Formal Statistical Framework Research Articles

Statistical analysis of the gravitational anomaly in Gaia wide binaries

ABSTRACT The exploration of the low acceleration a < a0 regime, where a0 = 1.2 × 10−10 m s−2 is the acceleration scale of MOND around which gravitational anomalies at galactic scale appear, has recently been extended to the much smaller mass and length scales of local wide binaries thanks to the availability of the Gaia catalogue. Statistical methods to test the underlying structure of gravity using large samples of such binary stars and dealing with the necessary presence of kinematic contaminants in such samples have also been presented. However, an alternative approach using binary samples carefully selected to avoid any such contaminants, and consequently much smaller samples, has been lacking a formal statistical development. In the interest of having independent high-quality checks on the results of wide binary gravity tests, we here develop a formal statistical framework for treating small, clean, wide binary samples in the context of testing modifications to gravity of the form G → γG. The method is validated through extensive tests with synthetic data samples, and applied to recent Gaia DR3 binary star observational samples of relative velocities and internal separations on the plane of the sky, v2D and r2D, respectively. Our final results for a high acceleration r2D < 0.01 pc region are of γ = 1.000 ± 0.096, in full accordance with Newtonian expectations. For a low acceleration r2D > 0.01 pc region, however, we obtain γ = 1.5 ± 0.2, inconsistent with the Newtonian value of γ = 1 at a 2.6σ level, and much more indicative of MOND AQUAL predictions of close to γ = 1.4.

Black-box tests for algorithmic stability.

Algorithmic stability is a concept from learning theory that expresses the degree to which changes to the input data (e.g. removal of a single data point) may affect the outputs of a regression algorithm. Knowing an algorithm's stability properties is often useful for many downstream applications-for example, stability is known to lead to desirable generalization properties and predictive inference guarantees. However, many modern algorithms currently used in practice are too complex for a theoretical analysis of their stability properties, and thus we can only attempt to establish these properties through an empirical exploration of the algorithm's behaviour on various datasets. In this work, we lay out a formal statistical framework for this kind of black-box testing without any assumptions on the algorithm or the data distribution, and establish fundamental bounds on the ability of any black-box test to identify algorithmic stability.

Spatially Clustered Survey Designs

Direct observation, through surveys, underpins nearly all aspects of environmental sciences. Survey design theory has evolved to make sure that sampling is as efficient as possible whilst remaining robust and fit-for-purpose. However, these methods frequently focus on theoretical aspects and often increase the logistical difficulty of performing the survey. Usually, the survey design process will place individual sampling locations one-by-one throughout the sampling area (e.g. random sampling). A consequence of these approaches is that there is usually a large cost in travel time between locations. This can be a huge problem for surveys that are large in spatial scale or are in inhospitable environments where travel is difficult and/or costly. Our solution is to constrain the sampling process so that the sample consists of spatially clustered observations, with all sites within a cluster lying within a predefined distance. The spatial clustering is achieved by a two-stage sampling process: first cluster centres are sampled and then sites within clusters are sampled. A novelty of our approach is that these clusters are allowed to overlap and we present the necessary calculations required to adjust the specified inclusion probabilities so that they are respected in the clustered sample. The process is illustrated with a real and on-going large-scale ecological survey. We also present simulation results to assess the methods performance. Spatially clustered survey design provides a formal statistical framework for grouping sample sites in space whilst maintaining multiple levels of spatial-balance. These designs reduce the logistical burden placed on field workers by decreasing total travel time and logistical overheads.Supplementary materials accompanying this paper appear on-line.

The many definitions of multiplicity of infection.

The presence of multiple genetically different pathogenic variants within the same individual host is common in infectious diseases. Although this is neglected in some diseases, it is well recognized in others like malaria, where it is typically referred to as multiplicity of infection (MOI) or complexity of infection (COI). In malaria, with the advent of molecular surveillance, data is increasingly being available with enough resolution to capture MOI and integrate it into molecular surveillance strategies. The distribution of MOI on the population level scales with transmission intensities, while MOI on the individual level is a confounding factor when monitoring haplotypes of particular interests, e.g., those associated with drug-resistance. Particularly, in high-transmission areas, MOI leads to a discrepancy between the likelihood of a haplotype being observed in an infection (prevalence) and its abundance in the pathogen population (frequency). Despite its importance, MOI is not universally defined. Competing definitions vary from verbal ones to those based on concise statistical frameworks. Heuristic approaches to MOI are popular, although they do not mine the full potential of available data and are typically biased, potentially leading to misinferences. We introduce a formal statistical framework and suggest a concise definition of MOI and its distribution on the host-population level. We show how it relates to alternative definitions such as the number of distinct haplotypes within an infection or the maximum number of alleles detectable across a set of genetic markers. It is shown how alternatives can be derived from the general framework. Different statistical methods to estimate the distribution of MOI and pathogenic variants at the population level are discussed. The estimates can be used as plug-ins to reconstruct the most probable MOI of an infection and set of infecting haplotypes in individual infections. Furthermore, the relation between prevalence of pathogenic variants and their frequency (relative abundance) in the pathogen population in the context of MOI is clarified, with particular regard to seasonality in transmission intensities. The framework introduced here helps to guide the correct interpretation of results emerging from different definitions of MOI. Especially, it excels comparisons between studies based on different analytical methods.

Ice model calibration using semicontinuous spatial data

Rapid changes in Earth’s cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets. However, these models are typically subject to large parametric uncertainties, due to poorly constrained model input parameters that govern the behavior of simulated ice sheets. Computer model calibration provides a formal statistical framework to infer parameters, using observational data, and to quantify the uncertainty in projections due to the uncertainty in these parameters. Calibration of ice sheet models is often challenging because the relevant model output and observational data take the form of semicontinuous spatial data with a point mass at zero and a right-skewed continuous distribution for positive values. Current calibration approaches cannot handle such data. Here, we introduce a hierarchical latent variable model that handles binary spatial patterns and positive continuous spatial patterns as separate components. To overcome challenges due to high dimensionality, we use likelihood-based generalized principal component analysis to impose low-dimensional structures on the latent variables for spatial dependence. We apply our methodology to calibrate a physical model for the Antarctic ice sheet and demonstrate that we can overcome the aforementioned modeling and computational challenges. As a result of our calibration, we obtain improved future ice-volume change projections.

PwrBRIDGE: a user-friendly web application for power and sample size estimation in batch-confounded microarray studies with dependent samples.

Batch effect Reduction of mIcroarray data with Dependent samples usinG Empirical Bayes (BRIDGE) is a recently developed statistical method to address the issue of batch effect correction in batch-confounded microarray studies with dependent samples. The key component of the BRIDGE methodology is the use of samples run as technical replicates in two or more batches, "bridging samples", to inform batch effect correction/attenuation. While previously published results indicate a relationship between the number of bridging samples, M, and the statistical power of downstream statistical testing on the batch-corrected data, there is of yet no formal statistical framework or user-friendly software, for estimating M to achieve a specific statistical power for hypothesis tests conducted on the batch-corrected data. To fill this gap, we developed pwrBRIDGE, a simulation-based approach to estimate the bridging sample size, M, in batch-confounded longitudinal microarray studies. To illustrate the use of pwrBRIDGE, we consider a hypothetical, longitudinal batch-confounded study whose goal is to identify Alzheimer's disease (AD) progression-associated genes from amnestic mild cognitive impairment (aMCI) to AD in human blood after a 5-year follow-up. pwrBRIDGE helps researchers design and plan batch-confounded microarray studies with dependent samples to avoid over- or under-powered studies.

A STATISTICAL INFERENCE ANALYSIS ON CRIME RATES IN PENINSULAR MALAYSIA USING GEOGRAPHICAL WEIGHTED REGRESSION

Geographical Weighted Regression (GWR) is used to improve decisionmaking in spatial analysis. Instead of the Ordinary Least Square (OLS) regression method that gives a single estimated parameter, the GWR method can provide unique estimated parameters in each location. This study aims to conduct a formal statistical inferential framework on the violent crime rate using the GWR. This analysis discovers the geographical distribution and pattern of criminal cases in Peninsular Malaysia using the average crime rates from 2000-2009, with focus on on violent crime. The comparison of OLS regression, known as Multiple Linear Regression (MLR) with the GWR method, was done to show that GWR was the best model. The GWR output suggests that about 30% of districts showed a significant correlation between violent crime and non-citizen rates. These findings contradict the result from the MLR model, also known global model. The global model could not create any other connection to explain the lack of parameter-location correspondence. Finally, the importance of local relationships in crime studies is necessary to understand the actual crime rate.

A framework for information synthesis into sentiment indicators using text mining methods

A formal statistical framework is proposed for synthesis of text information into sentiment indicators. Each text document is treated as an exchangeable collection of stems of words (tokens), and used in conjunction with a multinomial inverse regression approach to efficiently synthesize the information content in text documents. The proposed methodology is illustrated through the buildup of sentiment indicators using Twitter news outlet text information. These synthesizing indicators, quantitative in nature, can be built across disciplines to capture changes in the economic, financial, and social conditions, and also serve to reveal heterogeneity across countries, sectors, or markets. The proposed approach is computationally fast and allows for time variation in the indexes.

Tests for Network Cascades via Branching Processes

We consider a network setting where branches form under the null of normal periods and larger branches form under the alternative. Our goal is to distinguish abnormally large branches, which we term cascades, from the common branches formed under the null. Call detail records provide the motivating example, as large call branches form after disruptive events, yet call branches also form during normal periods. We introduce a formal statistical testing framework to distinguish between branches formed under the null and alternative based on expected branch size. After defining the characteristics of edge formation under the null, we derive the expected size and variance of branches using the machinery of branching processes. We introduce a test statistic that compares observed average branch size to expected branch size under the null, which allows us to quantify the probability a cascade has occurred. Our test statistic is semiparametric, consistent, and asymptotically distributed standard normal under the null. Using call detail records from Yemen, we find a significant calling cascade occurred after the Presidential Palace was bombed in 2011. Lastly, we employ our statistic for event detection and successfully detect key violent events during the 2011 Yemeni Revolution.

A New Method to Reconstruct Quantitative Food Webs and Nutrient Flows from Isotope Tracer Addition Experiments.

Understanding how nutrients flow through food webs is central in ecosystem ecology. Tracer addition experiments are powerful tools to reconstruct nutrient flows by adding an isotopically enriched element into an ecosystem and tracking its fate through time. Historically, the design and analysis of tracer studies have varied widely, ranging from descriptive studies to modeling approaches of varying complexity. Increasingly, isotope tracer data are being used to compare ecosystems and analyze experimental manipulations. Currently, a formal statistical framework for analyzing such experiments is lacking, making it impossible to calculate the estimation errors associated with the model fit, the interdependence of compartments, and the uncertainty in the diet of consumers. In this article we develop a method based on Bayesian hidden Markov models and apply it to the analysis of tracer additions in two Trinidadian streams in which light was experimentally manipulated. Through this case study, we illustrate how to estimate N fluxes between ecosystem compartments, turnover rates of N within those compartments, and the associated uncertainty. We also show how the method can be used to compare alternative models of food web structure, calculate the error around derived parameters, and make statistical comparisons between sites or treatments.

Regression methods for metacognitive sensitivity

Metacognition is an important component in basic science and clinical psychology, often studied through complex, cognitive experiments. While Signal Detection Theory (SDT) provides a popular and pervasive framework for modelling responses from such experiments, a shortfall remains that it cannot in a straightforward manner account for the often complex designs. Additionally, SDT does not provide direct estimates of metacognitive ability. This latter shortcoming has recently been sought remedied by introduction of a measure for metacognitive sensitivity dubbed meta-d′. The new sensitivity measure, however, further accentuates the need for a flexible modelling framework. In the present paper, we argue that a straightforward extension of SDT is obtained by identifying the model with the proportional odds model, a widely implemented, ordinal regression technique. We go on to develop a formal statistical framework for metacognitive sensitivity by defining a model that combines standard SDT with meta- d′ in a latent variable model. We show how this agrees with the literature on meta-d′ and constitutes a practical framework for extending the model. We supply several theoretical considerations on the model, including closed-form approximate estimates of meta- d′ and optimal weighing of response-specific meta-sensitivities. We discuss regression analysis as an application of the obtained model and illustrate our points through simulations. Lastly, we discuss a software implementation of the model in R. Our methods and their implementation extend the computational possibilities of SDT and meta- d′ and are useful for theoretical and practical researchers of metacognition.

Testing normality

Abstract In metrology, the normal distribution is often taken for granted, e. g. when evaluating the result of a measurement and its uncertainty, or when establishing the equivalence of measurements in key or supplementary comparisons. The correctness of this inference and subsequent conclusions is dependent on the normality assumption, such that a validation of this assumption is essential. Hypothesis testing is the formal statistical framework to do so, and this introduction will describe how statistical tests detect violations of a distributional assumption. In the metrological context we will advise on how to select such a hypothesis test, how to set it up, how to perform it and which conclusion(s) can be drawn. In addition, we calculate the number of measurements needed to decide whether a process departs from a normal distribution and quantify how sure one is about this decision then. These aspects are illustrated for the powerful Shapiro-Wilk test and by an example in legal metrology. For this application we recommend to perform 330 measurements. Briefly we also touch upon the issues of multiple testing and rounded measurements.

OSCR: a spatial capture–recapture R package for inference about spatial ecological processes

Spatial capture–recapture (SCR) methods have become widely applied in ecology. The immediate adoption of SCR is due to the fact that it resolves some major criticisms of traditional capture–recapture methods related to heterogeneity in detectabililty, and the emergence of new technologies (e.g. camera traps, non‐invasive genetics) that have vastly improved our ability to collection spatially explicit observation data on individuals. However, the utility of SCR methods reaches far beyond simply convenience and data availability. SCR presents a formal statistical framework that can be used to test explicit hypotheses about core elements of population and landscape ecology, and has profound implications for how we study animal populations. In this software note, we describe the technical basis and analytical workflow of oSCR, an R package for analyzing spatial encounter history data using a multi‐session sex‐structured likelihood. The impetus for developing oSCR was to create an accessible and transparent analysis tool that allows users to conveniently and intuitively formulate statistical models that map directly to fundamental processes of interest in spatial population ecology (e.g. space use, resource selection, density and connectivity). We have placed an emphasis on creating a transparent and accessible code base that is coupled with a logical workflow that we hope stimulates active participation in further technical developments.

Adaptive Markov chain Monte Carlo algorithms for Bayesian inference: recent advances and comparative study

Condition assessments of structures require prediction models such as empirical model and numerical simulation model. Generally, these prediction models have model parameters to be estimated from experimental data. Bayesian inference is the formal statistical framework to estimate the model parameters and their uncertainties. As a result, uncertainties associated with the model and measurement can be accounted for decision making. Markov Chain Monte Carlo (MCMC) algorithms have been widely employed. However, there still remain some implementation issues from the inappropriate selection of the proposal mechanism in Markov chain. Since the posterior density for a given problem is often problem-dependent and unknown, users require a trial-and-error approach to select and tune optimal proposal mechanism. To relieve this difficulty, various adaptive MCMC algorithms have been recently appeared. Users must understand their mechanism and limitations before applying the algorithms to their problems. However, there is no comprehensive work to provide detailed exposition and their performance comparison together. This study aims to bring together different adaptive MCMC algorithms with the goal of providing their mechanisms and evaluating their performances through comparative study. Three algorithms are chosen as the representative proposal mechanism. From comparative studies, the discussions were drawn in terms of performances, simplicity and computational costs for less-experienced users.

Latent space models for network perception data

AbstractSocial networks, wherein the edges represent nonbehavioral relations such as friendship, power, and influence, can be difficult to measure and model. A powerful tool to address this is cognitive social structures (Krackhardt, D. (1987). Cognitive social structures. Social Networks, 9(2), 109–134.), where the perception of the entire network is elicited from each actor. We provide a formal statistical framework to analyze informants’ perceptions of the network, implementing a latent space network model that can estimate, e.g., homophilic effects while accounting for informant error. Our model allows researchers to better understand why respondents’ perceptions differ. We also describe how to construct a meaningful single aggregated network that ameliorates potential respondent error. The proposed method provides a visualization method, an estimate of the informants’ biases and variances, and we describe a method for sidestepping forced-choice designs.

Making use of the social network in conservation genomics: Integrating kinship and network analyses to understand connectivity

Inferring and quantifying recent barriers to connectivity is increasingly important for conservation and management in a world undergoing rapid environmental change. Traditional measures of genetic differentiation can take many generations to reflect a new barrier to connectivity. Although methods that use the linkage disequilibrium signal in mixed genetic samples are able to reflect recent levels of gene flow, they are not suitable for use in situations with low levels of genetic differentiation. Kinship-based methods, those that assess the spatio-temporal distribution of related individuals, have been used in this context, but a formal statistical framework for such approaches has been lacking. In this issue of Molecular Ecology Resources, Escoda, et al. adapt the assortativity coefficient, AC, to analyse the networks of kin relationships in the Pyrenean desman (Galemys pyrenaicus) across potential barriers to dispersal. Their modified AC quantifies the proportion of missing kin relationships across putative dispersal barriers with respect to the expected proportion if there was no barrier. This application highlights that AC can be used to test the null hypothesis that a putative barrier has no effect on gene flow, in which case AC is not significantly different from 0. The method represents a useful step forward in conservation genomics by developing and adapting tools to assess contemporary connectivity using genomic data.

Decision trees in epidemiological research

BackgroundIn many studies, it is of interest to identify population subgroups that are relatively homogeneous with respect to an outcome. The nature of these subgroups can provide insight into effect mechanisms and suggest targets for tailored interventions. However, identifying relevant subgroups can be challenging with standard statistical methods.Main textWe review the literature on decision trees, a family of techniques for partitioning the population, on the basis of covariates, into distinct subgroups who share similar values of an outcome variable. We compare two decision tree methods, the popular Classification and Regression tree (CART) technique and the newer Conditional Inference tree (CTree) technique, assessing their performance in a simulation study and using data from the Box Lunch Study, a randomized controlled trial of a portion size intervention. Both CART and CTree identify homogeneous population subgroups and offer improved prediction accuracy relative to regression-based approaches when subgroups are truly present in the data. An important distinction between CART and CTree is that the latter uses a formal statistical hypothesis testing framework in building decision trees, which simplifies the process of identifying and interpreting the final tree model. We also introduce a novel way to visualize the subgroups defined by decision trees. Our novel graphical visualization provides a more scientifically meaningful characterization of the subgroups identified by decision trees.ConclusionsDecision trees are a useful tool for identifying homogeneous subgroups defined by combinations of individual characteristics. While all decision tree techniques generate subgroups, we advocate the use of the newer CTree technique due to its simplicity and ease of interpretation.

Use of haplotypes to identify regions harbouring lethal recessive variants in pigs

BackgroundLethal recessive genetic variants are maintained at relatively low frequencies in a population in the heterozygous state, but by definition are fatal and therefore unobserved in the homozygous state. Since haplotypes allow the tagging of rare and untyped genetic variants, they have potential for studying lethal recessive variants. In this study, we used a large commercial population to identify putative lethal recessive haplotypes that impact either the total number born (TNB) or the number born alive (NBA) as a proportion of the total number born (NBA/TNB). We also compared the use of haplotypes with a single nucleotide polymorphism (SNP)-by-SNP approach and examined the benefits of using additional haplotypes imputed from low-density genotype data for the detection of lethal recessive variants. Candidate haplotypes were identified using population-wide haplotype frequencies and within-family analyses. These candidate haplotypes were subsequently assessed for putative lethal recessive effects on TNB and NBA/TNB by comparing carrier-to-carrier matings with carrier-to-non-carrier matings.ResultsUsing both medium-density and imputed low-density genotype data six regions were identified as containing putative lethal recessive haplotypes that had an effect on TNB. It is likely that these regions were related to at least four putative lethal recessive variants, each located on a different chromosome. Evidence for putative lethal recessive effects on TNB was found on chromosomes 1, 6, 10 and 14 using haplotypes. Using haplotypes from individuals genotyped only at medium-density or a SNP-by-SNP approach did not detect any lethal recessive effects. No lethal recessive haplotypes or SNPs were detected that had an effect on NBA/TNB.ConclusionsWe show that the use of haplotypes from combining medium-density and imputed low-density genotype data is superior for the identification of lethal recessive variants compared to both a SNP-by-SNP approach and to the use of only medium-density data. We developed a formal statistical framework that provided sufficient power to detect lethal recessive variants in species, which produce large full-sib families, while reducing false positive or type I errors. Applying this framework results in improvements in reproductive performance by purging lethal recessive alleles from a population in a timely and cost-effective manner.

Characterization of dependencies between growth and division in budding yeast.

Cell growth and division are processes vital to the proliferation and development of life. Coordination between these two processes has been recognized for decades in a variety of organisms. In the budding yeast Saccharomyces cerevisiae, this coordination or 'size control' appears as an inverse correlation between cell size and the rate of cell-cycle progression, routinely observed in G1 prior to cell division commitment. Beyond this point, cells are presumed to complete S/G2/M at similar rates and in a size-independent manner. As such, studies of dependence between growth and division have focused on G1 Moreover, in unicellular organisms, coordination between growth and division has commonly been analysed within the cycle of a single cell without accounting for correlations in growth and division characteristics between cycles of related cells. In a comprehensive analysis of three published time-lapse microscopy datasets, we analyse both intra- and inter-cycle dependencies between growth and division, revisiting assumptions about the coordination between these two processes. Interestingly, we find evidence (i) that S/G2/M durations are systematically longer in daughters than in mothers, (ii) of dependencies between S/G2/M and size at budding that echo the classical G1 dependencies, and (iii) in contrast with recent bacterial studies, of negative dependencies between size at birth and size accumulated during the cell cycle. In addition, we develop a novel hierarchical model to uncover inter-cycle dependencies, and we find evidence for such dependencies in cells growing in sugar-poor environments. Our analysis highlights the need for experimentalists and modellers to account for new sources of cell-to-cell variation in growth and division, and our model provides a formal statistical framework for the continued study of dependencies between biological processes.

A powerful statistical framework for generalization testing in GWAS, with application to the HCHS/SOL

In genome-wide association studies (GWAS), "generalization" is the replication of genotype-phenotype association in a population with different ancestry than the population in which it was first identified. Current practices for declaring generalizations rely on testing associations while controlling the family-wise error rate (FWER) in the discovery study, then separately controlling error measures in the follow-up study. This approach does not guarantee control over the FWER or false discovery rate (FDR) of the generalization null hypotheses. It also fails to leverage the two-stage design to increase power for detecting generalized associations. We provide a formal statistical framework for quantifying the evidence of generalization that accounts for the (in)consistency between the directions of associations in the discovery and follow-up studies. We develop the directional generalization FWER (FWERg ) and FDR (FDRg ) controlling r-values, which are used to declare associations as generalized. This framework extends to generalization testing when applied to a published list of Single Nucleotide Polymorphism-(SNP)-trait associations. Our methods control FWERg or FDRg under various SNP selection rules based on P-values in the discovery study. We find that it is often beneficial to use a more lenient P-value threshold than the genome-wide significance threshold. In a GWAS of total cholesterol in the Hispanic Community Health Study/Study of Latinos (HCHS/SOL), when testing all SNPs with P-values <5×10-8 (15 genomic regions) for generalization in a large GWAS of whites, we generalized SNPs from 15 regions. But when testing all SNPs with P-values <6.6×10-5 (89 regions), we generalized SNPs from 27 regions.