals, but that more ornamented males may have shorter lifespans. Using mark-recapture field observations, we found that more ornamented males had greater territory-holding success and that viability selection did not act on wing melanization. We then compared the aggression of territorial rivals to decoy males before and after experimentally augmenting wing melanization, finding that males significantly reduced aggression following the manipulation. We next hypothesized that wing melanization would signal fighting ability to territorial rivals by reflecting condition via investment in the costly melanin synthesis pathway. We observed a positive relationship between ornamentation and the likelihood of winning territorial disputes, suggesting that wing melanization provides information about fighting ability to rivals. We also found a positive relationship between melanin-based immune defence and ornamentation, supporting a link between the signal and condition. We conclude that wing melanization is a condition-related signal of fighting ability and suggest that this may be a common mechanism promoting the evolution of melanin ornamentation.

When an individual can selfishly cannibalize a relative or altruistically set it free, the benefits of altruism will be positively associated with the relative's fitness prospects (the benefits it receives from altruism). We tested the prediction that altruism should be preferentially directed toward high-quality relatives using larvae of the New Mexican spadefoot toad (Spea multiplicata), a species in which tadpoles plastically express omnivore and carnivore ecomorphs. In a no-choice design, we presented carnivores with sibling or nonsibling omnivores varying in developmental stage, which is positively associated with survival in this toad's ephemeral larval environment. There was a significant interaction between relatedness and developmental stage on the probability of cannibalism: carnivores were overall more likely to cannibalize less developed omnivores, but this effect was exaggerated when the potential victim was a sibling. This evidence that altruists favor relatives with high fitness prospects highlights the numerous factors shaping altruism's payoffs.

To start, we want to congratulate the authors of the paper for their very interesting contribution to the theory of credibility estimation. The proposed nonparametric generalization of Buhlmann's s...

Standard statistical methods, such as maximum likelihood, are often justified based on their asymptotic properties. For suitably regular models, this theory is standard, but when the model is non-regular, for example, the support depends on the parameter, these asymptotic properties may be difficult to assess. Recently, an inferential model (IM) framework has been developed that provides valid prior-free probabilistic inference without the need for asymptotic justification. In this paper, we construct an IM for a class of highly non-regular models with parameter-dependent support. This construction requires conditioning, which is facilitated through solving a particular differential equation. We prove that the plausibility intervals derived from this IM are exact, and we demonstrate, via simulations, that their exactness does not come at the cost of loss of efficiency. Copyright © 2016 John Wiley & Sons, Ltd.

The decision of stationarity is a fundamental prerequisite to geostatistical estimation and uncertainty characterization of natural resources. Great effort is given to delineate relevant spatial-statistical populations for modeling. Recently developed spatial clustering methodologies claim improvements over traditional methodologies for stationary decision making. However, these novel methods are generally unproven with respect to the geostatistical algorithms that generate the models upon which important and costly decisions are based. In this study, a new method to generate the prior parameter uncertainty for the decision of stationarity is established, and the effects of considering different (and uncertain) decisions of stationarity are explored through a K-Fold cross validation study applied to a nickel laterite dataset with complex multivariate relationships. Results show that, in terms of univariate regression metrics, geostatistical models generated with clustering-based modeling domains are competitive or better than those generated with the traditional merged-lithological domains. However, models generated from the clustering-based stationary domains are superior in terms of multivariate feature reproduction when compared to the merged-lithology domains. We also demonstrate a geostatistical modeling workflow that incorporates uncertainty associated with stationary domaining, with only a minimal extension to established techniques for geostatistical modeling with parameter uncertainty.

An (r − 1, 1)-coloring of an r-regular graph G is an edge coloring (with arbitrarily many colors) such that each vertex is incident to r − 1 edges of one color and 1 edge of a different color. In this paper, we completely characterize all 4-regular pseudographs (graphs that may contain parallel edges and loops) which do not have a (3, 1)-coloring. Also, for each r ≥ 6 we construct graphs that are not (r −1, 1)-colorable and, more generally, are not (r − t, t)-colorable for small t.

For many species, the timing of life cycle events is advancing under contemporary global climate change. However, much less is known regarding phenological shifts as a result of other sources of anthropogenic change, such as urban warming. In both cases, progress has been hampered by a focus on phenological traits such as the timing of emergence, rather than the phenology of more directly related fitness traits such as the timing of reproduction. Here we explore how urban heat island effects shape the timing of reproduction in an acorn-dwelling ant. We used a common garden experiment with acorn ants collected from three cities in the eastern United States along a latitudinal gradient and reared long-term in the laboratory under five temperature treatments. This allowed us to quantify the effects of temperature on reproductive phenology across three scales-a biogeographic temperature cline, three urban vs. rural temperature comparisons, and five laboratory rearing temperatures. At our northernmost and southernmost cities (spanning 6° of latitude), we found both urbanization and warmer laboratory rearing temperature significantly advanced reproductive phenology; ants from the lowest latitude city also had earlier reproductive phenology compared with the higher latitude cities. In the field, the differences in urban versus rural acorn ant reproductive phenology translate to approximately one month earlier reproduction in the urban populations. For insects with synchronous mating events, such as ants, shifts in the already short window of time to reproduce could limit mating across environments, potentially leading to reproductive isolation between urban and rural populations.

The environment shapes the evolution of secondary sexual traits by determining how their costs and benefits vary across the landscape. Given the thermal properties of dark coloration generally, temperature should crucially influence the costs, benefits and geographic diversification of many secondary sexual colour patterns. We tested this hypothesis using sexually selected wing coloration in a dragonfly. We find that greater wing coloration heats males - the magnitude of which improves flight performance under cool conditions but dramatically reduces it under warm conditions. In a colder region of the species' range, behavioural observations of a wild population show that these thermal effects translate into greater territorial acquisition on thermally variable days. Finally, geo-referenced photographs taken by citizen scientists reveal that this sexually selected wing coloration is dramatically reduced in the hottest portions of the species' range. Collectively, our results underscore temperature's capacity to promote and constrain the evolution of sexual coloration.

Floral traits are hypothesized to evolve primarily in response to selection by pollinators. However, selection can also be mediated by other environmental factors. To understand the relative importance of pollinator-mediated selection and its variation among trait and pollinator types, we analyzed directional selection gradients on floral traits from experiments that manipulated the environment to identify agents of selection. Pollinator-mediated selection was stronger than selection by other biotic factors (e.g., herbivores), but similar in strength to selection by abiotic factors (e.g., soil water), providing partial support for the hypothesis that floral traits evolve primarily in response to pollinators. Pollinator-mediated selection was stronger on pollination efficiency traits than on other trait types, as expected if efficiency traits affect fitness via interactions with pollinators, but other trait types also affect fitness via other environmental factors. In addition to varying among trait types, pollinator-mediated selection varied among pollinator taxa: selection was stronger when bees, long-tongued flies, or birds were the primary visitors than when the primary visitors were Lepidoptera or multiple animal taxa. Finally, reducing pollinator access to flowers had a relatively small effect on selection on floral traits, suggesting that anthropogenic declines in pollinator populations would initially have modest effects on floral evolution.