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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation

This paper is a further development of the results of [20] where, based on the negative binomial model for the duration of wet periods measured in days [16], an asymptotic approximation was proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the form of a scale mixture of the Fr´echet distribution with the gamma mixing distribution and coincides with the distribution of a positive power of a random variable having the Snedecor–Fisher distribution. Here we extend this result to the mth extremes, m ∈ ℕ, and sample quantiles. The proof of this result is based on the representation of the negative binomial distribution as a mixed geometric (and hence, mixed Poisson) distribution [17] and limit theorems for extreme order statistics in samples with random sizes having mixed Poisson distributions [10]. Some analytic properties of the obtained limit distribution are described. In particular, it is demonstrated that under certain conditions the limit distribution of the maximum precipitation is mixed exponential and hence, is infinitely divisible. It is shown that under the same conditions this limit distribution can be represented as a scale mixture of stable or Weibull or Pareto or folded normal laws. The corresponding product representations for the limit random variable can be used for its computer simulation. The results of fitting this distribution to real data are presented illustrating high adequacy of the proposed model. It is also shown that the limit distribution of sample quantiles is the well-known Student distribution. Several methods are proposed for the estimation of the parameters of the asymptotic distributions. The obtained mixture representations for the limit laws and the corresponding asymptotic approximations provide better insight into the nature of mixed probability (“Bayesian”) models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Approximating Photo- z PDFs for Large Surveys

Modern galaxy surveys produce redshift probability density functions (PDFs) in addition to traditional photometric redshift (photo-z) point estimates. However, the storage of photo-z PDFs may present a challenge with increasingly large catalogs, as we face a trade-off between the accuracy of subsequent science measurements and the limitation of finite storage resources. This work presents qp, a Python package for manipulating parameterizations of one-dimensional PDFs, as suitable for photo-z PDF compression. We use qp to investigate the performance of three simple PDF storage formats (quantiles, samples, and step functions) as a function of the number of stored parameters on two realistic mock data sets, representative of upcoming surveys with different data qualities. We propose some best practices for choosing a photo-z PDF approximation scheme and demonstrate the approach on a science case using performance metrics on both ensembles of individual photo-z PDFs and an estimator of the overall redshift distribution function. We show that both the properties of the set of PDFs we wish to approximate and the fidelity metric(s) chosen affect the optimal parameterization. Additionally, we find that quantiles and samples outperform step functions, and we encourage further consideration of these formats for PDF approximation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Trigger Detection for Adaptive Scientific Workflows Using Percentile Sampling

The increasing complexity of both scientific simulations and high-performance computing system architectures are driving the need for adaptive workflows, in which the composition and execution of computational and data manipulation steps dynamically depend on the evolutionary state of the simulation itself. Consider, for example, the frequency of data storage. Critical phases of the simulation should be captured with high frequency and with high fidelity for postanalysis; however, we cannot afford to retain the same frequency for the full simulation due to the high cost of data movement. We can instead look for triggers, indicators that the simulation will be entering a critical phase, and adapt the workflow accordingly. In this paper, we present a methodology for detecting triggers and demonstrate its use in the context of direct numerical simulations of turbulent combustion using S3D. We show that chemical explosive mode analysis (CEMA) can be used to devise a noise-tolerant indicator for rapid increase in heat release. However, exhaustive computation of CEMA values dominates the total simulation, and thus is prohibitively expensive. To overcome this computational bottleneck, we propose a quantile sampling approach. Our sampling-based algorithm comes with provable error/confidence bounds, as a function of the number of samples. Most importantly, the number of samples is independent of the problem size, and thus our proposed sampling algorithm offers perfect scalability. Our experiments on homogeneous charge compression ignition and reactivity controlled compression ignition simulations show that the proposed method can detect rapid increases in heat release, and its computational overhead is negligible. Our results will be used to make dynamic workflow decisions regarding data storage and mesh resolution in future combustion simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient Sampling Allocation Procedures for Optimal Quantile Selection

We propose a dynamic sampling allocation and selection paradigm for finding the alternative with the optimal quantile in a Bayesian framework. Myopic allocation policies (MAPs), analogous to existing methods in classic ranking and selection for selecting the alternative with the optimal mean, and computationally efficient selection policies are derived for selecting the alternative with the optimal quantile. Under certain conditions, we prove that the proposed MAPs and selection procedures are consistent, which means that the best quantile would be eventually correctly selected as the sample size goes to infinity. Numerical experiments demonstrate that the proposed schemes can significantly improve the performance.

Computer Science↗
DOE OSTI2022

Quantile-specific heritability of plasma fibrinogen concentrations

Fibrinogen is a moderately heritable blood protein showing different genetic effects by sex, race, smoking status, pollution exposure, and disease status. These interactions may be explained in part by “quantile-dependent expressivity”, where the effect size of a genetic variant depends upon whether the phenotype (e.g. plasma fibrinogen concentration) is high or low relative to its distribution. Determine whether fibrinogen heritability (h 2 ) is quantile-specific, and whether quantile-specific h 2 could account for fibrinogen gene-environment interactions. Plasma fibrinogen concentrations from 5689 offspring-parent pairs and 1932 sibships from the Framingham Heart Study were analyzed. Quantile-specific heritability from offspring-parent (β OP , h 2 = 2β OP /(1+r spouse )) and full-sib regression slopes (β FS , h 2 = {(1+8r spouse β FS ) 0.05 –1}/(2r spouse )) were robustly estimated by quantile regression with nonparametric significance assigned from 1000 bootstrap samples. Quantile-specific h 2 (±SE) increased with increasing percentiles of the offspring’s age- and sex-adjusted fibrinogen distribution when estimated from β OP (P trend = 5.5x10 -6 ): 0.30±0.05 at the 10 th , 0.37±0.04 at the 25 th , 0.48±0.05 at the 50 th , 0.61±0.06 at the 75 th , and 0.65±0.08 at the 90 th percentile, and when estimated from β FS (P trend = 0.008): 0.28±0.04 at the 10 th , 0.31±0.04 at the 25 th , 0.36±0.03 at the 50 th , 0.41±0.05 at the 75 th , and 0.50±0.06 at the 90 th percentile. The larger genetic effect at higher average fibrinogen concentrations may contribute to fibrinogen’s greater heritability in women than men and in Blacks than Whites, and greater increase from smoking and air pollution for the FGB -455G>A A-allele. It may also explain greater fibrinogen differences between: 1) FGB -455G>A genotypes during acute phase reactions than usual conditions, 2) GTSM1 and IL-6 -572C>G genotypes in smokers than nonsmokers, 3) FGB -148C>T genotypes in untreated than treated diabetics, and LPL PvuII genotypes in macroalbuminuric than normoalbuminuric patients. Fibrinogen heritability is quantile specific, which may explain or contribute to its gene-environment interactions. The analyses do not disprove the traditional gene-environment interpretations of these examples, rather quantile-dependent expressivity provides an alternative explanation that warrants consideration.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Quantile-dependent expressivity of plasma adiponectin concentrations may explain its sex-specific heritability, gene-environment interactions, and genotype-specific response to postprandial lipemia

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g. adiponectin) is high or low relative to its distribution. We have previously shown that the heritability ( h 2 ) of adiposity, lipoproteins, postprandial lipemia, pulmonary function, and coffee and alcohol consumption are quantile-specific. Whether adiponectin heritability is quantile specific remains to be determined. Plasma adiponectin concentrations from 4,182 offspring-parent pairs and 1,662 sibships from the Framingham Heart Study were analyzed. Quantile-specific heritability from offspring-parent (β OP , h 2 = 2 β OP /(1 + r spouse )) and full-sib regression slopes ( β FS , h 2 = {(1 + 8r spouse β FS ) 0.05 -1}/(2r spouse )) were robustly estimated by quantile regression with nonparametric significance assigned from 1,000 bootstrap samples. Quantile-specific h 2 (± SE) increased with increasing percentiles of the offspring’s age- and sex-adjusted adiponectin distribution when estimated from β OP ( P trend = 2.2 × 10 -6 ): 0.30 ± 0.03 at the 10th, 0.33 ± 0.04 at the 25th, 0.43 ± 0.04 at the 50th, 0.55 ± 0.05 at the 75th, and 0.57 ± 0.08 at the 90th percentile, and when estimated from β FS (P trend = 7.6 × 10 -7 ): 0.42 ± 0.03 at the 10th, 0.44 ± 0.04 at the 25th, 0.56 ± 0.05 at the 50th, 0.73 ± 0.08 at the 75th, and 0.79 ± 0.11 at the 90th percentile. Consistent with quantile-dependent expressivity, adiponectin’s: (1) heritability was greater in women in accordance with their higher adiponection concentrations; (2) relationships to ADIPOQ polymorphisms were modified by adiposity in accordance with its adiponectin-lowering effect; (3) response to rosiglitazone was predicted by the 45T> G ADIPOQ polymorphism; (4) difference by ADIPOQ haplotypes increased linearly with increasing postprandial adiponectin concentrations. Adiponectin heritability is quantile dependent, which may explain sex-specific heritability, gene-environment and gene-drug interactions, and postprandial response by haplotypes.

Postprandial↗
DOE OSTI2019

Practical rare event sampling for extreme mesoscale weather

Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here, we present a new rare event sampling algorithm called quantile diffusion Monte Carlo (quantile DMC). Quantile DMC is a simple-to-use algorithm that can sample extreme tail behavior for a wide class of processes. We demonstrate the advantages of quantile DMC compared to other sampling methods and discuss practical aspects of implementing quantile DMC. To test the feasibility of quantile DMC for extreme mesoscale weather, we sample extremely intense realizations of two historical tropical cyclones, 2010 Hurricane Earl and 2015 Hurricane Joaquin. Our results demonstrate quantile DMC’s potential to provide low-variance extreme weather statistics while highlighting the work that is necessary for quantile DMC to attain greater efficiency in future applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Rare Event Sampling Improves Mercury Instability Statistics

Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury's orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare-event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately 10 –4 in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Quantile-Dependent Expressivity of Serum Uric Acid Concentrations

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g., serum uric acid) is high or low relative to its distribution. Analyses were performed to test whether serum uric acid heritability is quantile-specific and whether this could explain some reported gene-environment interactions. Methods. Serum uric acid concentrations were analyzed from 2151 sibships and 12,068 offspring-parent pairs from the Framingham Heart Study. Quantile-specific heritability from offspring-parent regression slopes (β OP , h 2 = 2β OP /(1 + r spouse )) and full-sib regression slopes (β FS ,h 2 = {(1 + 8r spouse β FS ) 0.5 - 1}/(2r spouse ) was robustly estimated by quantile regression with nonparametric significance assigned from 1000 bootstrap samples. Results. Quantile-specific h 2 (±SE) increased with increasing percentiles of the offspring’s sex- and age-adjusted uric acid distribution when estimated from β OP (P trend = 0.001): 0.34 ± 0.03 at the 10th, 0.36 ± 0.03 at the 25th, 0.41 ± 0.03 at the 50th, 0.46 ± 0.04 at the 75th, and 0.49 ± 0.05 at the 90th percentile and when estimated from β FS (P trend = 0.006). This is consistent with the larger genetic effect size of (1) the SLC2A9 rs11722228 polymorphism in gout patients vs. controls, (2) the ABCG2 rs2231142 polymorphism in men vs. women, (3) the SLC2A9 rs13113918 polymorphism in obese patients prior to bariatric surgery vs. two-year postsurgery following 29 kg weight loss, (4) the ABCG2 rs6855911 polymorphism in obese vs. nonobese women, and (5) the LRP2 rs2544390 polymorphism in heavier drinkers vs. abstainers. Quantile-dependent expressivity may also explain the larger genetic effect size of an SLC2A9/PKD2/ABCG2 haplotype for high vs. low intakes of alcohol, chicken, or processed meats. Conclusions. Heritability of serum uric acid concentrations is quantile-specific.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Quantile-dependent expressivity of serum C-reactive protein concentrations in family sets

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g., C-reactive protein, CRP) is high or low relative to its distribution. We have previously shown that the heritabilities ( h 2 ) of coffee and alcohol consumption, postprandial lipemia, lipoproteins, leptin, adiponectin, adiposity, and pulmonary function are quantile-specific. Whether CRP heritability is quantile-specific is currently unknown. Methods Serum CRP concentrations from 2,036 sibships and 6,144 offspring-parent pairs were analyzed from the Framingham Heart Study. Quantile-specific heritability from full-sib (β FS , h 2 ={(1 + 8r spouse β FS ) 0.5 - 1}/(2r spouse )) and offspring-parent regression slopes (β OP , h 2 = 2β OP /(1 + r spouse )) were estimated robustly by quantile regression with nonparametric significance determined from 1,000 bootstrap samples. Results Quantile-specific h 2 (±SE) increased with increasing percentiles of the offspring’s age- and sex-adjusted CRP distribution when estimated from β OP ( P trend = 0.0004): 0.02 ± 0.01 at the 10th, 0.04 ± 0.01 at the 25th, 0.10 ± 0.02 at the 50th, 0.20 ± 0.05 at the 75th, and 0.33 ± 0.10 at the 90th percentile, and when estimated from β FS ( P trend = 0.0008): 0.03±0.01 at the 10th, 0.06 ± 0.02 at the 25th, 0.14 ± 0.03 at the 50th, 0.24 ± 0.05 at the 75th, and 0.53 ± 0.21 at the 90th percentile. Conclusion Heritability of serum CRP concentration is quantile-specific, which may explain or contribute to the inflated CRP differences between CRP (rs1130864, rs1205, rs1800947, rs2794521, rs3091244), FGB (rs1800787), IL-6 (rs1800795, rs1800796), IL6R (rs8192284), TNF- α (rs1800629) and APOE genotypes following CABG surgery, stroke, TIA, curative esophagectomy, intensive periodontal therapy, or acute exercise; during acute coronary syndrome or Staphylococcus aureus bacteremia; or in patients with chronic rheumatoid arthritis, diabetes, peripheral arterial disease, ankylosing spondylitis, obesity or inflammatory bowel disease or who smoke.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗
DOE OSTI2024

Implicit quantile networks for emulation in jet physics

Abstract The ability to model and sample from conditional densities is important in many physics applications. Implicit quantile networks (IQN) have been successfully applied to this task in domains outside physics. In this work, we illustrate the potential of IQNs as components of emulators using the simulation of jets as an example. Specifically, we use an IQN to map jets described by their 4-momenta at the generation level to jets at the event reconstruction level. The conditional densities emulated by our model closely match those generated by Delphes , while also enabling faster jet simulation.

Kronheim, Braden (ORCID:0000000307040972)↗
DOE OSTI2024

Interpretable Net Load Forecasting Using Smooth Multiperiodic Features

We consider the problem of forecasting net load over a horizon such as one day, using a trailing window of past net load values as well as date and time. We focus on three variations on this problem: point forecasts, marginal quantile forecasts, and generating conditional samples of the future value. We propose a method that relies on linear regression using some custom engineered time-based features to capture multiple periodicities, such as daily, weekly, and seasonal, and their interactions. Our proposed models are readily interpretable, and rely on efficient and reliable convex optimization [1] to fit. We illustrate our method on four years worth of hourly net load data, comparing predictions made with various subsets of the features.

Ogut, Mehmet G↗
DOE OSTI2024

Nonparametric Multiparticle Set Methods for Interpreting Environmental Samples

Collection and analysis of environmental samples is commonly used by a range of stakeholders in nuclear safeguards and security contexts. While the ubiquity of samples and their transport in the environment allow regular collection, developing and demonstrating methods for analyzing these samples is difficult. In this work, an environmental sample consists of a set of one or more individual particles. Recent advances in reactor simulation have allowed us to generate data that are more representative of real-world environmental samples, enabling statistically defensible method development and testing. The most notable of these advances is a drastic increase in the number of material depletion regions, which allows our simulations to capture the variation in isotopic composition seen at length scales consistent with environmental samples. Traditional approaches for handling multiparticle samples treat each particle in the sample individually, estimating the quantity of interest (e.g., core-average burnup) resulting from measurement and analysis of signatures (e.g., nuclide assays) from each individual particle. Individual estimates are then averaged to generate a single estimate of the quantity of interest over the entire sample. In this presentation, we introduce two novel approaches for interpreting environmental samples that comprise of multiple particles: (1) the Quantile-Quantile Comparator, which uses a multivariate generalization of quantile-quantile plots for comparing unknown statistical distributions, and (2) the Set Transformer, an attention-based neural network module designed to model interactions among elements (particles) in the input set (sample). Statistically representative sampling cannot be guaranteed as samples are passively collected and are beholden to what particles are available in the environment. These new analysis methods for set-input problems are expected to be more robust than traditional approaches to issues of sampling bias where particles are not uniformly distributed throughout regions of interest, as well as generally outperform traditional approaches by jointly considering all elements in the set. We will present results comparing the performance of traditional single particle approaches and the novel Quantile-Quantile Comparator and Set Transformer for interpretation of simulated environmental samples.

Phathanapirom, Birdy↗
DOE OSTI2020

Quantile-specific heritability of sibling leptin concentrations and its implications for gene-environment interactions

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g., leptin) is high or low relative to its distribution. Leptin concentrations are strongly related to adiposity, whose heritability is quantile dependent. Whether inheritance of leptin concentrations is quantile dependent, and whether this explains the greater heritability in women than men in accordance with their greater adiposity, and explains other gene-environment interactions, remains to be determined. Therefore, leptin and leptin receptor concentrations from 3068 siblings in 1133 sibships from the Framingham Heart Study Third Generation Cohort were analyzed. Free leptin index (FLI) was calculated as the ratio of leptin to soluble leptin receptor concentrations. Full-sib (β FS ) regression slopes were robustly estimated by quantile regression with nonparametric significance assigned from 1000 bootstrap samples. The analyses showed β FS increased significantly with increasing percentiles of the offspring’s age- and sex-adjusted leptin distribution (P linear = 0.0001), which was accelerated at the higher concentrations (P quadratic = 0.0003). β FS at the 90th percentile (0.418 ± 0.066) was 4.7-fold greater than at the 10th percentile (0.089 ± 0.032, P difference = 3.6 × 10 –6 ). Consistent with quantile-dependent expressivity, the β FS was greater in female sibs, which was attributable to their higher leptin concentrations. Reported gene-environment interactions involving adiposity and LEP , LEPR , MnSOD , PPARγ , PPARγ2 , and IRS-1 polymorphisms were consistent with quantile-dependent expressivity of leptin concentrations. β FS for leptin receptor concentrations and free leptin index also increased significantly with increasing percentiles of their distributions (P linear = 0.04 and P linear = 8.5 × 10 –6 , respectively). In conclusion, inherited genetic and shared environmental effects on leptin concentrations were quantile dependent, which likely explains male–female differences in heritability and some gene-environment interactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Flexible classification with spatial quantile comparison and novel statistical features applied to spent nuclear fuel analysis

Multivariate classification algorithms are a common tool in contemporary data science that have begun to be applied to nuclear forensic analyses. Using a multivariate generalization of quantile–quantile plots for comparing unknown statistical distributions, a new model-free multivariate classifier called the Quantile–Quantile Comparator has been developed and tested on the analysis of simulated irradiated nuclear fuel. A method to estimate the sample-specific probability of having made an incorrect classification decision by analyzing the distribution of quantile comparisons has been developed, and methods have been developed to analyze the partition of the known data library used to analyze unknown data. By analyzing this partition, the analyst may identify classes that are likely to be confused, identify test data that are inconsistent with the data library and return a “None-of-the-Above” classification decision, and optimize the class boundaries. In this paper, the development of these capabilities is described, and a case study using real experimental assay data collected from nuclear fuel extracted from the newly-released In conclusion, Spent Fuel Isotopic Composition Database to demonstrate the efficacy of these capabilities is presented.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Spirometric traits show quantile-dependent heritability, which may contribute to their gene-environment interactions with smoking and pollution

Background: “Quantile-dependent expressivity” refers to a genetic effect that is dependent upon whether the phenotype (e.g., spirometric data) is high or low relative to its population distribution. Forced vital capacity (FVC), forced expiratory volume in 1 second (FEV 1 ), and the FEV 1 /FVC ratio are moderately heritable spirometric traits. The aim of the analyses is to test whether their heritability (h 2 ) is constant over all quantiles of their distribution. Methods: Quantile regression was applied to the mean age, sex, height and smoking-adjusted spirometric data over multiple visits in 9,993 offspring-parent pairs and 1,930 sibships from the Framingham Heart Study to obtain robust estimates of offspring-parent (β OP ), offspring-midparent (β OM ), and full-sib regression slopes (β FS ). Nonparametric significance levels were obtained from 1,000 bootstrap samples. β OP s were used as simple indicators of quantile-specific heritability (i.e.,h 2 = 2β OP /(1+r spouse ), where r spouse was the correlation between spouses). Results: β OP ± standard error (SE) decreased by 0.0009 ± 0.0003 (P = 0.003) with every one-percent increment in the population distribution of FEV 1 /FVC, i.e., β OP ± SE were: 0.182 ± 0.031, 0.152 ± 0.015; 0.136 ± 0.011; 0.121 ± 0.013; and 0.099 ± 0.013 at the 10th, 25th, 50th, 75th, and 90th percentiles of the FEV 1 /FVC distribution, respectively. These correspond to h 2 ± SEs of 0.350 ± 0.060 at the 10th, 0.292 ± 0.029 at the 25th, 0.262 ± 0.020 at the 50th, 0.234 ± 0.025 at the 75th, and 0.191 ± 0.025 at the 90th percentiles of the FEV 1 /FVC ratio. Maximum mid-expiratory flow (MMEF) h 2 ± SEs increased 0.0025 ± 0.0007 (P = 0.0004) with every one-percent increment in its distribution, i.e.: 0.467 ± 0.046, 0.467 ± 0.033, 0.554 ± 0.038, 0.615 ± 0.042, and 0.675 ± 0.060 at the 10th, 25th, 50th, 75th, and 90th percentiles of its distribution. This was due to forced expiratory flow at 75% of FVC (FEF75%), whose quantile-specific h 2 increased an average of 0.0042 ± 0.0008 for every one-percent increment in its distribution. It is speculated that previously reported gene-environment interactions may be partially attributable to quantile-specific h 2 , i.e., greater heritability in individuals with lower FEV 1 /FVC due to smoking or airborne particles exposure vs. nonsmoking, unexposed individuals. Conclusion: Heritabilities of FEV 1 /FVC, MMEF, and FEF75% from quantile-regression of offspring-parent and sibling spirometric data suggest their quantile-dependent expressivity.

59 BASIC BIOLOGICAL SCIENCES↗