Coherent Statistical Framework Research Articles

Climatic signatures in early modern European grain harvest yields

Abstract. The association between climate variability and grain harvest yields has been an important component of food security and economy in European history. Yet, inter-regional comparisons of climate–yield relationships have been hampered by locally varying data types and the use of different statistical methods. Using a coherent statistical framework, considering the effects of diverse serial correlations on statistical significance, we assess the temperature and hydroclimate (precipitation and drought) signatures in grain harvest yields across varying environmental settings of early modern (ca. 1500–1800) Europe. An unprecedentedly large network of yield records from northern (Sweden), central (Switzerland), and southern (Spain) Europe are compared with a diverse set of seasonally and annually resolved palaeoclimate reconstructions. Considering the effects of different crop types and time series frequencies, we find within regions consistent climate–harvest yield associations characterized by a significant summer soil moisture signal in Sweden, winter temperature and precipitation signals in Switzerland, and spring and annual mean temperature signals in Spain. The regional-scale climate–harvest associations are weaker than the recently revealed climate signals in early modern grain prices but similar in strength to modern climate–harvest relationships at comparable spatial scales. This is a noteworthy finding considering the uncertainties inherent in both historical harvest and palaeoclimate data.

The recent normalization of historical marine heat extremes

Climate change exposes marine ecosystems to extreme conditions with increasing frequency. Capitalizing on the global reconstruction of sea surface temperature (SST) records from 1870-present, we present a centennial-scale index of extreme marine heat within a coherent and comparable statistical framework. A spatially (1° × 1°) and temporally (monthly) resolved index of the normalized historical extreme marine heat events was expressed as a fraction of a year that exceeds a locally determined, monthly varying 98th percentile of SST gradients derived from the first 50 years of climatological records (1870–1919). For the year 2019, our index reports that 57% of the global ocean surface recorded extreme heat, which was comparatively rare (approximately 2%) during the period of the second industrial revolution. Significant increases in the extent of extreme marine events over the past century resulted in many local climates to have shifted out of their historical SST bounds across many economically and ecologically important marine regions. For the global ocean, 2014 was the first year to exceed the 50% threshold of extreme heat thereby becoming “normal”, with the South Atlantic (1998) and Indian (2007) basins crossing this barrier earlier. By focusing on heat extremes, we provide an alternative framework that may help better contextualize the dramatic changes currently occurring in marine systems.

A Dynamic Structural Equation Approach to Modeling Wage Dynamics and Cumulative Advantage across the Lifespan

Wages and wage dynamics directly affect individuals’ and families’ daily lives. In this article, we show how major theoretical branches of research on wages and inequality—that is, cumulative advantage (CA), human capital theory, and the lifespan perspective—can be integrated into a coherent statistical framework and analyzed with multilevel dynamic structural equation modeling (DSEM). This opens up a new way to empirically investigate the mechanisms that drive growing inequality over time. We demonstrate the new approach by making use of longitudinal, representative U.S. data (NLSY-79). Analyses revealed fundamental between-person differences in both initial wages and autoregressive wage growth rates across the lifespan. Only 0.5% of the sample experienced a “strict” CA and unbounded wage growth, whereas most individuals revealed logarithmic wage growth over time. Adolescent intelligence and adult educational levels explained substantial heterogeneity in both parameters. We discuss how DSEM may help researchers study CA processes and related developmental dynamics, and we highlight the extensions and limitations of the DSEM framework.

Topological Learning and Its Application to Multimodal Brain Network Integration.

A long-standing challenge in multimodal brain network analyses is to integrate topologically different brain networks obtained from diffusion and functional MRI in a coherent statistical framework. Existing multimodal frameworks will inevitably destroy the topological difference of the networks. In this paper, we propose a novel topological learning framework that integrates networks of different topology through persistent homology. Such challenging task is made possible through the introduction of a new topological loss that bypasses intrinsic computational bottlenecks and thus enables us to perform various topological computations and optimizations with ease. We validate the topological loss in extensive statistical simulations with ground truth to assess its effectiveness of discriminating networks. Among many possible applications, we demonstrate the versatility of topological loss in the twin imaging study where we determine the extend to which brain networks are genetically heritable.

A sequential dynamic Bayesian network for pore-pressure estimation with uncertainty quantification

Pore-pressure estimation is an important part of oil-well drilling because drilling into unexpected highly pressured fluids can be costly and dangerous. However, standard estimation methods rarely account for the many sources of uncertainty, or for the multivariate nature of the system. We have developed the pore-pressure sequential dynamic Bayesian network (PP SDBN) as an appropriate solution to both these issues. The PP SDBN models the relationships between quantities in the pore-pressure system, such as pressures, porosity, lithology, and wireline-log data, using conditional probability distributions based on geophysical relationships to capture our uncertainty about these variables and the relationships between them. When wireline log data are given to the PP SDBN, the probability distributions are updated, providing an estimate of pore pressure along with a probabilistic measure of uncertainty that reflects the data acquired and our understanding of the system. This is the advantage of a Bayesian approach. Our model provides a coherent statistical framework for modeling the pore-pressure system. The specific geophysical relationships used can be changed to better suit a particular setting, or reflect geoscientists’ knowledge. We determine the PP SDBN on an offshore well from West Africa. We also perform a sensitivity analysis, demonstrating how this can be used to better understand the working of the model and which parameters are the most influential. The dynamic nature of the model makes it suitable for real-time estimation during logging while drilling. The PP SDBN models the shale pore pressure in shale-rich formations with mechanical compaction as the overriding source of overpressure. The PP SDBN improves on existing methods because it produces a probabilistic estimate that reflects the many sources of uncertainty present.

A state transition framework for patient-level modeling of engagement and retention in HIV care using longitudinal cohort data.

The human immunodeficiency virus (HIV) care cascade is a conceptual model used to outline the benchmarks that reflects effectiveness of HIV care in the whole HIV care continuum. The models can be used to identify barriers contributing to poor outcomes along each benchmark in the cascade such as disengagement from care or death. Recently, the HIV care cascade has been widely applied to monitor progress towards HIV prevention and care goals in an attempt to develop strategies to improve health outcomes along the care continuum. Yet, there are challenges in quantifying successes and gaps in HIV care using the cascade models that are partly due to the lack of analytic approaches. The availability of large cohort data presents an opportunity to develop a coherent statistical framework for analysis of the HIV care cascade. Motivated by data from the Academic Model Providing Access to Healthcare, which has provided HIV care to nearly 200,000 individuals in Western Kenya since 2001, we developed a state transition framework that can characterize patient-level movements through the multiple stages of the HIV care cascade. We describe how to transform large observational data into an analyzable format. We then illustrate the state transition framework via multistate modeling to quantify dynamics in retention aspects of care. The proposed modeling approach identifies the transition probabilities of moving through each stage in the care cascade. In addition, this approach allows regression-based estimation to characterize effects of (time-varying) predictors of within and between state transitions such as retention, disengagement, re-entry into care, transfer-out, and mortality. Copyright © 2017 John Wiley & Sons, Ltd.

Covariations in ecological scaling laws fostered by community dynamics

Scaling laws in ecology, intended both as functional relationships among ecologically relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances, and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked has been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply, and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such a framework is consistent with the stationary-state statistics of a broad class of resource-limited community dynamics models, regardless of parameterization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations.

From information processing to decisions: Formalizing and comparing psychologically plausible choice models

Decision strategies explain how people integrate multiple sources of information to make probabilistic inferences. In the past decade, increasingly sophisticated methods have been developed to determine which strategy explains decision behavior best. We extend these efforts to test psychologically more plausible models (i.e., strategies), including a new, probabilistic version of the take-the-best (TTB) heuristic that implements a rank order of error probabilities based on sequential processing. Within a coherent statistical framework, deterministic and probabilistic versions of TTB and other strategies can directly be compared using model selection by minimum description length or the Bayes factor. In an experiment with inferences from given information, only three of 104 participants were best described by the psychologically plausible, probabilistic version of TTB. Similar as in previous studies, most participants were classified as users of weighted-additive, a strategy that integrates all available information and approximates rational decisions.

A STATISTICAL FRAMEWORK FOR DATA INTEGRATION THROUGH GRAPHICAL MODELS WITH APPLICATION TO CANCER GENOMICS.

Recent advances in high-throughput biotechnologies have generated var-ious types of genetic, genomic, epigenetic, transcriptomic and proteomic data across different biological conditions. It is likely that integrating data from diverse experiments may lead to a more unified and global view of biolog-ical systems and complex diseases. We present a coherent statistical frame-work for integrating various types of data from distinct but related biological conditions through graphical models. Specifically, our statistical framework is designed for modeling multiple networks with shared regulatory mech-anisms from heterogeneous high-dimensional datasets. The performance of our approach is illustrated through simulations and its applications to cancer genomics.

A Framework for Assessing High School Students' Statistical Reasoning.

Based on a synthesis of literature, earlier studies, analyses and observations on high school students, this study developed an initial framework for assessing students’ statistical reasoning about descriptive statistics. Framework descriptors were established across five levels of statistical reasoning and four key constructs. The former consisted of idiosyncratic reasoning, verbal reasoning, transitional reasoning, procedural reasoning, and integrated process reasoning. The latter include describing data, organizing and reducing data, representing data, and analyzing and interpreting data. In contrast to earlier studies, this initial framework formulated a complete and coherent statistical reasoning framework. A statistical reasoning assessment tool was then constructed from this initial framework. The tool was administered to 10 tenth-grade students in a task-based interview. The initial framework was refined, and the statistical reasoning assessment tool was revised. The ten students then participated in the second task-based interview, and the data obtained were used to validate the framework. The findings showed that the students’ statistical reasoning levels were consistent across the four constructs, and this result confirmed the framework’s cohesion. Developed to contribute to statistics education, this newly developed statistical reasoning framework provides a guide for planning learning goals and designing instruction and assessments.

Connecting the dots: network data and models in HIV epidemiology.

Effective HIV prevention requires knowledge of the structure and dynamics of the social networks across which infections are transmitted. These networks most commonly comprise chains of sexual relationships, but in some populations, sharing of contaminated needles is also an important, or even the main mechanism that connects people in the network. Whereas network data have long been collected during survey interviews, new data sources have become increasingly common in recent years, because of advances in molecular biology and the use of partner notification services in HIV prevention and treatment programmes. We review current and emerging methods for collecting HIV-related network data, as well as modelling frameworks commonly used to infer network parameters and map potential HIV transmission pathways within the network. We discuss the relative strengths and weaknesses of existing methods and models, and we propose a research agenda for advancing network analysis in HIV epidemiology. We make the case for a combination approach that integrates multiple data sources into a coherent statistical framework.

Host ecology determines the dispersal patterns of a plant virus.

Since its isolation in 1966 in Kenya, rice yellow mottle virus (RYMV) has been reported throughout Africa resulting in one of the economically most important tropical plant emerging diseases. A thorough understanding of RYMV evolution and dispersal is critical to manage viral spread in tropical areas that heavily rely on agriculture for subsistence. Phylogenetic analyses have suggested a relatively recent expansion, perhaps driven by the intensification of agricultural practices, but this has not yet been examined in a coherent statistical framework. To gain insight into the historical spread of RYMV within Africa rice cultivations, we analyse a dataset of 300 coat protein gene sequences, sampled from East to West Africa over a 46-year period, using Bayesian evolutionary inference. Spatiotemporal reconstructions date the origin of RMYV back to 1852 (1791–1903) and confirm Tanzania as the most likely geographic origin. Following a single long-distance transmission event from East to West Africa, separate viral populations have been maintained for about a century. To identify the factors that shaped the RYMV distribution, we apply a generalised linear model (GLM) extension of discrete phylogenetic diffusion and provide strong support for distances measured on a rice connectivity landscape as the major determinant of RYMV spread. Phylogeographic estimates in continuous space further complement this by demonstrating more pronounced expansion dynamics in West Africa that are consistent with agricultural intensification and extensification. Taken together, our principled phylogeographic inference approach shows for the first time that host ecology dynamics have shaped the historical spread of a plant virus.

Estimating mean plant cover from different types of cover data: a coherent statistical framework

Plant cover is measured by different methods and it is important to be able to estimate mean cover and to compare estimates of plant cover across different sampling methods in a coherent statistical framework. Here, a framework that incorporates (1) pin‐point cover data, (2) visually determined cover data, and (3) ordinal cover classification systems (e.g., Braun‐Blanquet cover data) is presented and tested on simulated plant cover data. The effect of measurement error when applying a visual determination of plant cover is considered. Generally, the estimation of the mean plant cover was well‐behaved and unbiased for all the three methods, whereas the estimate of the intra‐plot correlation tended to be upward biased and especially so if the plant cover data was collected using the Braun‐Blanquet method. It was surprising that the Braun‐Blanquet sampling procedure provided mean plant cover estimates that were comparable to the other sampling schemes. This method shows promise in the attempt to use the large amount of historic Braun‐Blanquet plant cover data in the investigation of the underlying causes for observed vegetation changes.

Effect of uncertainty in surface mass balance–elevation feedback on projections of the future sea level contribution of the Greenland ice sheet

Abstract. We apply a new parameterisation of the Greenland ice sheet (GrIS) feedback between surface mass balance (SMB: the sum of surface accumulation and surface ablation) and surface elevation in the MAR regional climate model (Edwards et al., 2014) to projections of future climate change using five ice sheet models (ISMs). The MAR (Modèle Atmosphérique Régional: Fettweis, 2007) climate projections are for 2000–2199, forced by the ECHAM5 and HadCM3 global climate models (GCMs) under the SRES A1B emissions scenario. The additional sea level contribution due to the SMB–elevation feedback averaged over five ISM projections for ECHAM5 and three for HadCM3 is 4.3% (best estimate; 95% credibility interval 1.8–6.9%) at 2100, and 9.6% (best estimate; 95% credibility interval 3.6–16.0%) at 2200. In all results the elevation feedback is significantly positive, amplifying the GrIS sea level contribution relative to the MAR projections in which the ice sheet topography is fixed: the lower bounds of our 95% credibility intervals (CIs) for sea level contributions are larger than the "no feedback" case for all ISMs and GCMs. Our method is novel in sea level projections because we propagate three types of modelling uncertainty – GCM and ISM structural uncertainties, and elevation feedback parameterisation uncertainty – along the causal chain, from SRES scenario to sea level, within a coherent experimental design and statistical framework. The relative contributions to uncertainty depend on the timescale of interest. At 2100, the GCM uncertainty is largest, but by 2200 both the ISM and parameterisation uncertainties are larger. We also perform a perturbed parameter ensemble with one ISM to estimate the shape of the projected sea level probability distribution; our results indicate that the probability density is slightly skewed towards higher sea level contributions.

Temporal and micro-spatial heterogeneity in the distribution of Anopheles vectors of malaria along the Kenyan coast

BackgroundThe distribution of anopheline mosquitoes is determined by temporally dynamic environmental and human-associated variables, operating over a range of spatial scales. Macro-spatial short-term trends are driven predominantly by prior (lagged) seasonal changes in climate, which regulate the abundance of suitable aquatic larval habitats. Micro-spatial distribution is determined by the location of these habitats, proximity and abundance of available human bloodmeals and prevailing micro-climatic conditions. The challenge of analysing—in a single coherent statistical framework—the lagged and distributed effect of seasonal climate changes simultaneously with the effects of an underlying hierarchy of spatial factors has hitherto not been addressed.MethodsData on Anopheles gambiae sensu stricto and A. funestus collected from households in Kilifi district, Kenya, were analysed using polynomial distributed lag generalized linear mixed models (PDL GLMMs).ResultsAnopheline density was positively and significantly associated with amount of rainfall between 4 to 47 days, negatively and significantly associated with maximum daily temperature between 5 and 35 days, and positively and significantly associated with maximum daily temperature between 29 and 48 days in the past (depending on Anopheles species). Multiple-occupancy households harboured greater mosquito numbers than single-occupancy households. A significant degree of mosquito clustering within households was identified.ConclusionsThe PDL GLMMs developed here represent a generalizable framework for analysing hierarchically-structured data in combination with explanatory variables which elicit lagged effects. The framework is a valuable tool for facilitating detailed understanding of determinants of the spatio-temporal distribution of Anopheles. Such understanding facilitates delivery of targeted, cost-effective and, in certain circumstances, preventative antivectorial interventions against malaria.

Estimating species composition and quantifying uncertainty in multispecies fisheries: hierarchical Bayesian models for stratified sampling protocols with missing data

Accurate landing statistics are among the most important data for the management of sustainable fisheries. For many fisheries, however, estimating species-specific landings and the associated uncertainty can be difficult, especially in the case of complex multispecies fisheries. Here we develop general and flexible methods for estimating species-specific landings, motivated by the mixed-species California groundfish fishery. We describe Bayesian generalized linear and hierarchical models for estimating species compositions from port sampling data and illustrate the application of each to several examples from California fisheries. Our hierarchical modeling approach provides a coherent statistical framework that can provide estimates of landings and uncertainty in the face of sparse and missing sampling data that compliment existing procedures for estimating landings. Furthermore, our methods provide ways to compare alternative model formulations and to maintain estimates of uncertainty when landings are aggregated across temporal or spatial scales. Our model structure is applicable to fisheries worldwide.

Model selection and adaptive Markov chain Monte Carlo for Bayesian cointegrated {VAR} models

This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorithm of Roberts and Rosenthal (2009). Developing the adaptive MCMC framework for Bayesian CVAR models allows for efficient estimation of posterior parameters in significantly higher dimensional CVAR series than previously possible with existing griddy Gibbs samplers. For a n-dimensional CVAR series, the matrix-variate posterior is in dimension $3n^2 + n$, with significant correlation present between the blocks of matrix random variables. Hence, utilizing a griddy Gibbs sampler for large n becomes computationally impractical as it involves approximating an $n \times n$ full conditional posterior using a spline over a high dimensional $n \times n$ grid. The adaptive MCMC approach is demonstrated to be ideally suited to learning on-line a proposal to reflect the posterior correlation structure, therefore improving the computational efficiency of the sampler. We also treat the rank of the CVAR model as a random variable and perform joint inference on the rank and model parameters. This is achieved with a Bayesian posterior distribution defined over both the rank and the CVAR model parameters, and inference is made via Bayes Factor analysis of rank. Practically the adaptive sampler also aids in the development of automated Bayesian cointegration models for algorithmic trading systems considering instruments made up of several assets, such as currency baskets. Previously the literature on financial applications of CVAR trading models typically only considers pairs trading (n=2) due to the computational cost of the griddy Gibbs. We are able to extend under our adaptive framework to $n >> 2$ and demonstrate an example with n = 10, resulting in a posterior distribution with parameters up to dimension 310. By also considering the rank as a random quantity we can ensure our resulting trading models are able to adjust to potentially time varying market conditions in a coherent statistical framework.

Model selection and adaptive Markov chain Monte Carlo for Bayesian cointegrated {VAR} models

This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorithm of Roberts and Rosenthal (2009). Developing the adaptive MCMC framework for Bayesian CVAR models allows for efficient estimation of posterior parameters in significantly higher dimensional CVAR series than previously possible with existing griddy Gibbs samplers. For a n-dimensional CVAR series, the matrix-variate posterior is in dimension $3n^2 + n$, with significant correlation present between the blocks of matrix random variables. Hence, utilizing a griddy Gibbs sampler for large n becomes computationally impractical as it involves approximating an $n \times n$ full conditional posterior using a spline over a high dimensional $n \times n$ grid. The adaptive MCMC approach is demonstrated to be ideally suited to learning on-line a proposal to reflect the posterior correlation structure, therefore improving the computational efficiency of the sampler. We also treat the rank of the CVAR model as a random variable and perform joint inference on the rank and model parameters. This is achieved with a Bayesian posterior distribution defined over both the rank and the CVAR model parameters, and inference is made via Bayes Factor analysis of rank. Practically the adaptive sampler also aids in the development of automated Bayesian cointegration models for algorithmic trading systems considering instruments made up of several assets, such as currency baskets. Previously the literature on financial applications of CVAR trading models typically only considers pairs trading (n=2) due to the computational cost of the griddy Gibbs. We are able to extend under our adaptive framework to $n >> 2$ and demonstrate an example with n = 10, resulting in a posterior distribution with parameters up to dimension 310. By also considering the rank as a random quantity we can ensure our resulting trading models are able to adjust to potentially time varying market conditions in a coherent statistical framework.

Stochastic algorithm for Bayesian mixture effect template estimation

The estimation of probabilistic deformable template models in computer vision or of probabilistic atlases in Computational Anatomy are core issues in both fields. A first coherent statistical framework where the geometrical variability is modelled as a hidden random variable has been given by [S. Allassonnière et al., J. Roy. Stat. Soc. 69 (2007) 3–29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models. A consistent stochastic algorithm has been introduced in [S. Allassonnière et al. (in revision)] to face the problem encountered in [S. Allassonnière et al., J. Roy. Stat. Soc. 69 (2007) 3–29] for the convergence of the estimation algorithm for the one component model in the presence of noise. We propose here to go on in this direction of using some “SAEM-like” algorithm to approximate the MAP estimator in the general Bayesian setting of mixture of deformable template models. We also prove the convergence of our algorithm toward a critical point of the penalised likelihood of the observations and illustrate this with handwritten digit images and medical images.

Construction of Bayesian deformable models via a stochastic approximation algorithm: A convergence study

The problem of the definition and estimation of generative models based on deformable templates from raw data is of particular importance for modeling non-aligned data affected by various types of geometric variability. This is especially true in shape modeling in the computer vision community or in probabilistic atlas building in computational anatomy. A first coherent statistical framework modeling geometric variability as hidden variables was described in Allassonnière, Amit and Trouvé [J. R. Stat. Soc. Ser. B Stat. Methodol. 69 (2007) 3–29]. The present paper gives a theoretical proof of convergence of effective stochastic approximation expectation strategies to estimate such models and shows the robustness of this approach against noise through numerical experiments in the context of handwritten digit modeling.